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10th Standard English Medium Maths Subject Relations and Functions Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If n(A x B) = 6 and A = {1,3} then n(B) is

• 2)

  A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A U C) x B] is

• 3)

  If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

• 4)

  If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 5)

  The range of the relation R = {(x, x²) |x is a prime number less than 13} is

10th Standard English Medium Maths Subject Relations and Functions Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

• 2)

  Let f and g be two functions given by
  f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
  g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 3)

  Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

• 4)

  If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

• 5)

  f(x) = (x + 1)³ - (x - 1)³ represents a function which is

10th Standard English Medium Maths Subject Relations and Functions Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If A = {1,3,5} and B = {2,3} then
  (i) find A x B and B x A
  (ii) Is A x B = B x A? If not why?
  (iii) Show that n(A x B) = n(B x A) = n(A) x n(B)

• 2)

  If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

• 3)

  Find A x B, A x A and B x A
  A = {2, -2, 3} and B = {1,-4}

• 4)

  Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
  R₁ = {(3,7), (4,7), (7,10), (8,1)}

• 5)

  The arrow diagram shows a relationship between the sets P and Q. Write the relation in
  (i) Set builder form
  (ii) Roster form
  (iii) What is the domain and range of R.
  

10th Standard English Medium Maths Subject Relations and Functions Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.
  

• 2)

  Let A = {1,2,3}, B = {4, 5, 6,7}, and f = {(1, 4),(2, 5),(3, 6)}  be a function from A to B. Show that f is one – one but not onto function.

• 3)

  Let f be a function from R to R defined by f(x) = 3x - 5. Find the values of a and b given that (a,4) and (1,b) belong to f.

• 4)

  Determine whether the graph given below represent functions. Give a reason for your answer concerning the graph.
  

• 5)

  Let A = {1, 2, 3, 4} and B = N. Let f: A ⟶ B be defined by f(x) = x³ then
  (i) find the range of f
  (ii) identify the type of function

10th Standard English Medium Maths Subject Relations and Functions Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The data in the adjacent table depicts the length of a person forehand and her corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length(x) as y = ax + b,  where a, b are constants.
  (i) Check if this relation is a function.
  (ii) Find a and b.
  (iii) Find the height of a woman whose forehand length is 40 cm.
  (iv) Find the length of forehand of a woman if her height is 53.3 inches.

  Length ‘x’ of forehand (in cm)	Height 'y' (in inches)
  35	56
  45	65
  50	69.5
  55	74

• 2)

  Let f: A ⟶ B be a function defined by f(x) = \(\frac{x}{2}\)-1, where A = {2, 4 , 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}, Represent f by
  (i) set of ordered pairs
  (ii) a table
  (iii) an arrow diagram
  (iv) a graph

• 3)

  The function ‘t’ which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F =  \(\frac{9}{5}\)C + 32. Find,
  (i) t(0)
  (ii) t(28)
  (iii) t(-10)
  (iv) the value of C when t(C) = 212
  (v) the temperature when the Celsius value is equal to the Fahrenheit value.

• 4)

  If f(x) = 2x + 3, g(x) = 1 - 2x and h(x) = 3x. Prove that f o(g o h) = (f o g) o h.

• 5)

  Find x if gff(x) = fgg(x), given f(x) = 3x + 1 and g(x) = x + 3.

10th Standard English Medium Maths Subject Relations and Functions Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Given A = {1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5}, check if (A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D) is true?

• 2)

  Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
  A x (B U C) = (A x B) U (A x C)

• 3)

  Given the function f:x ⟶ x²- 5x + 6, evaluate
  i) f( -1)
  ii) f (2a)
  iii) f (2)
  iv) f (x - 1)

• 4)

  If the function f: R⟶ R defined by 
  \(f(x)=\left\{\begin{array}{l} 2 x+7, x<-2 \\ x^{2}-2,-2 \leq x<3 \\ 3 x-2, x \geq 3 \end{array}\right.\)
  (i) f( 4)
  (ii) f( -2)
  (iii) f(4) + 2f(1)
  (iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

• 5)

  Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}, Verify whether A x C is a subset of B x D?

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

• 2)

  Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 3)

  If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

  The sum of the exponents of the prime factors in the prime factorization of 1729 is

• 5)

  The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

• 2)

  If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² +...+ 2⁰ Which of the following is true?

• 3)

  The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

• 4)

  If the sequence t₁, t₂, t₃... are in A.P. then the sequence t₆, t₁₂, t₁₈,.... is 

• 5)

  The value of (1³ + 2³ + 3³ +...+15³) - (1 + 2 + 3 +...+ 15)is 

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?

• 2)

  Find the quotient and remainder when a is divided by b in the following a = −12, b = 5

• 3)

  Show that the square of an odd integer is of the form 4q + 1, for some integer q.

• 4)

  Find all positive integers, when divided by 3 leaves remainder 2.

• 5)

  A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over.

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Find the next three terms of the sequences.
   \(\frac { 1 }{ 2 } ,\frac { 1 }{ 6 } ,\frac { 1 }{ 10 },\frac { 1 }{ 14 } \), ..... ,

• 2)

  The general term of a sequence is defined as 
  a_n = \(\begin{cases} n\left( n+3 \right) ;n\in N\quad is\quad odd \\ { n }^{ 2 }+1;n\in N\quad is\quad even \end{cases}\)
  Find the eleventh and eighteenth terms.

• 3)

  Find a₈ and a₁₅ whose n^th term is
  a_n = \(\begin{cases} \frac { { n }^{ 2 }-1 }{ n+3 } ;n\quad is\quad even,\quad n\epsilon N \\ \begin{matrix} \\ \frac { { n }^{ 2 } }{ 2n+1 } ,n\quad is\quad odd,\quad n\epsilon N \end{matrix} \end{cases}\)

• 4)

  First term a and common difference d are given below. Find the corresponding A.P
  a = 5, d = 6

• 5)

  How many consecutive odd integers beginning with 5 will sum to 480?

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

• 2)

  Use Euclid’s Division Algorithm to find the Highest Common Factor (HCF) of 
  340 and 412

• 3)

  ' a '  and '  b ' are two positive integers such that a^b x b^a = 800. Find ' a ' and ' b'

• 4)

  If 13824 = 2^a x 3^b then find a and b.

• 5)

  Find the LCM and HCF of 408 and 170 by applying the fundamental theorem of arithmetic.

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The sum of first n terms of a certain series is given as 2n² - 3n.Show that the series is an A.P

• 2)

  In a G.P. the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is \(\frac { 57 }{ 2 } \). Find the three terms.

• 3)

  If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of G.P then prove that x^b-c x y^c-a x z^a-b = 1

• 4)

  A person saved money every year, half as much as he could in the previous year. If he had totally saved Rs.7875 in 6 years then how much did he save in the first year?

• 5)

  If 1³ + 2³ + 3³+...k³ = 44100 then find 1 + 2 + 3 +...+ k

10th Standard English Medium Maths Subject Algebra Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A system of three linear equations in three variables is inconsistent if their planes

• 2)

  The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is

• 3)

  If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is

• 4)

  \(\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}\) is

• 5)

  y² + \(\frac {1}{y^{2}}\) is not equal to

10th Standard English Medium Maths Subject Algebra Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Which of the following should be added to make x⁴ + 64 a perfect square

• 2)

  The solution of (2x - 1)² = 9 is equal to

• 3)

  The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are

• 4)

  If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0, then q, p, r are in __________.

• 5)

  Graph of a linear equation is a ____________

10th Standard English Medium Maths Subject Algebra Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Solve 2x − 3y = 6, x + y = 1

• 2)

  Find the LCM of the following
  8x⁴y², 48x²y⁴

• 3)

  Find the LCM of the given expressions.
  4x²y, 8x³y²

• 4)

  Find the LCM and GCD for the following and verify that f(x) x g(x) = LCM x GCD
  21x²y, 35 xy²

• 5)

  Reduce the rational expressions to its lowest form
  \(\frac { x-3 }{ { x }^{ 2 }-9 } \)

10th Standard English Medium Maths Subject Algebra Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Solve the following quadratic equations by completing the square method
  9x² - 12x + 4 = 0

• 2)

  If the difference between a number and its reciprocal is \(\frac {24}{5}\), find the number.

• 3)

  Determine the nature of roots for the following quadratic equations
  x² - x - 20 = 0

• 4)

  If α, β are the roots of 7x² + ax + 2 = 0 and if β - α = \(\frac {-13}{7}\). Find the values of a.

• 5)

  If one root of the equation 3x² + kx + 81 = 0 (having real roots) is the square of the other then find k.

10th Standard English Medium Maths Subject Algebra Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Solve \(\frac {1}{3}\) (x + y - 5) = y - z = 2x - 11 = 9 - (x + 2z).

• 2)

  One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections.

• 3)

  In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number.

• 4)

  Find the least common multiple of xy(k² + 1) + k(x² + y²) and xy(k² - 1) + k(x² - y²)

• 5)

  Find the GCD of the following by division algorithm 2x⁴ + 13x³ + 27x²+23x + 7, x³ + 3x² + 3x + 1, x² + 2x + 1

10th Standard English Medium Maths Subject Algebra Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A = \(\left( \begin{matrix} 3 & 0 \\ 4 & 5 \end{matrix} \right) \), B = \(\left( \begin{matrix} 6 & 3 \\ 8 & 5 \end{matrix} \right) \), C = \(\left( \begin{matrix} 3 & 6 \\ 1 & 1 \end{matrix} \right) \) find the matrix D, such that CD – AB = 0

• 2)

  Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

• 3)

  Vani, her father and her grand father have an average age of 53. One-half of her grand father’s age plus one-third of her father’s age plus one fourth of Vani’s age is 65. Four years ago if Vani’s grandfather was four times as old as Vani then how old are they all now?

• 4)

  The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the former number. If the hundreds digit plus twice the tens digit is equal to the units digit, then find the original three digit number?

• 5)

  Find the GCD of the given polynomials
  x⁴ + 3x³ - x - 3, x³ + x² - 5x + 3

10th Standard English Medium Maths Subject Algebra Book Back 8 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Discuss the nature of solutions of the following quadratic equations.
  x² + x - 12 = 0

• 2)

  Draw the graph of y = 2x² and hence solve 2x² - x - 6 = 0

• 3)

  Draw the graph of y = x² + 4x + 3 and hence find the roots of x² + x + 1 = 0

• 4)

  Draw the graph of y = x² + x - 2 and hence solve x² + x - 2 = 0

• 5)

  Draw the graph of y = x² - 4x + 3 and use it to solve x² - 6x + 9 = 0

10th Standard English Medium Maths Subject Algebra Book Back 8 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Graph the following quadratic equations and state their nature of solutions x² - 9x + 20 = 0.

• 2)

  Discuss the nature of solutions of the following quadratic equations.
  x² - 8x + 16 = 0

• 3)

  Graph the following quadratic equations and state their nature of solutions.
  x² + x + 7 = 0

• 4)

  Graph the following quadratic equations and state their nature of solutions.
  x² - 9 = 0

• 5)

  Graph the following quadratic equations and state their nature of solutions.
  (2x - 3)(x + 2) = 0

10th Standard English Medium Maths Subject Geometry Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

• 2)

  In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

• 3)

  If \(\triangle\)ABC is an isosceles triangle with \(\angle\)C = 90^o and AC = 5 cm, then AB is

• 4)

  In a given figure ST || QR, PS = 2 cm and SQ = 3 cm. Then the ratio of the area of \(\triangle\)PQR to the area \(\triangle\)PST is 
  

• 5)

  If in \(\triangle\)ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

10th Standard English Medium Maths Subject Geometry Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  In the given figure, PR = 26 cm, QR = 24 cm, \(\angle PAQ\) = 90^o, PA = 6 cm and QA = 8 cm. Find \(\angle\)PQR
  

• 2)

  A tangent is perpendicular to the radius at the

• 3)

  How many tangents can be drawn to the circle from an exterior point?

• 4)

  The two tangents from an external points P to a circle with centre at O are PA and PB. If \(\angle APB\) = 70^o then the value of \(\angle AOB\) is

• 5)

  In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is
  

10th Standard English Medium Maths Subject Geometry Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Show that \(\triangle\) PST~\(\triangle\) PQR 
  

• 2)

  Check whether the which triangles are similar and find the value of x.
  (i)
  
  (ii)
  

• 3)

  A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower.

• 4)

  In the adjacent figure, \(\triangle\)ABC is right angled at C and DE\(\bot \) AB. Prove that \(\triangle\)ABC~\(\triangle\)ADE and hence find the lengths of AE and DE.
  

• 5)

  In the Figure, AD is the bisector of \(\angle\)BAC, if A = 10 cm, AC = 14 cm and BC = 6 cm. Find BD and DC.
  

10th Standard English Medium Maths Subject Geometry Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  In the adjacent figure, \(\triangle\) ACB~\(\triangle\) APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.
  

• 2)

  In \(\triangle\)ABC,D and E are points on the sides AB and AC respectively such that DE||BC \(\frac { AD }{ DB } =\frac { 3 }{ 4 } \) and AC = 15cm find AE.

• 3)

  In the rectangle WXYZ, XY+YZ = 17 cm, and XZ + YW = 26 cm .Calculate the length and breadth of the rectangle
  

• 4)

  D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
  \({ b }^{ 2 }={ p }^{ 2 }+ax+\frac { { a }^{ 2 } }{ 4 } \)

• 5)

  If figure OPRQ is a square and \(\angle\)MLN=90^o. Prove that
  
  \(\triangle\)LOP~\(\triangle\)RPN

10th Standard English Medium Maths Subject Geometry Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.
  

• 2)

  Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac{3}{5}\) of the corresponding sides of the triangle PQR (scale factor \(\frac { 3 }{ 5 } <1\)) 

• 3)

  Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac { 7 }{ 4 } \) of the corresponding sides of the triangle PQR (scale factor \(\frac { 7 }{ 4 } \)>1)

• 4)

  A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamp post. The girl whose height is 12.5 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamp post are in a same line, find the height of the lamp post.

• 5)

  Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.
  

10th Standard English Medium Maths Subject Geometry Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  An Aeroplane after take off from an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1½ hours?
  

• 2)

  There are two paths that one can choose to go from Sarah’s house to James house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street? (Using figure).
  

• 3)

  In Fig, ABC is a triangle with \(\angle\)B=90^o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.
  

• 4)

  In a garden containing several trees, three particular trees P, Q, R are located in the following way, BP = 2 m, CQ = 3 m, RA = 10 m, PC = 6 m, QA = 5 m, RB = 2 m, where A, B, C are points such that P lies on BC, Q lies on AC and R lies on AB. Check whether the trees P, Q, R lie on a same straight line.
  

• 5)

  Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of 20 km/hr and the second train travels at 30 km/hr. After 2 hours, what is the distance between them?

10th Standard English Medium Maths Subject Geometry Book Back 8 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Construct a △PQR which the base PQ = 4.5 cm, ∠R = 35^oand the median RG  from R to PG is 6 cm

• 2)

  Construct a \(\triangle\)PQR in which QR = 5 cm, \(\angle\)P = 40^o and the median PG from P to QR is 4.4 cm. Find the length of the altitude from P to QR.

• 3)

  Construct a \(\triangle\)PQR such that QR = 6.5 cm,\(\angle\)P = 60^oand the altitude from P to QR is of length 4.5 cm.

• 4)

  Construct a \(\triangle\)ABC such that AB = 5.5 cm, \(\angle\)C = 25^o and the altitude from C to AB is 4 cm.

• 5)

  Draw a triangle ABC of base BC = 5.6 cm, \(\angle\)A = 40^o and the bisector of \(\angle\)A meets BC at D such that CD = 4 cm.

10th Standard English Medium Maths Subject Geometry Book Back 8 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre. Draw the two tangents PA and PB to the circle and measure their lengths.

• 2)

  Draw a tangent at any point R on the circle of radius 3.4 cm and centre at P ?

• 3)

  Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.

• 4)

  Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents

• 5)

  Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is at a distance 7.2 cm from the centre.

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

• 2)

  A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

• 3)

  The straight line given by the equation x = 11 is

• 4)

  If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

• 5)

  The point of intersection of 3x − y = 4 and x + y = 8 is

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

• 2)

  A straight line has equation 8y = 4x + 21. Which of the following is true

• 3)

  When proving that a quadrilateral is a trapezium, it is necessary to show

• 4)

  When proving that a quadrilateral is a parallelogram by using slopes you must find

• 5)

  (2, 1) is the point of intersection of two lines.

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If the area of the triangle formed by the vertices A(-1, 2), B(k, -2) and C(7, 4) (taken in order) is 22 sq. units, find the value of k.

• 2)

  Find the area of the triangle formed by the points (1, –1), (–4, 6) and (–3, –5)

• 3)

  Determine whether the sets of points are collinear? \((-\frac12 ,3)\), (- 5, 6) and (-8, 8)

• 4)

  Vertices of given triangles are taken in order and their areas are provided aside. In each case, find the value of ‘p’?

  S. No	Vertices	Area (sq. units)
  (i)	(0, 0), (p, 8), (6, 2)	20
  (ii)	(p, p), (5, 6), (5, -2)	32

• 5)

  In each of the following, Find the value of ‘a’ for which the given points are collinear. (2, 3), (4, a) and (6, –3)

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Find the equation of a straight line passing through (5, - 3) and (7, - 4).

• 2)

  A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3,8). Find its equation

• 3)

  Find the equation of a line through the given pair of points  \(\left( 2,\frac { 2 }{ 3 } \right) \) and \(\left( \frac { -1 }{ 2 } ,2 \right) \)

• 4)

  Find the slope of the straight line 6x + 8y + 7 = 0.

• 5)

  Show that the straight lines 2x + 3y - 8 = 0 and 4x + 6y + 18 = 0 are parallel.

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If the points P(-1, -4), Q (b, c) and R(5, -1) are collinear and if 2b + c = 4, then find the values of b and c.

• 2)

  Find the area of the quadrilateral formed by the points (8, 6), (5, 11), (-5, 12) and (-4, 3).

• 3)

  The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost Rs. 1300 per square feet. What will be the total cost for making the parking lot?

• 4)

  Find the area of the quadrilateral whose vertices are at (–9, –2), (–8, –4), (2, 2) and (1, –3)

• 5)

  Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (–4, –2), (–3, k), (3, –2) and (2, 3)

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A mobile phone is put to use when the battery power is 100%. The percent of battery power ‘y’ (in decimal) remaining after using the mobile phone for x hours is assumed as y  = − 0.25 x + 1
  
  Draw a graph of the equation.

• 2)

  A circular garden is bounded by East Avenue and Cross Road. Cross Road intersects North Street at D and East Avenue at E. AD is tangential to the circular garden at A(3, 10). Using the figure.
  
  Find the equation of
  (i) East Avenue.
  (ii) North Street
  (iii) Cross Road

• 3)

  You are downloading a song. The percent y (in decimal form) of mega bytes remaining to get downloaded in x seconds is given by y = -0.1x + 1.
  Graph the equation.

• 4)

  Find the equation of a straight line through the point of intersection of the lines 8x + 3y = 18, 4x + 5y = 9 and bisecting the line segment joining the points (5, –4) and (–7, 6).

• 5)

  PQRS is a rectangle formed by joining the points P(-1, -1), Q(-1, 4) , R(5 ,4) and S(5,-1) . A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

10th Standard English Medium Maths Subject Trigonometry Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

• 2)

  tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

• 3)

  If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

• 4)

  If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

• 5)

  If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

10th Standard English Medium Maths Subject Trigonometry Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

• 2)

  The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is

• 3)

  Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

• 4)

  The angle of elevation of a cloud from a point h metres above a lake is \(\beta \). The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

• 5)

  If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

10th Standard English Medium Maths Subject Statistics and Probability Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

• 2)

  If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

• 3)

  The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

• 4)

  The probability of getting a job for a person is \(\frac{x}{3}\). If the probability of not getting the job is \(\frac{2}{3}\)  then the value of x is

• 5)

  If a letter is chosen at random from the English alphabets {a, b,...,z}, then the probability that the letter chosen precedes x

10th Standard English Medium Maths Subject Trigonometry Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Prove that tan²\(\theta \)-sin² \(\theta \) = tan² \(\theta \) sin² \(\theta \)

• 2)

  prove that \(\sqrt { \frac { 1+cos\theta }{ 1-cos\theta } } \) = cosec \(\theta \) + cot\(\theta \)

• 3)

  prove that \(\frac { sec\theta }{ sin\theta } -\frac { sin\theta }{ cos\theta } =cot\theta \)

• 4)

  calculate \(\angle \)BAC in the given triangles (tan 38.7° = 0.8011 )
  

• 5)

  A tower stands vertically on the ground. from a point on the ground, which is 48m away from the foot of the tower, the angel of elevation of the top of  the tower is 30°.find the height of the tower.

10th Standard English Medium Maths Subject Trigonometry Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  prove that \(\frac { sinA }{ 1+cosA } =\frac { 1-cosA }{ sinA } \) 

• 2)

  prove that \(\frac { sec\theta }{ sin\theta } -\frac { sin\theta }{ cos\theta } =cot\theta \)

• 3)

  From the top of a rock \(50\sqrt { 3 } \)m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.

• 4)

  The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

• 5)

  A player sitting on the top of a tower of height 20 m observes the angle of depression of a ball lying on the ground as 60°. Find the distance between the foot of the tower and the ball.(\(\sqrt { 3 } \) = 1.732)

10th Standard English Medium Maths Subject Trigonometry Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Prove that sin² Acos² B + cos² Asin² B + cos² Acos² B + sin² Asin² B=1

• 2)

  if cos\(\theta \) + sin\(\theta \) =\(\sqrt { 2 } \) cos \(\theta \), then prove that cos\(\theta \) - sin\(\theta \) =\(\sqrt { 2 } \) sin\(\theta \) 

• 3)

  if cosec\(\theta \) + cot\(\theta \) = p, then prove that cos\(\theta \) = \(\frac { { p }^{ 2 }-1 }{ { p }^{ 2 }+1 } \)

• 4)

  if sin\(\theta \) + cos\(\theta \)  = \(\sqrt { 3 } \),then prove that tan\(\theta \) + cot\(\theta \) = 1

• 5)

  if \(\frac { cos\theta }{ 1+sin\theta } =\frac { 1 }{ a } \),then prove that \(\frac { { a }^{ 2 }-1 }{ a^{ 2 }+1 } \) = sin\(\theta \)

10th Standard English Medium Maths Subject Trigonometry Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A flag pole of height ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find (i) the height of the pole (ii) radius of the (\( \sqrt { 3 } \) =1.732)
  

• 2)

  The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30° . If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.

• 3)

  Three villagers A, B and C can see each other across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30° . Calculate : the vertical height between A and B.(tan20° = 0.3640,(\(\sqrt { 3 } \) = 1.732)
  

• 4)

  If x sin³\(\theta \) + ycos³\(\theta \) = sin\(\theta \) cos\(\theta \) and x sin\(\theta \) = ycos\(\theta \), then prove that x² + y² = 1.

• 5)

  A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away.
  How far is B to the North of A? (sin 55° = 0.8192, cos 55° = 0.5736,sin 42° = 0.6691.cos 42° = 0.7431)

Stateboard 10th Standard Maths Subject Public Question Paper - March 2022 updated Previous Year Question Papers - by QB Admin - May 13, 2022 - View & Read

10th Standard English Medium Maths Subject Mensuration Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

• 2)

  If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

• 3)

  The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

• 4)

  If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

• 5)

  The total surface area of a cylinder whose radius is \(\frac{1}{3}\)of its height is

10th Standard English Medium Maths Subject Mensuration Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

• 2)

  A shuttle cock used for playing badminton has the shape of the combination of

• 3)

  The volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

• 4)

  The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1:2 then r₂ : r₁ is

• 5)

  The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

10th Standard English Medium Maths Subject Mensuration Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A cylindrical drum has a height of 20 cm and base radius of 14 cm. Find its curved surface area and the total surface area.

• 2)

  The curved surface area of a right circular cylinder of height 14 cm is 88 cm² . Find the diameter of the cylinder.

• 3)

  A garden roller whose length is 3 m long and whose diameter is 2.8 m is rolled to level a garden. How much area will it cover in 8 revolutions?

• 4)

  If one litre of paint covers 10 m², how many litres of paint is required to paint the internal and external surface areas of a cylindrical tunnel whose thickness is 2 m, internal radius is 6 m and height is 25 m.
  

• 5)

  If the total surface area of a cone of radius 7cm is 704 cm², then find its slant height.

10th Standard English Medium Maths Subject Mensuration Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  4 persons live in a conical tent whose slant height is 19 cm. If each person require 22 cm² of the floor area, then find the height of the tent.

• 2)

  The ratio of the radii of two right circular cones of same height is 1 : 3. Find the ratio of their curved surface area when the height of each cone is 3 times the radius of the smaller cone.

• 3)

  Find the volume of a cylinder whose height is 2 m and whose base area is 250 m².

• 4)

  The volume of a solid right circular cone is 11088 cm³. If its height is 24 cm then find the radius of the cone.

• 5)

  The ratio of the volumes of two cones is 2 : 3. Find the ratio of their radii if the height of second cone is double the height of the first.

10th Standard English Medium Maths Subject Mensuration Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and base is hollowed out. Find the total surface area of the remaining solid.
  

• 2)

  The internal and external radii of a hollow hemispherical shell are 3 m and 5 m respectively. Find the T.S.A. and C.S.A. of the shell.
  

• 3)

  An industrial metallic bucket is in the shape of the frustum of a right circular cone whose top and bottom diameters are 10 m and 4 m and whose height is 4 m. Find the curved and total surface area of the bucket.
  

• 4)

  A right angled triangle PQR where ∠Q = 90^o is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle.

• 5)

  A girl wishes to prepare birthday caps in the form of right circular cones for her birthday party, using a sheet of paper whose area is 5720 cm², how many caps can be made with radius 5 cm and height 12 cm.

10th Standard English Medium Maths Subject Mensuration Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The volume of a solid hemisphere is 29106 cm³. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

• 2)

  A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the glass?

• 3)

  The volumes of two cones of same base radius are 3600 cm³ and 5040 cm³. Find the ratio of heights.

• 4)

  A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3\(\sqrt{3}\) : 4.

• 5)

  A toy is in the shape of a cylinder surrounded by a hemisphere. The height of the toy is 25 cm. Find the total surface area of the toy if its common diameter is 12 cm.
  

10th Standard English Medium Maths Subject Statistics and Probability Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

• 2)

  A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

• 3)

  The probability of getting a job for a person is \(\frac{x}{3}\). If the probability of not getting the job is \(\frac{2}{3}\)  then the value of x is

• 4)

  Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac{1}{9}\), then the number of tickets bought by Kamalam is

• 5)

  A purse contains 10 notes of Rs. 2000, 15 notes of Rs. 500, and 25 notes of Rs. 200. One note is drawn at random. What is the probability that the note is either a Rs. 500 note or Rs. 200 note?

10th Standard English Medium Maths Subject Statistics and Probability Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Find the range and coefficient of range of the following data: 25, 67, 48, 53, 18, 39, 44.

• 2)

  Find the range of the following distribution..

  Age (in years)	16-18	18-20	20-22	22-24	24-26	26-28
  Number of students	0	4	6	8	2	2

• 3)

  The range of a set of data is 13.67 and the largest value is 70.08. Find the smallest value.

• 4)

  Find the range and coefficient of range of the following data. 63, 89, 98, 125, 79, 108, 117, 68

• 5)

  If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

10th Standard English Medium Maths Subject Statistics and Probability Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school.

  	Height	Weight
  Mean	155 cm	46.50 kg
  Variance	72.25 cm2	28.09 kg

  Which is more varying than the other?

• 2)

  The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.

• 3)

  If n = 5 , \(\bar { x } \) = 6, Σx² = 765 then calculate the coefficient of variation.

• 4)

  Two coins are tossed together. What is the probability of getting different faces on the coins?

• 5)

  A die is rolled and a coin is tossed simultaneously. Find the probability that the die shows an odd number and the coin shows a head.

10th Standard English Medium Maths Subject Statistics and Probability Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find its standard deviation.

• 2)

  The amount of rainfall in a particular season for 6 days are given as 17.8 cm, 19.2 cm, 16.3 cm, 12.5 cm, 12.8 cm and 11.4 cm. Find its standard deviation.

• 3)

  The marks scored by 10 students in a class test are 25, 29, 30, 33, 35, 37, 38, 40, 44, 48. Find the standard deviation.

• 4)

  The amount that the children have spent for purchasing some eatables in one day trip of a school are 5, 10, 15, 20, 25, 30, 35, 40. Using step deviation method, find the standard deviation of the amount they have spent.

• 5)

  Find the standard deviation of the following data 7, 4, 8, 10, 11. Add 3 to all the values then find the standard deviation for the new values.

10th Standard English Medium Maths Subject Statistics and Probability Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The consumption of number of guava and orange on a particular week by a family are given below.

  Number of Guavas	3	5	6	4	3	5	4
  Number of Oranges	1	3	7	9	2	6	2

  Which fruit is consistently consumed by the family?

• 2)

  The temperature of two cities A and B in a winter season are given below.

  Temperature of city A (in degree Celsius)	18	20	22	24	26
  Temperature of city B (in degree Celsius)	11	14	15	17	18

  Find which city is more consistent in temperature changes?

• 3)

  Two unbiased dice are rolled once. Find the probability of getting
  (i) a doublet (equal numbers on both dice)
  (ii) the product as a prime number
  (iii) the sum as a prime number
  (iv) the sum as 1

• 4)

  Three fair coins are tossed together. Find the probability of getting
  (i) all heads
  (ii) atleast one tail
  (iii) at most one head
  (iv) at most two tails

• 5)

  Some boys are playing a game, in which the stone thrown by them landing in a circular region (given in the figure) is considered as win and landing other than the circular region is considered as loss. What is the probability to win the game?
  

10th Standard English Medium Maths Subject Book Back 1 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

• 2)

  Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

• 3)

  The sum of the exponents of the prime factors in the prime factorization of 1729 is

• 4)

  The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

• 5)

  \(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

10th Standard English Medium Maths Subject Book Back 1 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If n(A x B) = 6 and A = {1,3} then n(B) is

• 2)

  If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

• 3)

  The range of the relation R = {(x, x²) |x is a prime number less than 13} is

• 4)

  Let f and g be two functions given by
  f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
  g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 5)

  Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

10th Standard English Medium Maths Subject Book Back 2 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

• 2)

  Let A = {1,2,3} and B = {x| x is a prime number less than 10}. Find A x B and B x A.

• 3)

  Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
  R₁ = {(3,7), (4,7), (7,10), (8,1)}

• 4)

  A plane is flying at a speed of 500 km per hour. Express the distanced travelled by the plane as function of time t in hours.

• 5)

  If f(x) = x² - 1. Find
  i. f o f
  ii. f o f o f

10th Standard English Medium Maths Subject Book Back 2 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

• 2)

  Let A = {1,2,3} and B = {x| x is a prime number less than 10}. Find A x B and B x A.

• 3)

  Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
  R₁ = {(3,7), (4,7), (7,10), (8,1)}

• 4)

  A Relation R is given by the set {(x, y) / y = x + 3, x \(\in \) {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

• 5)

  A relation ‘f’ \(X \rightarrow Y\) is defined by f(x) = x² - 2 where x \(\in \) {-2, -1, 0, 3} and Y = R
  (i) List the elements of f
  (ii) Is f a function?

10th Standard English Medium Maths Subject Book Back 5 Mark Questions with Solution Part - I updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If A = {5,6}, B = {4,5,6}, C = {5,6,7}, Show that A x A = (B x B) ∩ (C x C)

• 2)

  Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
  A x (B U C) = (A x B) U (A x C)

• 3)

  A graph representing the function f (x) is given in Fig it is clear that f (9) = 2.
  (i) Find the following values of the function
  (a) f(0)
  (b) f(7)
  (c) f(2)
  (d) f(10)
  (ii) For what value of x is f (x) = 1?
  (iii) Describe the following (i) Domain (ii) Range.
  (iv) What is the image of 6 under f ?
  

• 4)

  An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown Fig. Express the volume V of the box as a function of x.
  

• 5)

  A function f: [-5,9] ⟶ R is defined as follows:
  \(f(x)=\left[\begin{array}{ll} 6 x+1 & \text { if }-5 \leq x<2 \\ 5 x^{2}-1 & \text { if } 2 \leq x<6 \\ 3 x-4 & \text { if } 6 \leq x \leq 9 \end{array}\right.\)
  Find
  i) f(-3) + f(2)
  ii) f(7) - f(1)
  iii) 2f(4) + f(8)
  iv)  \(\frac { 2f(-2)-f(6) }{ f(4)+f(-2) } \)

10th Standard English Medium Maths Subject Book Back 5 Mark Questions with Solution Part - II updated Book back Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Solve \(\sqrt { y+1 } +\sqrt { 2y-5 } \) = 3

• 2)

  Simplify
  \(\frac { 4{ x }^{ 2 }y }{ 2{ x }^{ 2 } } \times \frac { 6x{ z }^{ 3 } }{ 20{ y }^{ 4 } } \)

• 3)

  Find the values of a and b if the following polynomials are perfect squares
  4x⁴ - 12x³ + 37x² + bx + a

• 4)

  If A = \(\left[ \begin{matrix} 1 & 2 & 1 \\ 2 & -1 & 1 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 2 & -1 \\ -1 & 4 \\ 0 & 2 \end{matrix} \right] \) show that (AB)^T = B^TA^T

• 5)

  If α, β are the roots of the equation 2x² - x - 1 = 0, then form the equation whose roots are
  2α + β, 2β + α

10th Standard English Medium Maths Subject Relations and Functions Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  \((x-\frac { 1 }{ x } )={ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) then f(x) =

• 2)

  The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

• 3)

  If \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

• 4)

  If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

• 5)

  If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

10th Standard English Medium Maths Subject Relations and Functions Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

• 2)

  If f(x) = ax - 2, g(x) = 2x - 1 and fog = gof, the value of a is ___________

• 3)

  If f(x) = 2 - 3x, then f o f(1 - x) = ?

• 4)

  If f is constant function of value \(\frac { 1 }{ 10 } \), the value of f(1) + f(2) + ... + f(100) is _________

• 5)

  If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

10th Standard English Medium Maths Subject Relations and Functions Creative 2 Mark Questions with Solution updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

• 2)

  State whether the graph represent a function. Use vertical line test.
  

• 3)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table.

• 4)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

• 5)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

10th Standard English Medium Maths Subject Relations and Functions Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  find 2f(-4) + 3f(2)

• 2)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  \(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

• 3)

  Let A = {1, 2, 3, 4, 5}, B = N and f: A \(\rightarrow\)B be defined by f(x) = x². Find the range of f. Identify the type of function.

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(3),

• 5)

  The following table represents a function from A = {5, 6, 8, 10} to B = {19, 15, 9, 11}, where f(x) = 2x - 1. Find the values of a and b.

  x	5	6	8	10
  f(x)	a	11	b	19

10th Standard English Medium Maths Subject Relations and Functions Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  f(-7) - f(-3)

• 2)

  f(x) = (1+ x)
  g(x) = (2x - 1)
  Show that fo(g(x)) = gof(x)

• 3)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(5),

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(2) - f( 4).

• 5)

  If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and 

10th Standard English Medium Maths Subject Numbers and Sequences Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If a and b are the two positive integers when a > b and b is a factor of a then HCF (a, b) is ____________

• 2)

  How many terms are there in the G.P : 5, 20, 80, 320,..., 20480

• 3)

  Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

• 4)

  A boy saves Rs. 1 on the first day Rs. 2 on the second day, Rs. 4 on the third day and so on. How much did the boy will save upto 20 days?

• 5)

  If p, q, r, x, y, z are in A.P, then 5p + 3, 5r + 3, 5x + 3, 5y + 3, 5z + 3 form ____________

10th Standard English Medium Maths Subject Numbers and Sequences Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If m and n are the two positive integers then m² and n² are ____________

• 2)

  In the arithmetic series Sn = k + 2k + 3k +...+ 100, k is positive integer and k is a factor 100 then S_n is ____________

• 3)

  If p^th, q^th and r^th terms of an A.P. are a, b, c respectively, then (a(q - r) + b(r - p) + c(p - q) is____________

• 4)

  The sum of first n terms of the series a, 3a, 5a...is ____________

• 5)

  In an A.P if the p^th term is q and the q^th term is p, then its n^th term is ____________

10th Standard English Medium Maths Subject Numbers and Sequences Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  4,10,16, 22, ...

• 2)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  1,-1,-3, -5, ...

• 3)

  Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
  1, 1, 1, 2, 2, 2, 3, 3,  3

• 4)

  In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

• 5)

  How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

10th Standard English Medium Maths Subject Numbers and Sequences Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  4,10,16, 22, ...

• 2)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  -2, 2, -2, 2, -2

• 3)

  Determine the AP whose 3rd term is 5 and the 7^th term is 9.

• 4)

  If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

• 5)

  Find the sum of first 24 terms of the list of numbers whose nth term is given by a_n = 3 + 2n.

10th Standard English Medium Maths Subject Algebra Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Graphically an infinite number of solutions represents ___________

• 2)

  If \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

• 3)

  The real roots of the quadratic equation x²-x-1 are ___________

• 4)

  The parabola y = -3x² is ___________

• 5)

  If \(A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right] _{ 3\times 2 }\) \(B=\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \right] _{ 2\times 3 }\) then which of the following products can be made from these matrices 
  (i) A²
  (ii) B²
  (iii) AB
  (iv) BA

10th Standard English Medium Maths Subject Algebra Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Which of the following is correct
  (i) Every polynomial has finite number of multiples
  (ii) LCM of two polynomials of degree 2 may be a constant
  (iii) HCF of 2 polynomials may be constant
  (iv) Degree of HCF of two polynomials is always less then degree of LCM

• 2)

  \(\frac { { x }^{ 2 }+7x12 }{ { x }^{ 2 }+8x+15 } \times \frac { { x }^{ 2 }+5x }{ { x }^{ 2 }+6x+8 } =\_ \_ \_ \_ \_ \_ \_ \_ \_ \)

• 3)

  The square root of 4m² - 24m + 36 is ___________

• 4)

  The product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³) = 0 is ___________

• 5)

  If P and Q are matrices, then which of the following is true?

10th Standard English Medium Maths Subject Algebra Creative 2 Mark Questions with Solution updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Solve the following system of linear equations in three variables.
  x + y + z = 6; 2x + 3y + 4z = 20;
  3x + 2y + 5z = 22

• 2)

  Using quadratic formula solve the following equations.
  p²x² + (P² -q²) X - q² = 0

• 3)

  Using quadratic formula solve the following equations.9x²-9(a+b)x+(2a²+5ab+2b²)=0

• 4)

  Find the values of k for which the following equation has equal roots.
  (k - 12)r + 2(k - 12)x + 2 = 0

• 5)

  Prove that the equation x²(a²+b²)+2x(ac+bd)+(c²+ d²) = 0 has no real root if ad≠bc.

10th Standard English Medium Maths Subject Algebra Creative 5 Mark Questions with Solution updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

• 2)

  A two digit number is such that the product of its digits is 12. When 36 is added to the number the digits interchange their places. Find the number.

• 3)

  Seven years ago, Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

• 4)

  A chess board contains 64 equal squares and the area of each square is 6.25 cm², A border round the board is 2 cm wide.

• 5)

  Find two consecutive natural numbers whose product is 20.

10th Standard English Medium Maths Subject Geometry Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  I the given figure DE||AC which of the following is true.

• 2)

  In the given figure DE||BC:BD = x - 3, BA = 2x,CE = x- 2, and AC = 2x + 3, Find the value of x.

• 3)

  If ABC is a triangle and AD bisects A, AB = 4cm, BD = 6cm, DC = 8cm then the value of AC is ____________

• 4)

  A line which intersects a circle at two distinct points is called ____________

• 5)

  In figure \(\angle OAB={ 60 }^{ o }\) and OA = 6cm then radius of the circle is ____________

10th Standard English Medium Maths Subject Geometry Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  S and T are points on sides PQ and PR respectively of \(\Delta PQR\) If PS = 3cm, AQ = 6 cm, PT = 5 cm, and TR = 10 cm and then QR

• 2)

  The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the triangle is ____________

• 3)

  If the angle between two radio of a circle is ^o, the angle between the tangents at the end of the radii is ____________

• 4)

  In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

• 5)

  Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two if the sides of the triangle are 2cm,3cm and 4 cm. find the diameter of the smallest circle.

10th Standard English Medium Maths Subject Geometry Creative 5 Mark Questions with Solution updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  In \(AD\bot BC\) prove that AB² + CD² = BD² + AC². 

• 2)

  BL and CM are medians of a triangle ABC right angled at A.
  Prove that 4(BL² + CM²) = 5BC².

• 3)

  Prove that in a right triangle, the square of 8. the hypotenuse is equal to the sum of the squares of the others two sides.

• 4)

  In figure 0 is any point inside a rectangle ABCD. Prove that OB² + OD² = OA² + OC²

• 5)

  In \(\angle ACD={ 90 }^{ 0 }\) and \(CD\bot AB\) Prove that \(\cfrac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\cfrac { BD }{ AD } \)

10th Standard English Medium Maths Subject Coordinate Geometry Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If the points (0, 0), (a, 0) and (0, b) are collinear, then ____________

• 2)

  Find the value of P, given that the line  \(\frac { y }{ 2 } =x-p\) passes through the point (-4, 4) is ____________

• 3)

  Find the value of 'a' if the lines 7y = ax + 4 and 2y = 3 - x are parallel

• 4)

  Find the equation of the line passing through the point (0, 4) and is parallel to 3x+5y+15 = 0 the line is ___________

• 5)

  The lines y = 5x - 3, y = 2x + 9 intersect at A. The coordinates of A are ___________

10th Standard English Medium Maths Subject Coordinate Geometry Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

• 2)

  If the mid-point of the line segment joining \(A\left( \frac { x }{ 2 } ,\frac { y+1 }{ 2 } \right) \) and B(x + 1, y-3) is C(5, -2) then find the values of x, y ____________

• 3)

  A line passing through the point (2, 2) and the axes enclose an area ∝. The intercept on the axes made by the line are given by the roots of ____________

• 4)

  In a right angle triangle, right angled at B, if the side BC is parallel to x axis, then the slope of AB is ___________

• 5)

  The lines y = 5x - 3, y = 2x + 9 intersect at A. The coordinates of A are ___________

10th Standard English Medium Maths Subject Coordinate Geometry Creative 5 Mark Questions with Solution updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

• 2)

  Find the area of a triangle vertices are(1, -1), (-4, 6) and (-3, -5).

• 3)

  Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

• 4)

  Find the area of the triangle formed by the points P(-1, 5, 3), Q(6, -2) and R(-3, 4).

• 5)

  Find the value of k if the points A(2, 3), B(4, k) and (6, -3) are collinear.

10th Standard English Medium Maths Subject Trigonometry Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If sin A = \(\frac{1}{2}\), then the value of cot A is ___________

• 2)

  Given that sinθ = \(\frac{a}{b}\), then cosθ is equal to ___________

• 3)

  If 4 tan θ = 3, then \(\left( \frac { 4sin\theta -cos\theta }{ 4sin\theta +cos\theta } \right) \) is equal to ___________

• 4)

  Sin(45^o+ θ ) - cos(45^o - θ) is equal to ___________

• 5)

  If cotθ = b/a then value of \(\frac { cos\theta +sin\theta }{ cos\theta -sin\theta } \) a

10th Standard English Medium Maths Subject Trigonometry Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  The value of the expression [cosec (75^o + θ) - sec (15^o - θ) - tan (55^o + θ) + cot(35^o - θ] is ___________

• 2)

  If sin θ - cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is ___________

• 3)

  A pole 6 m high a shadow 2\(\sqrt{3}\) m long on the ground, then the sun's elevation is ___________

• 4)

  If sec θ + tan θ = n, and sec θ - tan θ = 0, then the value of mn is ___________

• 5)

  The blanks of river are parallel. A swimmer starts from a point on one of the banks and swims in a straight line to the bank at 45^o and reaches the opposite bank at a point 20 m, from the point opposite to the straight point. The breadth of the river is equal to ____________

10th Standard English Medium Maths Subject Trigonometry Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Prove that \(\frac { sin\theta -cos\theta +1 }{ sin\theta +cos\theta -1 } =\frac { 1 }{ sec\theta -tan\theta } \) using the identity sec²θ= 1+ tan²θ.

• 2)

  In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.

10th Standard English Medium Maths Subject Trigonometry Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

10th Standard English Medium Maths Subject Trigonometry Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Express the ratios cos A, tan A and sec A in terms of sin A.

• 2)

  If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.

• 3)

  From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.

• 4)

  P.T (1+tan∝tan∝tanβ)² +(tan∝-tanβ)² =sec² ∝sec²β.

• 5)

  \(P.T\left( \frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } \right) ={ \left( \frac { 1-tan\quad A }{ 1-cot\quad A } \right) }^{ 2 }={ tan }^{ 2 }A\)

10th Standard English Medium Maths Subject Trigonometry Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Evaluate \(\frac { tan{ 65 }^{ o } }{ tan{ 25 }^{ o } } \)

• 2)

  Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

• 3)

  If ATB=90^o then prove that
  \(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)

• 4)

  If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

• 5)

  If tanθ+sinθ=P; tanθ-sinθ=q P.T P²-q²=4\(\sqrt{pq}\)

10th Standard English Medium Maths Subject Mensuration Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

• 2)

  How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

• 3)

  The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

• 4)

  When Karuna divided surface area of a sphere by the sphere's volume, he got the answer as \(\frac { 1 }{ 3 } \). What is the radius of the sphere?

• 5)

  Kamalam went to play a lucky draw contest 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac { 1 }{ 9 } \), then the number of tickets bought by kamalam is ____________

10th Standard English Medium Maths Subject Mensuration Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

• 2)

  A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is ___________

• 3)

  The curved surface area of a cylinder is 264 cm² and its volume is 924 cm². The ratio of diameter to its height is ___________

• 4)

  A floating boat having a length 3m and breadth 2m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is (density of water is 10000 kg/m³)

• 5)

  If a letter is chosen at random from the English alphabets {a, b....,z}, then the probability that the letter chosen precedes x ____________

10th Standard English Medium Maths Subject Statistics and Probability Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Two dice are through simultaneously the probability if getting a double is ___________

• 2)

  A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4 find the probability that |x| ≤ 4

• 3)

  If the smallest value and co-efficient of range a data are 25 and 0.5 respectively. Then the largest value is ___________

• 4)

  If the standard deviation of a variable x is 4 and if = \(\frac { 3x+5 }{ 4 } \) , then the standard deviation of y is ___________

• 5)

  In a competition containing two events A and B, the probability of winning the events A and B are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \) respectively and the probability if winning both events is ___________

10th Standard English Medium Maths Subject Statistics and Probability Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A girl calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game ___________

• 2)

  If the observations 1, 2, 3, ... 50 have the variance V₁ and the observations 51, 52, 53, ... 100 have the variance V₂ then \(\frac { { V }_{ 1 } }{ { V }_{ 2 } } \) is ___________

• 3)

  If the data is multiplied by 4, then the corresponding variances is get multiplied by ___________

• 4)

  Th4e batsman A is more consistent than batsman B if ___________

• 5)

  A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

10th Standard English Medium Maths Subject Statistics and Probability Creative 5 Mark Questions with Solution updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Σx = 99, n = 9, Σ(x - 10)² = 79, then find,
  (i) Σx²
  (ii) Σ(x - \(\bar { x } \))²

• 2)

  Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

• 3)

  S.D. of a data is 2102, mean is 36.6, then find its C.V.

• 4)

  Team A	50	20	10	30	30
  Team B	40	60	20	20	10

  Which team is more consistent?

• 5)

  Final the probability of choosing a spade or a heart card from a deck of cards.

10th Standard English Medium Maths Subject Creative 1 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  \((x-\frac { 1 }{ x } )={ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) then f(x) =

• 2)

  If the order pairs (a, -1) and (5, b) belongs to {(x, y) | y = 2x + 3}, then a and b are __________

• 3)

  The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

• 4)

  If \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

• 5)

  If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

10th Standard English Medium Maths Subject Creative 1 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

• 2)

  If function f : N⟶N, f(x) = 2x then the function is, then the function is ___________

• 3)

  If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

• 4)

  If f(x) = 2 - 3x, then f o f(1 - x) = ?

• 5)

  If f is constant function of value \(\frac { 1 }{ 10 } \), the value of f(1) + f(2) + ... + f(100) is _________

10th Standard English Medium Maths Subject Creative 2 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

• 2)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table.

• 3)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

• 4)

  Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

• 5)

  Prove that \(\sqrt { 3 } \) is irrational

10th Standard English Medium Maths Subject Creative 2 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B be a relation. Show that R is a function and find its domain, co-domain and the range of R.

• 2)

  State whether the graph represent a function. Use vertical line test.
  

• 3)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

• 4)

  Use Euclid's algorithm to find the HCF of 4052 and 12756.

• 5)

  Find the LCM and HCF of 6 and 20 by the prime factorisation method.

10th Standard English Medium Maths Subject Creative 5 Mark Questions with Solution Part - I updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  find 2f(-4) + 3f(2)

• 2)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  \(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

• 3)

  Let A = {1, 2, 3, 4, 5}, B = N and f: A \(\rightarrow\)B be defined by f(x) = x². Find the range of f. Identify the type of function.

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(3),

• 5)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  -2, 2, -2, 2, -2

10th Standard English Medium Maths Subject Creative 5 Mark Questions with Solution Part - II updated Creative Questions - by Question Bank Software - May 13, 2022 - View & Read

• 1)

  Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this
  (i) an one-one function
  (ii) an onto function,
  (iii) both one and onto function?

• 2)

  f(x) = (1+ x)
  g(x) = (2x - 1)
  Show that fo(g(x)) = gof(x)

• 3)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(5),

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(2) - f( 4).

• 5)

  Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
  1, 1, 1, 2, 2, 2, 3, 3,  3

10th Standard English Medium Maths Subject Statistics and Probability Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 07, 2021 - View & Read

• 1)

  The standard deviation of a data is 3. If each value is multiplied by 5 then the new variance is

• 2)

  If the mean and coefficient of variation of a data are 4 and 87.5% then the standard deviation is

• 3)

  The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

• 4)

  The probability of getting a job for a person is \(\frac{x}{3}\). If the probability of not getting the job is \(\frac{2}{3}\)  then the value of x is

• 5)

  If a letter is chosen at random from the English alphabets {a, b,...,z}, then the probability that the letter chosen precedes x

10th Standard English Medium Maths Subject Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this
  (i) an one-one function
  (ii) an onto function,
  (iii) both one and onto function?

• 2)

  f(x) = (1+ x)
  g(x) = (2x - 1)
  Show that fo(g(x)) = gof(x)

• 3)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(5),

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(2) - f( 4).

• 5)

  Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
  1, 1, 1, 2, 2, 2, 3, 3,  3

10th Standard English Medium Maths Subject Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  find 2f(-4) + 3f(2)

• 2)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  \(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

• 3)

  Let A = {1, 2, 3, 4, 5}, B = N and f: A \(\rightarrow\)B be defined by f(x) = x². Find the range of f. Identify the type of function.

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(3),

• 5)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  -2, 2, -2, 2, -2

10th Standard English Medium Maths Subject Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B be a relation. Show that R is a function and find its domain, co-domain and the range of R.

• 2)

  State whether the graph represent a function. Use vertical line test.
  

• 3)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

• 4)

  Use Euclid's algorithm to find the HCF of 4052 and 12756.

• 5)

  Find the LCM and HCF of 6 and 20 by the prime factorisation method.

10th Standard English Medium Maths Subject Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

• 2)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table.

• 3)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

• 4)

  Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

• 5)

  Prove that \(\sqrt { 3 } \) is irrational

10th Standard English Medium Maths Subject Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

• 2)

  If function f : N⟶N, f(x) = 2x then the function is, then the function is ___________

• 3)

  If f(x) = mx + n, when m and n are integers f(-2) = 7, and f(3) = 2 then m and n are equal to ___________

• 4)

  If f(x) = 2 - 3x, then f o f(1 - x) = ?

• 5)

  If f is constant function of value \(\frac { 1 }{ 10 } \), the value of f(1) + f(2) + ... + f(100) is _________

10th Standard English Medium Maths Subject Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  \((x-\frac { 1 }{ x } )={ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) then f(x) =

• 2)

  If the order pairs (a, -1) and (5, b) belongs to {(x, y) | y = 2x + 3}, then a and b are __________

• 3)

  The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

• 4)

  If \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

• 5)

  If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

10th Standard English Medium Maths Subject Statistics and Probability Creative 5 Mark Questions with Solution - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Σx = 99, n = 9, Σ(x - 10)² = 79, then find,
  (i) Σx²
  (ii) Σ(x - \(\bar { x } \))²

• 2)

  Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

• 3)

  S.D. of a data is 2102, mean is 36.6, then find its C.V.

• 4)

  Team A	50	20	10	30	30
  Team B	40	60	20	20	10

  Which team is more consistent?

• 5)

  Final the probability of choosing a spade or a heart card from a deck of cards.

10th Standard English Medium Maths Subject Statistics and Probability Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  A girl calculates the probability of her winning in a match is 0.08 what is the probability of her losing the game ___________

• 2)

  If the observations 1, 2, 3, ... 50 have the variance V₁ and the observations 51, 52, 53, ... 100 have the variance V₂ then \(\frac { { V }_{ 1 } }{ { V }_{ 2 } } \) is ___________

• 3)

  If the data is multiplied by 4, then the corresponding variances is get multiplied by ___________

• 4)

  Th4e batsman A is more consistent than batsman B if ___________

• 5)

  A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4. The probability that \(\left| x \right| \le 3\) is ___________

10th Standard English Medium Maths Subject Statistics and Probability Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Two dice are through simultaneously the probability if getting a double is ___________

• 2)

  A number x is chosen at random from -4, -3, -2, -1, 0, 1, 2, 3, 4 find the probability that |x| ≤ 4

• 3)

  If the smallest value and co-efficient of range a data are 25 and 0.5 respectively. Then the largest value is ___________

• 4)

  If the standard deviation of a variable x is 4 and if = \(\frac { 3x+5 }{ 4 } \) , then the standard deviation of y is ___________

• 5)

  In a competition containing two events A and B, the probability of winning the events A and B are \(\frac { 1 }{ 3 } \) and \(\frac { 1 }{ 4 } \) respectively and the probability if winning both events is ___________

10th Standard English Medium Maths Subject Mensuration Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  A cylinder 10 cone and have there are of a equal base and have the same height. what is the ratio of there volumes?

• 2)

  A solid is hemispherical at the bottom and conical above. If the curved surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is ___________

• 3)

  The curved surface area of a cylinder is 264 cm² and its volume is 924 cm². The ratio of diameter to its height is ___________

• 4)

  A floating boat having a length 3m and breadth 2m is floating on a lake. The boat sinks by 1 cm when a man gets into it. The mass of the man is (density of water is 10000 kg/m³)

• 5)

  If a letter is chosen at random from the English alphabets {a, b....,z}, then the probability that the letter chosen precedes x ____________

10th Standard English Medium Maths Subject Mensuration Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

• 2)

  How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius cm?

• 3)

  The material of a cone is converted into the shape of a cylinder of equal radius. If the height of the cylinder is 5 cm, then height of the cone is ___________

• 4)

  When Karuna divided surface area of a sphere by the sphere's volume, he got the answer as \(\frac { 1 }{ 3 } \). What is the radius of the sphere?

• 5)

  Kamalam went to play a lucky draw contest 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac { 1 }{ 9 } \), then the number of tickets bought by kamalam is ____________

10th Standard English Medium Maths Subject Trigonometry Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Evaluate \(\frac { tan{ 65 }^{ o } }{ tan{ 25 }^{ o } } \)

• 2)

  Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

• 3)

  If ATB=90^o then prove that
  \(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)

• 4)

  If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

• 5)

  If tanθ+sinθ=P; tanθ-sinθ=q P.T P²-q²=4\(\sqrt{pq}\)

10th Standard English Medium Maths Subject Trigonometry Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Express the ratios cos A, tan A and sec A in terms of sin A.

• 2)

  If sin 3A = cos (A - 26°), where 3A is an acute angle, find the value at A.

• 3)

  From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.

• 4)

  P.T (1+tan∝tan∝tanβ)² +(tan∝-tanβ)² =sec² ∝sec²β.

• 5)

  \(P.T\left( \frac { 1+{ tan }^{ 2 }A }{ 1+{ cot }^{ 2 }A } \right) ={ \left( \frac { 1-tan\quad A }{ 1-cot\quad A } \right) }^{ 2 }={ tan }^{ 2 }A\)

10th Standard English Medium Maths Subject Trigonometry Creative 2 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

10th Standard English Medium Maths Subject Trigonometry Creative 2 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Prove that \(\frac { sin\theta -cos\theta +1 }{ sin\theta +cos\theta -1 } =\frac { 1 }{ sec\theta -tan\theta } \) using the identity sec²θ= 1+ tan²θ.

• 2)

  In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.

10th Standard English Medium Maths Subject Trigonometry Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  The value of the expression [cosec (75^o + θ) - sec (15^o - θ) - tan (55^o + θ) + cot(35^o - θ] is ___________

• 2)

  If sin θ - cos θ = 0, then the value of (sin⁴ θ + cos⁴ θ) is ___________

• 3)

  A pole 6 m high a shadow 2\(\sqrt{3}\) m long on the ground, then the sun's elevation is ___________

• 4)

  If sec θ + tan θ = n, and sec θ - tan θ = 0, then the value of mn is ___________

• 5)

  The blanks of river are parallel. A swimmer starts from a point on one of the banks and swims in a straight line to the bank at 45^o and reaches the opposite bank at a point 20 m, from the point opposite to the straight point. The breadth of the river is equal to ____________

10th Standard English Medium Maths Subject Trigonometry Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  If sin A = \(\frac{1}{2}\), then the value of cot A is ___________

• 2)

  Given that sinθ = \(\frac{a}{b}\), then cosθ is equal to ___________

• 3)

  If 4 tan θ = 3, then \(\left( \frac { 4sin\theta -cos\theta }{ 4sin\theta +cos\theta } \right) \) is equal to ___________

• 4)

  Sin(45^o+ θ ) - cos(45^o - θ) is equal to ___________

• 5)

  If cotθ = b/a then value of \(\frac { cos\theta +sin\theta }{ cos\theta -sin\theta } \) a

10th Standard English Medium Maths Subject Coordinate Geometry Creative 5 Mark Questions with Solution - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

• 2)

  Find the area of a triangle vertices are(1, -1), (-4, 6) and (-3, -5).

• 3)

  Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

• 4)

  Find the area of the triangle formed by the points P(-1, 5, 3), Q(6, -2) and R(-3, 4).

• 5)

  Find the value of k if the points A(2, 3), B(4, k) and (6, -3) are collinear.

10th Standard English Medium Maths Subject Coordinate Geometry Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Find the ratio in which the line segment joining the points (-3, 10) and (6,-8) is internally divided by (-1, 6) ____________

• 2)

  If the mid-point of the line segment joining \(A\left( \frac { x }{ 2 } ,\frac { y+1 }{ 2 } \right) \) and B(x + 1, y-3) is C(5, -2) then find the values of x, y ____________

• 3)

  A line passing through the point (2, 2) and the axes enclose an area ∝. The intercept on the axes made by the line are given by the roots of ____________

• 4)

  In a right angle triangle, right angled at B, if the side BC is parallel to x axis, then the slope of AB is ___________

• 5)

  The lines y = 5x - 3, y = 2x + 9 intersect at A. The coordinates of A are ___________

10th Standard English Medium Maths Subject Coordinate Geometry Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  If the points (0, 0), (a, 0) and (0, b) are collinear, then ____________

• 2)

  Find the value of P, given that the line  \(\frac { y }{ 2 } =x-p\) passes through the point (-4, 4) is ____________

• 3)

  Find the value of 'a' if the lines 7y = ax + 4 and 2y = 3 - x are parallel

• 4)

  Find the equation of the line passing through the point (0, 4) and is parallel to 3x+5y+15 = 0 the line is ___________

• 5)

  The lines y = 5x - 3, y = 2x + 9 intersect at A. The coordinates of A are ___________

10th Standard English Medium Maths Subject Geometry Creative 5 Mark Questions with Solution - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  In \(AD\bot BC\) prove that AB² + CD² = BD² + AC². 

• 2)

  BL and CM are medians of a triangle ABC right angled at A.
  Prove that 4(BL² + CM²) = 5BC².

• 3)

  Prove that in a right triangle, the square of 8. the hypotenuse is equal to the sum of the squares of the others two sides.

• 4)

  In figure 0 is any point inside a rectangle ABCD. Prove that OB² + OD² = OA² + OC²

• 5)

  In \(\angle ACD={ 90 }^{ 0 }\) and \(CD\bot AB\) Prove that \(\cfrac { { BC }^{ 2 } }{ { AC }^{ 2 } } =\cfrac { BD }{ AD } \)

10th Standard English Medium Maths Subject Geometry Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  S and T are points on sides PQ and PR respectively of \(\Delta PQR\) If PS = 3cm, AQ = 6 cm, PT = 5 cm, and TR = 10 cm and then QR

• 2)

  The perimeter of a right triangle is 36 cm. Its hypotenuse is 15 cm, then the area of the triangle is ____________

• 3)

  If the angle between two radio of a circle is ^o, the angle between the tangents at the end of the radii is ____________

• 4)

  In the given figure if OC = 9 cm and OB = 15 cm then OB + BD is equal to ____________

• 5)

  Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two if the sides of the triangle are 2cm,3cm and 4 cm. find the diameter of the smallest circle.

10th Standard English Medium Maths Subject Geometry Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  I the given figure DE||AC which of the following is true.

• 2)

  In the given figure DE||BC:BD = x - 3, BA = 2x,CE = x- 2, and AC = 2x + 3, Find the value of x.

• 3)

  If ABC is a triangle and AD bisects A, AB = 4cm, BD = 6cm, DC = 8cm then the value of AC is ____________

• 4)

  A line which intersects a circle at two distinct points is called ____________

• 5)

  In figure \(\angle OAB={ 60 }^{ o }\) and OA = 6cm then radius of the circle is ____________

10th Standard English Medium Maths Subject Algebra Creative 5 Mark Questions with Solution - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

• 2)

  A two digit number is such that the product of its digits is 12. When 36 is added to the number the digits interchange their places. Find the number.

• 3)

  Seven years ago, Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

• 4)

  A chess board contains 64 equal squares and the area of each square is 6.25 cm², A border round the board is 2 cm wide.

• 5)

  Find two consecutive natural numbers whose product is 20.

10th Standard English Medium Maths Subject Algebra Creative 2 Mark Questions with Solution - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Solve the following system of linear equations in three variables.
  x + y + z = 6; 2x + 3y + 4z = 20;
  3x + 2y + 5z = 22

• 2)

  Using quadratic formula solve the following equations.
  p²x² + (P² -q²) X - q² = 0

• 3)

  Using quadratic formula solve the following equations.9x²-9(a+b)x+(2a²+5ab+2b²)=0

• 4)

  Find the values of k for which the following equation has equal roots.
  (k - 12)r + 2(k - 12)x + 2 = 0

• 5)

  Prove that the equation x²(a²+b²)+2x(ac+bd)+(c²+ d²) = 0 has no real root if ad≠bc.

10th Standard English Medium Maths Subject Algebra Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Which of the following is correct
  (i) Every polynomial has finite number of multiples
  (ii) LCM of two polynomials of degree 2 may be a constant
  (iii) HCF of 2 polynomials may be constant
  (iv) Degree of HCF of two polynomials is always less then degree of LCM

• 2)

  \(\frac { { x }^{ 2 }+7x12 }{ { x }^{ 2 }+8x+15 } \times \frac { { x }^{ 2 }+5x }{ { x }^{ 2 }+6x+8 } =\_ \_ \_ \_ \_ \_ \_ \_ \_ \)

• 3)

  The square root of 4m² - 24m + 36 is ___________

• 4)

  The product of the sum and product of roots of equation (a²-b²)x²-(a+b)²x+(a³-b³) = 0 is ___________

• 5)

  If P and Q are matrices, then which of the following is true?

10th Standard English Medium Maths Subject Algebra Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Graphically an infinite number of solutions represents ___________

• 2)

  If \(\frac { p }{ q } =a\) then \(\frac { { p }^{ 2 }+{ q }^{ 2 } }{ { p }^{ 2 }-{ q }^{ 2 } } \) ___________

• 3)

  The real roots of the quadratic equation x²-x-1 are ___________

• 4)

  The parabola y = -3x² is ___________

• 5)

  If \(A=\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right] _{ 3\times 2 }\) \(B=\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{matrix} \right] _{ 2\times 3 }\) then which of the following products can be made from these matrices 
  (i) A²
  (ii) B²
  (iii) AB
  (iv) BA

10th Standard English Medium Maths Subject Numbers and Sequences Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  4,10,16, 22, ...

• 2)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  -2, 2, -2, 2, -2

• 3)

  Determine the AP whose 3rd term is 5 and the 7^th term is 9.

• 4)

  If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

• 5)

  Find the sum of first 24 terms of the list of numbers whose nth term is given by a_n = 3 + 2n.

10th Standard English Medium Maths Subject Numbers and Sequences Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  4,10,16, 22, ...

• 2)

  Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
  1,-1,-3, -5, ...

• 3)

  Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
  1, 1, 1, 2, 2, 2, 3, 3,  3

• 4)

  In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

• 5)

  How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

10th Standard English Medium Maths Subject Numbers and Sequences Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  If m and n are the two positive integers then m² and n² are ____________

• 2)

  In the arithmetic series Sn = k + 2k + 3k +...+ 100, k is positive integer and k is a factor 100 then S_n is ____________

• 3)

  If p^th, q^th and r^th terms of an A.P. are a, b, c respectively, then (a(q - r) + b(r - p) + c(p - q) is____________

• 4)

  The sum of first n terms of the series a, 3a, 5a...is ____________

• 5)

  In an A.P if the p^th term is q and the q^th term is p, then its n^th term is ____________

10th Standard English Medium Maths Subject Numbers and Sequences Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  If a and b are the two positive integers when a > b and b is a factor of a then HCF (a, b) is ____________

• 2)

  How many terms are there in the G.P : 5, 20, 80, 320,..., 20480

• 3)

  Sum of infinite terms of G.P is 12 and the first term is 8. What is the fourth term of the G.P?

• 4)

  A boy saves Rs. 1 on the first day Rs. 2 on the second day, Rs. 4 on the third day and so on. How much did the boy will save upto 20 days?

• 5)

  If p, q, r, x, y, z are in A.P, then 5p + 3, 5r + 3, 5x + 3, 5y + 3, 5z + 3 form ____________

10th Standard English Medium Maths Subject Relations and Functions Creative 5 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  f(-7) - f(-3)

• 2)

  f(x) = (1+ x)
  g(x) = (2x - 1)
  Show that fo(g(x)) = gof(x)

• 3)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(5),

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(2) - f( 4).

• 5)

  If R = {(a, -2), (-5, b), (8, c), (d, -1)} represents the identity function, find the values of a, b, c and 

10th Standard English Medium Maths Subject Relations and Functions Creative 5 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  find 2f(-4) + 3f(2)

• 2)

  A function f: [-7,6) \(\rightarrow\) R is defined as follows.
  
  \(\cfrac { 4f(-3)+2f(4) }{ f(-6)-3f(1) } \)

• 3)

  Let A = {1, 2, 3, 4, 5}, B = N and f: A \(\rightarrow\)B be defined by f(x) = x². Find the range of f. Identify the type of function.

• 4)

  A function f: (1,6) \(\rightarrow\)R is defined as follows:
  
  Find the value of f(3),

• 5)

  The following table represents a function from A = {5, 6, 8, 10} to B = {19, 15, 9, 11}, where f(x) = 2x - 1. Find the values of a and b.

  x	5	6	8	10
  f(x)	a	11	b	19

10th Standard English Medium Maths Subject Relations and Functions Creative 2 Mark Questions with Solution - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a set of ordered pairs.

• 2)

  State whether the graph represent a function. Use vertical line test.
  

• 3)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as  a table.

• 4)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

• 5)

  Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f: A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as a graph.

10th Standard English Medium Maths Subject Relations and Functions Creative 1 Mark Questions with Solution Part - II - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  Let f(x) = x² - x, then f(x- 1) - (x + 1) is ___________

• 2)

  If f(x) = ax - 2, g(x) = 2x - 1 and fog = gof, the value of a is ___________

• 3)

  If f(x) = 2 - 3x, then f o f(1 - x) = ?

• 4)

  If f is constant function of value \(\frac { 1 }{ 10 } \), the value of f(1) + f(2) + ... + f(100) is _________

• 5)

  If f is identify function, then the value of f(1) - 2f(2) + f(3) is: 

10th Standard English Medium Maths Subject Relations and Functions Creative 1 Mark Questions with Solution Part - I - by Question Bank Software - Jul 03, 2021 - View & Read

• 1)

  \((x-\frac { 1 }{ x } )={ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \) then f(x) =

• 2)

  The function t which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined Fahrenheit degree is 95, then the value of  C \(t(C)=\frac { 9c }{ 5 } +32\) is ___________

• 3)

  If \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

• 4)

  If f(x) + f(1 - x) = 2 then \(f\left( \frac { 1 }{ 2 } \right) \) is ___________

• 5)

  If \(f(x)=\frac { x+1 }{ x-2 } ,g(x)=\frac { 1+2x }{ x-1 } \) then fog(x) is ___________

10th Standard English Medium Maths Subject Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Solve \(\sqrt { y+1 } +\sqrt { 2y-5 } \) = 3

• 2)

  Simplify
  \(\frac { 4{ x }^{ 2 }y }{ 2{ x }^{ 2 } } \times \frac { 6x{ z }^{ 3 } }{ 20{ y }^{ 4 } } \)

• 3)

  Find the values of a and b if the following polynomials are perfect squares
  4x⁴ - 12x³ + 37x² + bx + a

• 4)

  If A = \(\left[ \begin{matrix} 1 & 2 & 1 \\ 2 & -1 & 1 \end{matrix} \right] \) and B = \(\left[ \begin{matrix} 2 & -1 \\ -1 & 4 \\ 0 & 2 \end{matrix} \right] \) show that (AB)^T = B^TA^T

• 5)

  If α, β are the roots of the equation 2x² - x - 1 = 0, then form the equation whose roots are
  2α + β, 2β + α

10th Standard English Medium Maths Subject Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If A = {5,6}, B = {4,5,6}, C = {5,6,7}, Show that A x A = (B x B) ∩ (C x C)

• 2)

  Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
  A x (B U C) = (A x B) U (A x C)

• 3)

  A graph representing the function f (x) is given in Fig it is clear that f (9) = 2.
  (i) Find the following values of the function
  (a) f(0)
  (b) f(7)
  (c) f(2)
  (d) f(10)
  (ii) For what value of x is f (x) = 1?
  (iii) Describe the following (i) Domain (ii) Range.
  (iv) What is the image of 6 under f ?
  

• 4)

  An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown Fig. Express the volume V of the box as a function of x.
  

• 5)

  A function f: [-5,9] ⟶ R is defined as follows:
  \(f(x)=\left[\begin{array}{ll} 6 x+1 & \text { if }-5 \leq x<2 \\ 5 x^{2}-1 & \text { if } 2 \leq x<6 \\ 3 x-4 & \text { if } 6 \leq x \leq 9 \end{array}\right.\)
  Find
  i) f(-3) + f(2)
  ii) f(7) - f(1)
  iii) 2f(4) + f(8)
  iv)  \(\frac { 2f(-2)-f(6) }{ f(4)+f(-2) } \)

10th Standard English Medium Maths Subject Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

• 2)

  Let A = {1,2,3} and B = {x| x is a prime number less than 10}. Find A x B and B x A.

• 3)

  Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
  R₁ = {(3,7), (4,7), (7,10), (8,1)}

• 4)

  A Relation R is given by the set {(x, y) / y = x + 3, x \(\in \) {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

• 5)

  A relation ‘f’ \(X \rightarrow Y\) is defined by f(x) = x² - 2 where x \(\in \) {-2, -1, 0, 3} and Y = R
  (i) List the elements of f
  (ii) Is f a function?

10th Standard English Medium Maths Subject Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

• 2)

  Let A = {1,2,3} and B = {x| x is a prime number less than 10}. Find A x B and B x A.

• 3)

  Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
  R₁ = {(3,7), (4,7), (7,10), (8,1)}

• 4)

  A plane is flying at a speed of 500 km per hour. Express the distanced travelled by the plane as function of time t in hours.

• 5)

  If f(x) = x² - 1. Find
  i. f o f
  ii. f o f o f

10th Standard English Medium Maths Subject Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If n(A x B) = 6 and A = {1,3} then n(B) is

• 2)

  If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

• 3)

  The range of the relation R = {(x, x²) |x is a prime number less than 13} is

• 4)

  Let f and g be two functions given by
  f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
  g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 5)

  Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

10th Standard English Medium Maths Subject Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

• 2)

  Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

• 3)

  The sum of the exponents of the prime factors in the prime factorization of 1729 is

• 4)

  The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

• 5)

  \(\frac { x }{ { x }^{ 2 }-25 } -\frac { 8 }{ { x }^{ 2 }+6x+5 } \) gives

10th Standard English Medium Maths Subject Statistics and Probability Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The consumption of number of guava and orange on a particular week by a family are given below.

  Number of Guavas	3	5	6	4	3	5	4
  Number of Oranges	1	3	7	9	2	6	2

  Which fruit is consistently consumed by the family?

• 2)

  The temperature of two cities A and B in a winter season are given below.

  Temperature of city A (in degree Celsius)	18	20	22	24	26
  Temperature of city B (in degree Celsius)	11	14	15	17	18

  Find which city is more consistent in temperature changes?

• 3)

  Two unbiased dice are rolled once. Find the probability of getting
  (i) a doublet (equal numbers on both dice)
  (ii) the product as a prime number
  (iii) the sum as a prime number
  (iv) the sum as 1

• 4)

  Three fair coins are tossed together. Find the probability of getting
  (i) all heads
  (ii) atleast one tail
  (iii) at most one head
  (iv) at most two tails

• 5)

  Some boys are playing a game, in which the stone thrown by them landing in a circular region (given in the figure) is considered as win and landing other than the circular region is considered as loss. What is the probability to win the game?
  

10th Standard English Medium Maths Subject Statistics and Probability Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The number of televisions sold in each day of a week are 13, 8, 4, 9, 7, 12, 10. Find its standard deviation.

• 2)

  The amount of rainfall in a particular season for 6 days are given as 17.8 cm, 19.2 cm, 16.3 cm, 12.5 cm, 12.8 cm and 11.4 cm. Find its standard deviation.

• 3)

  The marks scored by 10 students in a class test are 25, 29, 30, 33, 35, 37, 38, 40, 44, 48. Find the standard deviation.

• 4)

  The amount that the children have spent for purchasing some eatables in one day trip of a school are 5, 10, 15, 20, 25, 30, 35, 40. Using step deviation method, find the standard deviation of the amount they have spent.

• 5)

  Find the standard deviation of the following data 7, 4, 8, 10, 11. Add 3 to all the values then find the standard deviation for the new values.

10th Standard English Medium Maths Subject Statistics and Probability Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The following table gives the values of mean and variance of heights and weights of the 10th standard students of a school.

  	Height	Weight
  Mean	155 cm	46.50 kg
  Variance	72.25 cm2	28.09 kg

  Which is more varying than the other?

• 2)

  The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.

• 3)

  If n = 5 , \(\bar { x } \) = 6, Σx² = 765 then calculate the coefficient of variation.

• 4)

  Two coins are tossed together. What is the probability of getting different faces on the coins?

• 5)

  A die is rolled and a coin is tossed simultaneously. Find the probability that the die shows an odd number and the coin shows a head.

10th Standard English Medium Maths Subject Statistics and Probability Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Find the range and coefficient of range of the following data: 25, 67, 48, 53, 18, 39, 44.

• 2)

  Find the range of the following distribution..

  Age (in years)	16-18	18-20	20-22	22-24	24-26	26-28
  Number of students	0	4	6	8	2	2

• 3)

  The range of a set of data is 13.67 and the largest value is 70.08. Find the smallest value.

• 4)

  Find the range and coefficient of range of the following data. 63, 89, 98, 125, 79, 108, 117, 68

• 5)

  If the range and the smallest value of a set of data are 36.8 and 13.4 respectively, then find the largest value.

10th Standard English Medium Maths Subject Statistics and Probability Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The probability a red marble selected at random from a jar containing p red, q blue and r green marbles is

• 2)

  A page is selected at random from a book. The probability that the digit at units place of the page number chosen is less than 7 is

• 3)

  The probability of getting a job for a person is \(\frac{x}{3}\). If the probability of not getting the job is \(\frac{2}{3}\)  then the value of x is

• 4)

  Kamalam went to play a lucky draw contest. 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac{1}{9}\), then the number of tickets bought by Kamalam is

• 5)

  A purse contains 10 notes of Rs. 2000, 15 notes of Rs. 500, and 25 notes of Rs. 200. One note is drawn at random. What is the probability that the note is either a Rs. 500 note or Rs. 200 note?

10th Standard English Medium Maths Subject Mensuration Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The volume of a solid hemisphere is 29106 cm³. Another hemisphere whose volume is two-third of the above is carved out. Find the radius of the new hemisphere.

• 2)

  A cylindrical glass with diameter 20 cm has water to a height of 9 cm. A small cylindrical metal of radius 5 cm and height 4 cm is immersed it completely. Calculate the raise of the water in the glass?

• 3)

  The volumes of two cones of same base radius are 3600 cm³ and 5040 cm³. Find the ratio of heights.

• 4)

  A solid sphere and a solid hemisphere have equal total surface area. Prove that the ratio of their volume is 3\(\sqrt{3}\) : 4.

• 5)

  A toy is in the shape of a cylinder surrounded by a hemisphere. The height of the toy is 25 cm. Find the total surface area of the toy if its common diameter is 12 cm.
  

10th Standard English Medium Maths Subject Mensuration Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and base is hollowed out. Find the total surface area of the remaining solid.
  

• 2)

  The internal and external radii of a hollow hemispherical shell are 3 m and 5 m respectively. Find the T.S.A. and C.S.A. of the shell.
  

• 3)

  An industrial metallic bucket is in the shape of the frustum of a right circular cone whose top and bottom diameters are 10 m and 4 m and whose height is 4 m. Find the curved and total surface area of the bucket.
  

• 4)

  A right angled triangle PQR where ∠Q = 90^o is rotated about QR and PQ. If QR = 16 cm and PR = 20 cm, compare the curved surface areas of the right circular cones so formed by the triangle.

• 5)

  A girl wishes to prepare birthday caps in the form of right circular cones for her birthday party, using a sheet of paper whose area is 5720 cm², how many caps can be made with radius 5 cm and height 12 cm.

10th Standard English Medium Maths Subject Mensuration Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  4 persons live in a conical tent whose slant height is 19 cm. If each person require 22 cm² of the floor area, then find the height of the tent.

• 2)

  The ratio of the radii of two right circular cones of same height is 1 : 3. Find the ratio of their curved surface area when the height of each cone is 3 times the radius of the smaller cone.

• 3)

  Find the volume of a cylinder whose height is 2 m and whose base area is 250 m².

• 4)

  The volume of a solid right circular cone is 11088 cm³. If its height is 24 cm then find the radius of the cone.

• 5)

  The ratio of the volumes of two cones is 2 : 3. Find the ratio of their radii if the height of second cone is double the height of the first.

10th Standard English Medium Maths Subject Mensuration Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A cylindrical drum has a height of 20 cm and base radius of 14 cm. Find its curved surface area and the total surface area.

• 2)

  The curved surface area of a right circular cylinder of height 14 cm is 88 cm² . Find the diameter of the cylinder.

• 3)

  A garden roller whose length is 3 m long and whose diameter is 2.8 m is rolled to level a garden. How much area will it cover in 8 revolutions?

• 4)

  If one litre of paint covers 10 m², how many litres of paint is required to paint the internal and external surface areas of a cylindrical tunnel whose thickness is 2 m, internal radius is 6 m and height is 25 m.
  

• 5)

  If the total surface area of a cone of radius 7cm is 704 cm², then find its slant height.

10th Standard English Medium Maths Subject Mensuration Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A frustum of a right circular cone is of height 16 cm with radii of its ends as 8 cm and 20 cm. Then, the volume of the frustum is

• 2)

  A shuttle cock used for playing badminton has the shape of the combination of

• 3)

  The volume (in cm³) of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

• 4)

  The height and radius of the cone of which the frustum is a part are h₁ units and r₁ units respectively. Height of the frustum is h₂ units and radius of the smaller base is r₂ units. If h₂ : h₁ = 1:2 then r₂ : r₁ is

• 5)

  The ratio of the volumes of a cylinder, a cone and a sphere, if each has the same diameter and same height is

10th Standard English Medium Maths Subject Mensuration Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is

• 2)

  If two solid hemispheres of same base radius r units are joined together along their bases, then curved surface area of this new solid is

• 3)

  The height of a right circular cone whose radius is 5 cm and slant height is 13 cm will be

• 4)

  If the radius of the base of a right circular cylinder is halved keeping the same height, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

• 5)

  The total surface area of a cylinder whose radius is \(\frac{1}{3}\)of its height is

10th Standard English Medium Maths Subject Trigonometry Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A flag pole of height ‘h’ metres is on the top of the hemispherical dome of radius ‘r’ metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find (i) the height of the pole (ii) radius of the (\( \sqrt { 3 } \) =1.732)
  

• 2)

  The angle of elevation of the top of a cell phone tower from the foot of a high apartment is 60° and the angle of depression of the foot of the tower from the top of the apartment is 30° . If the height of the apartment is 50 m, find the height of the cell phone tower. According to radiations control norms, the minimum height of a cell phone tower should be 120 m. State if the height of the above mentioned cell phone tower meets the radiation norms.

• 3)

  Three villagers A, B and C can see each other across a valley. The horizontal distance between A and B is 8 km and the horizontal distance between B and C is 12 km. The angle of depression of B from A is 20° and the angle of elevation of C from B is 30° . Calculate : the vertical height between A and B.(tan20° = 0.3640,(\(\sqrt { 3 } \) = 1.732)
  

• 4)

  If x sin³\(\theta \) + ycos³\(\theta \) = sin\(\theta \) cos\(\theta \) and x sin\(\theta \) = ycos\(\theta \), then prove that x² + y² = 1.

• 5)

  A bird is flying from A towards B at an angle of 35°, a point 30 km away from A. At B it changes its course of flight and heads towards C on a bearing of 48° and distance 32 km away.
  How far is B to the North of A? (sin 55° = 0.8192, cos 55° = 0.5736,sin 42° = 0.6691.cos 42° = 0.7431)

10th Standard English Medium Maths Subject Trigonometry Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Prove that sin² Acos² B + cos² Asin² B + cos² Acos² B + sin² Asin² B=1

• 2)

  if cos\(\theta \) + sin\(\theta \) =\(\sqrt { 2 } \) cos \(\theta \), then prove that cos\(\theta \) - sin\(\theta \) =\(\sqrt { 2 } \) sin\(\theta \) 

• 3)

  if cosec\(\theta \) + cot\(\theta \) = p, then prove that cos\(\theta \) = \(\frac { { p }^{ 2 }-1 }{ { p }^{ 2 }+1 } \)

• 4)

  if sin\(\theta \) + cos\(\theta \)  = \(\sqrt { 3 } \),then prove that tan\(\theta \) + cot\(\theta \) = 1

• 5)

  if \(\frac { cos\theta }{ 1+sin\theta } =\frac { 1 }{ a } \),then prove that \(\frac { { a }^{ 2 }-1 }{ a^{ 2 }+1 } \) = sin\(\theta \)

10th Standard English Medium Maths Subject Trigonometry Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  prove that \(\frac { sinA }{ 1+cosA } =\frac { 1-cosA }{ sinA } \) 

• 2)

  prove that \(\frac { sec\theta }{ sin\theta } -\frac { sin\theta }{ cos\theta } =cot\theta \)

• 3)

  From the top of a rock \(50\sqrt { 3 } \)m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.

• 4)

  The horizontal distance between two buildings is 70 m. The angle of depression of the top of the first building when seen from the top of the second building is 45°. If the height of the second building is 120 m, find the height of the first building.

• 5)

  A player sitting on the top of a tower of height 20 m observes the angle of depression of a ball lying on the ground as 60°. Find the distance between the foot of the tower and the ball.(\(\sqrt { 3 } \) = 1.732)

10th Standard English Medium Maths Subject Trigonometry Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Prove that tan²\(\theta \)-sin² \(\theta \) = tan² \(\theta \) sin² \(\theta \)

• 2)

  prove that \(\sqrt { \frac { 1+cos\theta }{ 1-cos\theta } } \) = cosec \(\theta \) + cot\(\theta \)

• 3)

  prove that \(\frac { sec\theta }{ sin\theta } -\frac { sin\theta }{ cos\theta } =cot\theta \)

• 4)

  calculate \(\angle \)BAC in the given triangles (tan 38.7° = 0.8011 )
  

• 5)

  A tower stands vertically on the ground. from a point on the ground, which is 48m away from the foot of the tower, the angel of elevation of the top of  the tower is 30°.find the height of the tower.

10th Standard English Medium Maths Subject Trigonometry Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The electric pole subtends an angle of 30° at a point on the same level as its foot. At a second point ‘b’ metres above the first, the depression of the foot of the pole is 60°. The height of the pole (in metres) is equal to

• 2)

  The angle of depression of the top and bottom of 20 m tall building from the top of a multistoried building are 30° and 60° respectively. The height of the multistoried building and the distance between two buildings (in metres) is

• 3)

  Two persons are standing ‘x’ metres apart from each other and the height of the first person is double that of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the shorter person (in metres) is

• 4)

  The angle of elevation of a cloud from a point h metres above a lake is \(\beta \). The angle of depression of its reflection in the lake is 45°. The height of location of the cloud from the lake is

• 5)

  If (sin α + cosec α)² + (cos α + sec α)² = k + tan²α + cot²α, then the value of k is equal to

10th Standard English Medium Maths Subject Trigonometry Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The value of \(si{ n }^{ 2 }\theta +\frac { 1 }{ 1+ta{ n }^{ 2 }\theta } \) is equal to

• 2)

  tan \(\theta \) cosec²\(\theta \) - tan\(\theta \) is equal to 

• 3)

  If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

• 4)

  If 5x = sec\(\theta \) and \(\frac { 5 }{ x } \) = tan\(\theta \), then x² - \(\frac { 1 }{ { x }^{ 2 } } \) is equal to 

• 5)

  If sin \(\theta \) = cos \(\theta \), then 2 tan² \(\theta \) + sin² \(\theta \) -1 is equal to 

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A mobile phone is put to use when the battery power is 100%. The percent of battery power ‘y’ (in decimal) remaining after using the mobile phone for x hours is assumed as y  = − 0.25 x + 1
  
  Draw a graph of the equation.

• 2)

  A circular garden is bounded by East Avenue and Cross Road. Cross Road intersects North Street at D and East Avenue at E. AD is tangential to the circular garden at A(3, 10). Using the figure.
  
  Find the equation of
  (i) East Avenue.
  (ii) North Street
  (iii) Cross Road

• 3)

  You are downloading a song. The percent y (in decimal form) of mega bytes remaining to get downloaded in x seconds is given by y = -0.1x + 1.
  Graph the equation.

• 4)

  Find the equation of a straight line through the point of intersection of the lines 8x + 3y = 18, 4x + 5y = 9 and bisecting the line segment joining the points (5, –4) and (–7, 6).

• 5)

  PQRS is a rectangle formed by joining the points P(-1, -1), Q(-1, 4) , R(5 ,4) and S(5,-1) . A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If the points P(-1, -4), Q (b, c) and R(5, -1) are collinear and if 2b + c = 4, then find the values of b and c.

• 2)

  Find the area of the quadrilateral formed by the points (8, 6), (5, 11), (-5, 12) and (-4, 3).

• 3)

  The given diagram shows a plan for constructing a new parking lot at a campus. It is estimated that such construction would cost Rs. 1300 per square feet. What will be the total cost for making the parking lot?

• 4)

  Find the area of the quadrilateral whose vertices are at (–9, –2), (–8, –4), (2, 2) and (1, –3)

• 5)

  Find the value of k, if the area of a quadrilateral is 28 sq. units, whose vertices are (–4, –2), (–3, k), (3, –2) and (2, 3)

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Find the equation of a straight line passing through (5, - 3) and (7, - 4).

• 2)

  A line makes positive intercepts on coordinate axes whose sum is 7 and it passes through (-3,8). Find its equation

• 3)

  Find the equation of a line through the given pair of points  \(\left( 2,\frac { 2 }{ 3 } \right) \) and \(\left( \frac { -1 }{ 2 } ,2 \right) \)

• 4)

  Find the slope of the straight line 6x + 8y + 7 = 0.

• 5)

  Show that the straight lines 2x + 3y - 8 = 0 and 4x + 6y + 18 = 0 are parallel.

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If the area of the triangle formed by the vertices A(-1, 2), B(k, -2) and C(7, 4) (taken in order) is 22 sq. units, find the value of k.

• 2)

  Find the area of the triangle formed by the points (1, –1), (–4, 6) and (–3, –5)

• 3)

  Determine whether the sets of points are collinear? \((-\frac12 ,3)\), (- 5, 6) and (-8, 8)

• 4)

  Vertices of given triangles are taken in order and their areas are provided aside. In each case, find the value of ‘p’?

  S. No	Vertices	Area (sq. units)
  (i)	(0, 0), (p, 8), (6, 2)	20
  (ii)	(p, p), (5, 6), (5, -2)	32

• 5)

  In each of the following, Find the value of ‘a’ for which the given points are collinear. (2, 3), (4, a) and (6, –3)

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If A is a point on the Y axis whose ordinate is 8 and B is a point on the X axis whose abscissae is 5 then the equation of the line AB is

• 2)

  A straight line has equation 8y = 4x + 21. Which of the following is true

• 3)

  When proving that a quadrilateral is a trapezium, it is necessary to show

• 4)

  When proving that a quadrilateral is a parallelogram by using slopes you must find

• 5)

  (2, 1) is the point of intersection of two lines.

10th Standard English Medium Maths Subject Coordinate Geometry Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The area of triangle formed by the points (−5, 0), (0, −5) and (5, 0) is

• 2)

  A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y axis. The path travelled by the man is

• 3)

  The straight line given by the equation x = 11 is

• 4)

  If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is

• 5)

  The point of intersection of 3x − y = 4 and x + y = 8 is

10th Standard English Medium Maths Subject Geometry Book Back 8 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Draw a circle of diameter 6 cm from a point P, which is 8 cm away from its centre. Draw the two tangents PA and PB to the circle and measure their lengths.

• 2)

  Draw a tangent at any point R on the circle of radius 3.4 cm and centre at P ?

• 3)

  Draw the two tangents from a point which is 10 cm away from the centre of a circle of radius 5 cm. Also, measure the lengths of the tangents.

• 4)

  Draw the two tangents from a point which is 5 cm away from the centre of a circle of diameter 6 cm. Also, measure the lengths of the tangents

• 5)

  Draw a tangent to the circle from the point P having radius 3.6 cm, and centre at O. Point P is at a distance 7.2 cm from the centre.

10th Standard English Medium Maths Subject Geometry Book Back 8 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Construct a △PQR which the base PQ = 4.5 cm, ∠R = 35^oand the median RG  from R to PG is 6 cm

• 2)

  Construct a \(\triangle\)PQR in which QR = 5 cm, \(\angle\)P = 40^o and the median PG from P to QR is 4.4 cm. Find the length of the altitude from P to QR.

• 3)

  Construct a \(\triangle\)PQR such that QR = 6.5 cm,\(\angle\)P = 60^oand the altitude from P to QR is of length 4.5 cm.

• 4)

  Construct a \(\triangle\)ABC such that AB = 5.5 cm, \(\angle\)C = 25^o and the altitude from C to AB is 4 cm.

• 5)

  Draw a triangle ABC of base BC = 5.6 cm, \(\angle\)A = 40^o and the bisector of \(\angle\)A meets BC at D such that CD = 4 cm.

10th Standard English Medium Maths Subject Geometry Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  An Aeroplane after take off from an airport and flies due north at a speed of 1000 km/hr. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km/hr. How far apart will be the two planes after 1½ hours?
  

• 2)

  There are two paths that one can choose to go from Sarah’s house to James house. One way is to take C street, and the other way requires to take B street and then A street. How much shorter is the direct path along C street? (Using figure).
  

• 3)

  In Fig, ABC is a triangle with \(\angle\)B=90^o, BC=3cm and AB=4 cm. D is point on AC such that AD=1 cm and E is the midpoint of AB. Join D and E and extend DE to meet CB at F. Find BF.
  

• 4)

  In a garden containing several trees, three particular trees P, Q, R are located in the following way, BP = 2 m, CQ = 3 m, RA = 10 m, PC = 6 m, QA = 5 m, RB = 2 m, where A, B, C are points such that P lies on BC, Q lies on AC and R lies on AB. Check whether the trees P, Q, R lie on a same straight line.
  

• 5)

  Two trains leave a railway station at the same time. The first train travels due west and the second train due north. The first train travels at a speed of 20 km/hr and the second train travels at 30 km/hr. After 2 hours, what is the distance between them?

10th Standard English Medium Maths Subject Geometry Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A boy of height 90cm is walking away from the base of a lamp post at a speed of 1.2m/sec. If the lamppost is 3.6m above the ground, find the length of his shadow cast after 4 seconds.
  

• 2)

  Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac{3}{5}\) of the corresponding sides of the triangle PQR (scale factor \(\frac { 3 }{ 5 } <1\)) 

• 3)

  Construct a triangle similar to a given triangle PQR with its sides equal to \(\frac { 7 }{ 4 } \) of the corresponding sides of the triangle PQR (scale factor \(\frac { 7 }{ 4 } \)>1)

• 4)

  A girl looks the reflection of the top of the lamp post on the mirror which is 6.6 m away from the foot of the lamp post. The girl whose height is 12.5 m is standing 2.5 m away from the mirror. Assuming the mirror is placed on the ground facing the sky and the girl, mirror and the lamp post are in a same line, find the height of the lamp post.

• 5)

  Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.
  

10th Standard English Medium Maths Subject Geometry Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  In the adjacent figure, \(\triangle\) ACB~\(\triangle\) APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.
  

• 2)

  In \(\triangle\)ABC,D and E are points on the sides AB and AC respectively such that DE||BC \(\frac { AD }{ DB } =\frac { 3 }{ 4 } \) and AC = 15cm find AE.

• 3)

  In the rectangle WXYZ, XY+YZ = 17 cm, and XZ + YW = 26 cm .Calculate the length and breadth of the rectangle
  

• 4)

  D is the mid point of side BC and AE \(\bot \) BC. If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that
  \({ b }^{ 2 }={ p }^{ 2 }+ax+\frac { { a }^{ 2 } }{ 4 } \)

• 5)

  If figure OPRQ is a square and \(\angle\)MLN=90^o. Prove that
  
  \(\triangle\)LOP~\(\triangle\)RPN

10th Standard English Medium Maths Subject Geometry Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Show that \(\triangle\) PST~\(\triangle\) PQR 
  

• 2)

  Check whether the which triangles are similar and find the value of x.
  (i)
  
  (ii)
  

• 3)

  A vertical stick of length 6 m casts a shadow 400 cm long on the ground and at the same time a tower casts a shadow 28 m long. Using similarity, find the height of the tower.

• 4)

  In the adjacent figure, \(\triangle\)ABC is right angled at C and DE\(\bot \) AB. Prove that \(\triangle\)ABC~\(\triangle\)ADE and hence find the lengths of AE and DE.
  

• 5)

  In the Figure, AD is the bisector of \(\angle\)BAC, if A = 10 cm, AC = 14 cm and BC = 6 cm. Find BD and DC.
  

10th Standard English Medium Maths Subject Geometry Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  In the given figure, PR = 26 cm, QR = 24 cm, \(\angle PAQ\) = 90^o, PA = 6 cm and QA = 8 cm. Find \(\angle\)PQR
  

• 2)

  A tangent is perpendicular to the radius at the

• 3)

  How many tangents can be drawn to the circle from an exterior point?

• 4)

  The two tangents from an external points P to a circle with centre at O are PA and PB. If \(\angle APB\) = 70^o then the value of \(\angle AOB\) is

• 5)

  In figure if PR is tangent to the circle at P and O is the centre of the circle, then \(\angle PQR\) is
  

10th Standard English Medium Maths Subject Geometry Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If in triangles ABC and EDF,\(\cfrac { AB }{ DE } =\cfrac { BC }{ FD } \) then they will be similar, when

• 2)

  In ∆LMN, \(\angle\)L = 60^o, \(\angle\)M = 50^o. If ∆LMN ~ ∆PQR then the value of \(\angle\)R is

• 3)

  If \(\triangle\)ABC is an isosceles triangle with \(\angle\)C = 90^o and AC = 5 cm, then AB is

• 4)

  In a given figure ST || QR, PS = 2 cm and SQ = 3 cm. Then the ratio of the area of \(\triangle\)PQR to the area \(\triangle\)PST is 
  

• 5)

  If in \(\triangle\)ABC, DE || BC, AB = 3.6 cm, AC = 2.4 cm and AD = 2.1 cm then the length of AE is

10th Standard English Medium Maths Subject Algebra Book Back 8 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Graph the following quadratic equations and state their nature of solutions x² - 9x + 20 = 0.

• 2)

  Discuss the nature of solutions of the following quadratic equations.
  x² - 8x + 16 = 0

• 3)

  Graph the following quadratic equations and state their nature of solutions.
  x² + x + 7 = 0

• 4)

  Graph the following quadratic equations and state their nature of solutions.
  x² - 9 = 0

• 5)

  Graph the following quadratic equations and state their nature of solutions.
  (2x - 3)(x + 2) = 0

10th Standard English Medium Maths Subject Algebra Book Back 8 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Discuss the nature of solutions of the following quadratic equations.
  x² + x - 12 = 0

• 2)

  Draw the graph of y = 2x² and hence solve 2x² - x - 6 = 0

• 3)

  Draw the graph of y = x² + 4x + 3 and hence find the roots of x² + x + 1 = 0

• 4)

  Draw the graph of y = x² + x - 2 and hence solve x² + x - 2 = 0

• 5)

  Draw the graph of y = x² - 4x + 3 and use it to solve x² - 6x + 9 = 0

10th Standard English Medium Maths Subject Algebra Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A = \(\left( \begin{matrix} 3 & 0 \\ 4 & 5 \end{matrix} \right) \), B = \(\left( \begin{matrix} 6 & 3 \\ 8 & 5 \end{matrix} \right) \), C = \(\left( \begin{matrix} 3 & 6 \\ 1 & 1 \end{matrix} \right) \) find the matrix D, such that CD – AB = 0

• 2)

  Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

• 3)

  Vani, her father and her grand father have an average age of 53. One-half of her grand father’s age plus one-third of her father’s age plus one fourth of Vani’s age is 65. Four years ago if Vani’s grandfather was four times as old as Vani then how old are they all now?

• 4)

  The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the former number. If the hundreds digit plus twice the tens digit is equal to the units digit, then find the original three digit number?

• 5)

  Find the GCD of the given polynomials
  x⁴ + 3x³ - x - 3, x³ + x² - 5x + 3

10th Standard English Medium Maths Subject Algebra Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Solve \(\frac {1}{3}\) (x + y - 5) = y - z = 2x - 11 = 9 - (x + 2z).

• 2)

  One hundred and fifty students are admitted to a school. They are distributed over three sections A, B and C. If 6 students are shifted from section A to section C, the sections will have equal number of students. If 4 times of students of section C exceeds the number of students of section A by the number of students in section B, find the number of students in the three sections.

• 3)

  In a three-digit number, when the tens and the hundreds digit are interchanged the new number is 54 more than three times the original number. If 198 is added to the number, the digits are reversed. The tens digit exceeds the hundreds digit by twice as that of the tens digit exceeds the unit digit. Find the original number.

• 4)

  Find the least common multiple of xy(k² + 1) + k(x² + y²) and xy(k² - 1) + k(x² - y²)

• 5)

  Find the GCD of the following by division algorithm 2x⁴ + 13x³ + 27x²+23x + 7, x³ + 3x² + 3x + 1, x² + 2x + 1

10th Standard English Medium Maths Subject Algebra Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Solve the following quadratic equations by completing the square method
  9x² - 12x + 4 = 0

• 2)

  If the difference between a number and its reciprocal is \(\frac {24}{5}\), find the number.

• 3)

  Determine the nature of roots for the following quadratic equations
  x² - x - 20 = 0

• 4)

  If α, β are the roots of 7x² + ax + 2 = 0 and if β - α = \(\frac {-13}{7}\). Find the values of a.

• 5)

  If one root of the equation 3x² + kx + 81 = 0 (having real roots) is the square of the other then find k.

10th Standard English Medium Maths Subject Algebra Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Solve 2x − 3y = 6, x + y = 1

• 2)

  Find the LCM of the following
  8x⁴y², 48x²y⁴

• 3)

  Find the LCM of the given expressions.
  4x²y, 8x³y²

• 4)

  Find the LCM and GCD for the following and verify that f(x) x g(x) = LCM x GCD
  21x²y, 35 xy²

• 5)

  Reduce the rational expressions to its lowest form
  \(\frac { x-3 }{ { x }^{ 2 }-9 } \)

10th Standard English Medium Maths Subject Algebra Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Which of the following should be added to make x⁴ + 64 a perfect square

• 2)

  The solution of (2x - 1)² = 9 is equal to

• 3)

  The values of a and b if 4x⁴ - 24x³ + 76x² + ax + b is a perfect square are

• 4)

  If the roots of the equation q²x² + p²x + r² = 0 are the squares of the roots of the equation qx² + px + r = 0, then q, p, r are in __________.

• 5)

  Graph of a linear equation is a ____________

10th Standard English Medium Maths Subject Algebra Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  A system of three linear equations in three variables is inconsistent if their planes

• 2)

  The solution of the system x + y − 3z = −6, −7y + 7z = 7, 3z = 9 is

• 3)

  If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is

• 4)

  \(\frac {3y - 3}{y} \div \frac {7y - 7}{3y^{2}}\) is

• 5)

  y² + \(\frac {1}{y^{2}}\) is not equal to

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The sum of first n terms of a certain series is given as 2n² - 3n.Show that the series is an A.P

• 2)

  In a G.P. the product of three consecutive terms is 27 and the sum of the product of two terms taken at a time is \(\frac { 57 }{ 2 } \). Find the three terms.

• 3)

  If a, b, c are three consecutive terms of an A.P. and x, y, z are three consecutive terms of G.P then prove that x^b-c x y^c-a x z^a-b = 1

• 4)

  A person saved money every year, half as much as he could in the previous year. If he had totally saved Rs.7875 in 6 years then how much did he save in the first year?

• 5)

  If 1³ + 2³ + 3³+...k³ = 44100 then find 1 + 2 + 3 +...+ k

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Find the greatest number that will divide 445 and 572 leaving remainders 4 and 5 respectively.

• 2)

  Use Euclid’s Division Algorithm to find the Highest Common Factor (HCF) of 
  340 and 412

• 3)

  ' a '  and '  b ' are two positive integers such that a^b x b^a = 800. Find ' a ' and ' b'

• 4)

  If 13824 = 2^a x 3^b then find a and b.

• 5)

  Find the LCM and HCF of 408 and 170 by applying the fundamental theorem of arithmetic.

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Find the next three terms of the sequences.
   \(\frac { 1 }{ 2 } ,\frac { 1 }{ 6 } ,\frac { 1 }{ 10 },\frac { 1 }{ 14 } \), ..... ,

• 2)

  The general term of a sequence is defined as 
  a_n = \(\begin{cases} n\left( n+3 \right) ;n\in N\quad is\quad odd \\ { n }^{ 2 }+1;n\in N\quad is\quad even \end{cases}\)
  Find the eleventh and eighteenth terms.

• 3)

  Find a₈ and a₁₅ whose n^th term is
  a_n = \(\begin{cases} \frac { { n }^{ 2 }-1 }{ n+3 } ;n\quad is\quad even,\quad n\epsilon N \\ \begin{matrix} \\ \frac { { n }^{ 2 } }{ 2n+1 } ,n\quad is\quad odd,\quad n\epsilon N \end{matrix} \end{cases}\)

• 4)

  First term a and common difference d are given below. Find the corresponding A.P
  a = 5, d = 6

• 5)

  How many consecutive odd integers beginning with 5 will sum to 480?

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  We have 34 cakes. Each box can hold 5 cakes only. How many boxes we need to pack and how many cakes are unpacked?

• 2)

  Find the quotient and remainder when a is divided by b in the following a = −12, b = 5

• 3)

  Show that the square of an odd integer is of the form 4q + 1, for some integer q.

• 4)

  Find all positive integers, when divided by 3 leaves remainder 2.

• 5)

  A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over.

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  In an A.P., the first term is 1 and the common difference is 4. How many terms of the A.P. must be taken for their sum to be equal to 120?

• 2)

  If A = 2⁶⁵ and B = 2⁶⁴ + 2⁶³ + 2⁶² +...+ 2⁰ Which of the following is true?

• 3)

  The next term of the sequence \(\frac { 3 }{ 16 } ,\frac { 1 }{ 8 } ,\frac { 1 }{ 12 } ,\frac { 1 }{ 18 } \), ..... is

• 4)

  If the sequence t₁, t₂, t₃... are in A.P. then the sequence t₆, t₁₂, t₁₈,.... is 

• 5)

  The value of (1³ + 2³ + 3³ +...+15³) - (1 + 2 + 3 +...+ 15)is 

10th Standard English Medium Maths Subject Numbers and Sequences Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r , where r must satisfy

• 2)

  Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

• 3)

  If the HCF of 65 and 117 is expressible in the form of 65m - 117 , then the value of m is

• 4)

  The sum of the exponents of the prime factors in the prime factorization of 1729 is

• 5)

  The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

10th Standard English Medium Maths Subject Relations and Functions Book Back 5 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Given A = {1,2,3}, B = {2,3,5}, C = {3,4} and D = {1,3,5}, check if (A ∩ C) x (B ∩ D) = (A x B) ∩ (C x D) is true?

• 2)

  Let A = {x \(\in \) W| x < 2}, B = {x \(\in \) N| 1 < x ≤ 4} and C = (3,5). Verify that
  A x (B U C) = (A x B) U (A x C)

• 3)

  Given the function f:x ⟶ x²- 5x + 6, evaluate
  i) f( -1)
  ii) f (2a)
  iii) f (2)
  iv) f (x - 1)

• 4)

  If the function f: R⟶ R defined by 
  \(f(x)=\left\{\begin{array}{l} 2 x+7, x<-2 \\ x^{2}-2,-2 \leq x<3 \\ 3 x-2, x \geq 3 \end{array}\right.\)
  (i) f( 4)
  (ii) f( -2)
  (iii) f(4) + 2f(1)
  (iv) \(\frac { f(1)-3f(4) }{ f(-3) } \)

• 5)

  Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}, Verify whether A x C is a subset of B x D?

10th Standard English Medium Maths Subject Relations and Functions Book Back 5 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  The data in the adjacent table depicts the length of a person forehand and her corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length(x) as y = ax + b,  where a, b are constants.
  (i) Check if this relation is a function.
  (ii) Find a and b.
  (iii) Find the height of a woman whose forehand length is 40 cm.
  (iv) Find the length of forehand of a woman if her height is 53.3 inches.

  Length ‘x’ of forehand (in cm)	Height 'y' (in inches)
  35	56
  45	65
  50	69.5
  55	74

• 2)

  Let f: A ⟶ B be a function defined by f(x) = \(\frac{x}{2}\)-1, where A = {2, 4 , 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}, Represent f by
  (i) set of ordered pairs
  (ii) a table
  (iii) an arrow diagram
  (iv) a graph

• 3)

  The function ‘t’ which maps temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F =  \(\frac{9}{5}\)C + 32. Find,
  (i) t(0)
  (ii) t(28)
  (iii) t(-10)
  (iv) the value of C when t(C) = 212
  (v) the temperature when the Celsius value is equal to the Fahrenheit value.

• 4)

  If f(x) = 2x + 3, g(x) = 1 - 2x and h(x) = 3x. Prove that f o(g o h) = (f o g) o h.

• 5)

  Find x if gff(x) = fgg(x), given f(x) = 3x + 1 and g(x) = x + 3.

10th Standard English Medium Maths Subject Relations and Functions Book Back 2 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  Using horizontal line test (Fig.1.35(a), 1.35(b), 1.35(c)), determine which of the following functions are one – one.
  

• 2)

  Let A = {1,2,3}, B = {4, 5, 6,7}, and f = {(1, 4),(2, 5),(3, 6)}  be a function from A to B. Show that f is one – one but not onto function.

• 3)

  Let f be a function from R to R defined by f(x) = 3x - 5. Find the values of a and b given that (a,4) and (1,b) belong to f.

• 4)

  Determine whether the graph given below represent functions. Give a reason for your answer concerning the graph.
  

• 5)

  Let A = {1, 2, 3, 4} and B = N. Let f: A ⟶ B be defined by f(x) = x³ then
  (i) find the range of f
  (ii) identify the type of function

10th Standard English Medium Maths Subject Relations and Functions Book Back 2 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If A = {1,3,5} and B = {2,3} then
  (i) find A x B and B x A
  (ii) Is A x B = B x A? If not why?
  (iii) Show that n(A x B) = n(B x A) = n(A) x n(B)

• 2)

  If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

• 3)

  Find A x B, A x A and B x A
  A = {2, -2, 3} and B = {1,-4}

• 4)

  Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
  R₁ = {(3,7), (4,7), (7,10), (8,1)}

• 5)

  The arrow diagram shows a relationship between the sets P and Q. Write the relation in
  (i) Set builder form
  (ii) Roster form
  (iii) What is the domain and range of R.
  

10th Standard English Medium Maths Subject Relations and Functions Book Back 1 Mark Questions with Solution Part - II - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If f: A ⟶ B is a bijective function and if n(B) = 7, then n(A) is equal to

• 2)

  Let f and g be two functions given by
  f = {(0,1), (2,0), (3,-4), (4,2), (5,7)}
  g = {(0,2), (1,0), (2,4), (-4,2), (7,0)} then the  range of f o g is

• 3)

  Let f(x) = \(\sqrt { 1+x^{ 2 } } \) then

• 4)

  If g = {(1,1), (2,3), (3,5), (4,7)} is a function given by g(x) = αx + β then the values of α and β are

• 5)

  f(x) = (x + 1)³ - (x - 1)³ represents a function which is

10th Standard English Medium Maths Subject Relations and Functions Book Back 1 Mark Questions with Solution Part - I - by Question Bank Software - Jun 12, 2021 - View & Read

• 1)

  If n(A x B) = 6 and A = {1,3} then n(B) is

• 2)

  A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A U C) x B] is

• 3)

  If A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true..

• 4)

  If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

• 5)

  The range of the relation R = {(x, x²) |x is a prime number less than 13} is

Stateboard 10th Standard Maths Subject Public Question Paper - March 2019 - by QB Admin - May 19, 2021 - View & Read

10th Standard Maths Reduced Syllabus 2020-21 - by QB Admin - May 18, 2021 - View & Read

10th Standard Maths Text Book - 2021 - by QB Admin - Apr 26, 2021 - View & Read