Probability lies between _______.

The probability of an event cannot be _______.

A random experiment contains

The probability of all possible outcomes of a random experiment is always equal to _______.

If A is any event in S and its complement is A' then, P(A′) is equal to _______.

The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is _______.

The perimeter of an equilateral triangle is 30 cm. The area is _______.

The total surface area of a cuboid is ______________

The lateral surface area of a cube of side 12 cm is _______.

If the lateral surface area of a cube is 600 cm², then the total surface area is _______.

If tan \(\theta\) cot 37⁰ , then the value of \(\theta\) is ________.

The value of \(\frac { tan15° }{ cot75° } \) is

if sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and \(\alpha\) is a cute, then (3 cos\(\alpha\) - 4cos³ \(\alpha\)) is equal to

The value of 3 sin 70⁰sec 20⁰ + 2 sin 49⁰sec 51⁰ is ________.

The value of \(\frac { 1-{ tan }^{ 2 }{ 45 }^{ 0 } }{ 1+{ tan }^{ 2 }{ 45 }^{ 0 } } \) is ________.

The mean of 5, 9, x, 17, and 21 is 13, then find the value of x _______.

The mean of the first 10 prime numbers is ___________

The mean of a set of numbers is \(\bar X\). If each number is multiplied by z, the mean is _______.

Let be the mid point and b be the upper limit of a class in a continuous frequency distribution. The lower limit of the class is

The mean of set of seven number is 81. If one of the nimbers is discarded,the mean of remaining number is 78. The value of discarded number is

The point whose abscissa is 5 and lies on the x-axis is__________

A point on the y-axis is ________________

The distance between the points (a, 0) and (0, b) is____________

The point (0, -3) lies on _______________

The diagonal of a square formed by the points (1, 0), (0, 1), (-1, 0) and (0, - 1) is_______________

The exterior angle of a triangle is equal to the sum of two ________.

ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles with vertex O are ________.

The correct statement out of the following is ________.

If bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is ________.

Which of the following statement is correct?

Which of the following is trinomial?

The area of a rectangle with length \(2l^{ 2 }m\) and breadth \(3l^{ 2 }m\) is_______________________

The roots of the polynominal equation \({ x }^{ 2 }+2x=0\) are_______________

The degree of the polynomial \( \sqrt { 2 } { x }^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5x^{ 3 }\) is _______________ 

Divide x³-4x²+6x by "x" the result is _____________________

If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

Which of the following are irrational numbers?
\(\sqrt { 2+\sqrt { 3 } } \)
\(\sqrt [ 3 ]{ 5+\sqrt { 7 } } \)
\(\sqrt { 8-\sqrt [ 3 ]{ 8 } } \)
\(\sqrt { 4+\sqrt { 25 } } \)

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

The value of \(\bar { 0.03 } \) +\(\bar { 0.03 } \)  is ___________.

Number of subsets in set A = {1,2,3} is ________

Sets having the same number of elements are called ___________

The set of (A U B) - (A ก B) is ____________

The number of elements of the set {x : x ∈ Z, x² = I} is ________

The shade region with adjoint diagram represents ___________

Probability lies between _______.

The probability based on the concept of relative frequency theory is called _______.

The probability of an event cannot be _______.

A random experiment contains

The probability of all possible outcomes of a random experiment is always equal to _______.

The area of a triangle whose sides are a, b and c is ________

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is _______.

The perimeter of an equilateral triangle is 30 cm. The area is _______.

The total surface area of a cuboid is ______________

The lateral surface area of a cube of side 12 cm is _______.

if sin 30⁰ = x and cos 60⁰ = y, then x²  + y² is________.

The value of tan72° tan18° is ________.

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

If 2 sin 2\(\theta\) = \(\sqrt { 3 } \) , them the value of \(\theta\) is ________.

The value of 2tan30° tan60° is

The median of the first 10 whole numbers is ______________

Find the mean of the prime factors of 165.

Data available in an unorganized form is called__________data

Which one of the following is not a measure of central tendency?

A particular observation which occurs maximum number of times in a given data is called is

On which quadrant does the point (- 4, 3) lie?

A point which lies in the III quadrant is__________________

The distance between the points (4, -1) and the origin is___________

The centre of a circle is (0, 0). One end point of a diameter is (5, -1), then ______________

The point which is on y-axis with ordinate - 5 is _____________

The angle sum of a convex polygon with number of sides 7 is ________

One angle of a parallelogram is a right angle. The name of the quadrilateral is ______

In a parallelogram \(\angle{A}:\angle{B}=1:2\) Then ㄥA ............

Diagonal of which of the following quadrilaterals do not bisect it into two congruent triangles?

Orthocentre of a triangle is the point of concurrency of _______

If x³ + 6x² + kx + 6 is exactly divisible by (x + 2), then k= ?

The type of the polynomial 4–3x³ is  ________.

If x⁵¹ + 51 is divided by x + 1, then the remainder is _______.

The sum of the polynomials p(x) = x³ – x² – 2, q(x) = x²–3x+ 1 _______.

The value of the polynomial f(x) = 6x - 3x²+9 when x = -1 is _____________________

If n is a natural number then \(\sqrt { n } \) is ________.

Which one of the following, regarding sum of two irrational numbers, is true?

Which one of the following is an irrational number.

The smallest rational number by which \(\frac { 1 }{ 3 } \)  should be multiplied so that its decimal expansion terminates after one place of decimal is   ________.

The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is ____________

Which of the following is correct?

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If A = {x, y, z} then the number of non - empty subsets of A is ________.

If A∪B = A∩B, then ________.

The shaded region in the adjacent diagram represents ______________

Sets having the same number of elements are called ___________

In a town 30% like only coffee, 20% like only tea,10% like only like,15% like only any two of them, 5% only like all the three. What is the percentage of people who like none them.

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

The degree of the polynomial \( \sqrt { 2 } { x }^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5x^{ 3 }\) is _______________ 

In a parallelogram \(\angle{A}:\angle{B}=1:2\) Then ㄥA ............

The set does not have a proper subset is __________

\(\left[ n\left( A\cup B\cup C \right) ^{ ' } \right] \)=_______

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

if a polynominal p(x) is divided by (ax+b), then the reminder is _______________________

The angle sum of a convex polygon with number of sides 7 is ________

Sets having the same number of elements are called ___________

Irrational number has a________________ .

The coefficient of \({ x }^{ 2 }\ and\ x\ in\ 2{ x }^{ 3 }-5{ x }^{ 2 }+6x-3\) are respectively ____________

The angle sum of a convex polygon with number of sides 7 is ________

The angle subtend by equal chords of a circle at the centre is________

The set (A - B) U(B - A) is ___________

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

\(\sqrt [ 5 ]{ 21 } \times 6\sqrt { 10 } \)

if a polynominal p(x) is divided by (ax+b), then the reminder is _______________________

(a-b-c)² is equal to________

Number of subsets in set A = {1,2,3} is ________

Which one of the following has terminating decimal expansion?

\(\sqrt [ 5 ]{ 21 } \times 6\sqrt { 10 } \)

The area of a rectangle with length \(2l^{ 2 }m\) and breadth \(3l^{ 2 }m\) is_______________________

The degree of the polynomial \( \sqrt { 2 } { x }^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5x^{ 3 }\) is _______________ 

The set does not have a proper subset is __________

Which of the following are not rational numbers?

if a polynominal p(x) is divided by (ax+b), then the reminder is _______________________

Quadratic polynomial may have maximum of______linear factors

Which of the following is a formula to find the sum of interior angles of a quadrilateral of n-sides?

The shaded region in the adjacent diagram represents ______________

If n is a natural number then \(\sqrt { n } \) is ________.

x³ – x² is a …………..

If bisectors of ∠A and ∠B of a quadrilateral ABCD meet at O, then ∠AOB is ________.

On plotting the points O(0, 0), A(3, – 4), B(3, 4) and C(0, 4) and joining OA, AB, BC and CO, which of the following figure is obtained?

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

An irrational number between 2 and 2.5 is ________.

The zero of the polynomial 2x+5 is _______.

The GCD of x⁴-y⁴ and x²-y² is _______.

The exterior angle of a triangle is equal to the sum of two ________.

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ⋂ L is ________.

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

x³ – x² is a …………..

The exterior angle of a triangle is equal to the sum of two ________.

If B ⊆ A then n(A∩B) is –––––––––.

Which one of the following has a terminating decimal expansion?

The zero of the polynomial 2x+5 is _______.

The interior angle made by the side in a parallelogram is 90° then the parallelogram is a ________.

The point whose ordinate is 4 and which lies on the y-axis is ______.

If B ⊆ A then n(A∩B) is –––––––––.

Which of the following statement is false?

Degree of the polynomial (y³–2)(y³ + 1) is _______.

If the diagonal of a rhombus are equal, then the rhombus is a ________.

If \(P(\frac{a}{3},\frac{b}{2})\)is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is ______.

If n(A \(\cup \) B \(\cup \) C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A\(\cap \)B) = 12, n(B\(\cap \)C) = 18 and n(A\(\cap \)C) = 15 , then n(A\(\cap \)B\(\cap \)C) is ___________

The smallest rational number by which \(\frac { 1 }{ 3 } \)  should be multiplied so that its decimal expansion terminates after one place of decimal is   ________.

The sum of the polynomials p(x) = x³ – x² – 2, q(x) = x²–3x+ 1 _______.

The exterior angle of a triangle is equal to the sum of two ________.

The points (–5, 2) and (2, –5) lie in the ________.

The shaded region in the venn diagram is ___________

Irrational number has a________________ .

Which is the best example of a number written in scientific notation?

Degree of the polynomial (y³–2)(y³ + 1) is _______.

The polynomial whose factors are (x+2)(x+3)is_____

\(0.\overline { 34 } +0.3\bar { 4 } \) = ________.

If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

The remainder when p(x) = x³ – ax² + 6x – a is divided by (x – a) is ______________

Quadratic polynomial may have maximum of______linear factors

Which of the following statement is correct?

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ⋂ L is ________.

Find the odd one out of the following.

\(\sqrt [ 4 ]{ 405 } =h\sqrt [ 4 ]{ 5 } \), then h = ____________

If x³ + 6x² + kx + 6 is exactly divisible by (x + 2), then k= ?

The set (A - B) U(B - A) is ___________

For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is ________.

Find the odd one out of the following.

If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

The type of the polynomial 4–3x³ is  ________.

In a class of 50 boys, 35 boys play Carrom and 20 boys play Chess then the number of boys play both games is________.

The set of (A U B) - (A ก B) is ____________

The smallest rational number by which \(\frac { 1 }{ 3 } \)  should be multiplied so that its decimal expansion terminates after one place of decimal is   ________.

Which of the following are irrational numbers?
\(\sqrt { 2+\sqrt { 3 } } \)
\(\sqrt [ 3 ]{ 5+\sqrt { 7 } } \)
\(\sqrt { 8-\sqrt [ 3 ]{ 8 } } \)
\(\sqrt { 4+\sqrt { 25 } } \)

The Auto fare is found as minimum Rs. 25 for 3 kilometer and thereafter Rs. 12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

Which of the following is correct?

The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

If A and B are two non-empty sets, then (A-B)U(A⋂B) is _____________

Which one of the following is an irrational number.

If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

If B ⊆ A then n(A∩B) is –––––––––.

The shaded region in the venn diagram is ___________

An irrational number between 2 and 2.5 is ________.

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

The zero of the polynomial 2x+5 is _______.

Which of the following is correct?

For any three A, B and C, \(A-\left( B\cup C \right) \) ________

Which one of the following has a terminating decimal expansion?

Which of the following are not rational numbers?

Which is the best example of a number written in scientific notation?

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

Number of subsets in set A = {1,2,3} is ________

The smallest rational number by which \(\frac { 1 }{ 3 } \)  should be multiplied so that its decimal expansion terminates after one place of decimal is   ________.

The decimal form of -\(\frac { 3 }{ 4 } \) is_______________

\(\cfrac { \sqrt [ 3 ]{ 27 } }{ \sqrt [ 5 ]{ 3 } } \) is equal to_______

If A = {x, y, z} then the number of non - empty subsets of A is ________.

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

Which of the following are irrational numbers?
\(\sqrt { 2+\sqrt { 3 } } \)
\(\sqrt [ 3 ]{ 5+\sqrt { 7 } } \)
\(\sqrt { 8-\sqrt [ 3 ]{ 8 } } \)
\(\sqrt { 4+\sqrt { 25 } } \)

If p(a)= 0 then (x-a) is a _____ of p(x).

(a-b) (a²+ab+b²)=_________

If A is a proper subset of B, then A ∩ B = __________

The shaded region in the Venn diagram is ________.

Which of the following are not rational numbers?

4\(\sqrt{7}\) \(\times\) 2\(\sqrt{3}\) =  ________.

The roots of the polynominal equation \({ x }^{ 2 }+2x=0\) are_______________

If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is ________.

In a town 30% like only coffee, 20% like only tea,10% like only like,15% like only any two of them, 5% only like all the three. What is the percentage of people who like none them.

\(\sqrt{27}\)+\(\sqrt{12}\) = ________.

Rationalising the denominator \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)  ___________

If p(a)= 0 then (x-a) is a _____ of p(x).

If A∪B = A∩B, then ________.

In a town 30% like only coffee, 20% like only tea,10% like only like,15% like only any two of them, 5% only like all the three. What is the percentage of people who like none them.

The number \(0.\bar { 3 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

The rational number lying between \(\frac { 1 }{ 5 } \) and \(\frac { 1 }{ 2 } \) is___________.

Degree of the polynomial (y³–2)(y³ + 1) is _______.

If B ⊆ A then n(A∩B) is –––––––––.

Which of the following is true?

Which of the following is not true?

Which of the following is not an irrational number?

The remainder when p(x) = x³ – ax² + 6x – a is divided by (x – a) is ______________

If B - A is B, then A∩B is ________.

If U = {x : x\(\in \)W and x < 20}, A = {2,4,6,8}, B = {6,8,12,14} then\(\left[ n\left( A\cup B^{ ' } \right) \right] \)

When written with a rational denominator, the expression \(\frac { 2\sqrt { 3 } }{ 3\sqrt { 2 } } \) can be simplified as ________.

\(\sqrt [ 5 ]{ 21 } \times 6\sqrt { 10 } \)

If p(a)= 0 then (x-a) is a _____ of p(x).

Let A = {∅} and B = P(A), then A∩B is ________.

The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

The number \(0.\bar { 3 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

The Auto fare is found as minimum Rs. 25 for 3 kilometer and thereafter Rs. 12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is ________.

If A,B,C are non-overlapping sets, then n \(\left( A\cap B\cap C \right) \) is ___________

The value of \(\bar { 0.03 } \) +\(\bar { 0.03 } \)  is ___________.

\(\sqrt{27}\)+\(\sqrt{12}\) = ________.

Let the polynomials be
(A) –13q⁵ + 4q² + 12q
(B) (x² +4 )(x² + 9)
(C) 4q⁸ – q⁶ + 2
(D) -\(\frac {5}{7}\)y¹²+y³+y⁵
Then ascending order of their degree is _______.

If A∪B = A∩B, then ________.

The number of elements of the set {x : x ∈ Z, x² = I} is ________

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

Which one of the following is not a rational number?

The degree of the polynomial \( \sqrt { 2 } { x }^{ 2 }-\frac { 7 }{ 2 } { x }^{ 4 }+x-5x^{ 3 }\) is _______________ 

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

The set of (A U B) - (A ก B) is ____________

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

The remainder when p(x) = x³ – ax² + 6x – a is divided by (x – a) is ______________

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

The set does not have a proper subset is __________

An irrational number between 2 and 2.5 is ________.

The sum of the polynomials p(x) = x³ – x² – 2, q(x) = x²–3x+ 1 _______.

The area of a rectangle with length \(2l^{ 2 }m\) and breadth \(3l^{ 2 }m\) is_______________________

If A, B and C are overlapping sets, then draw Venn diagram for the following sets:
(i) (A-B)\(\cap \)C
(ii) (A\(\cup \)C)-B
(iii) A-(A\(\cap \)C)
(iv) (B\(\cup \)C)-A
(v) A\(\cap \)B\(\cap \)C

Draw Venn diagram for \(A\cap B\cap C\)

Verify \(n\left( A\cup B\cup C \right) \) = n(A) + n(B) +n(C) - \(n\left( A\cap B \right) -n\left( B\cap C \right) -n\left( A\cap C \right) -n\left( A\cap C \right) +\left( A\cap B\cap C \right) \) for the following A = {1,3,5,6,8} C = {1,2,3,6}

In an examination 50% of the students passed in Mathematics and 70% of students passed in Science while 10% students failed in both subjects. 300 students passed in atleast one subject. Find the total number of students who appeared in the examination, if they took examination in only two subjects.

Represent the following irrational numbers on the number line \(\sqrt { 6.5 } \)

Draw: Venn diagram for each of the following:
(i) \(A\cup (B\cap C)\)
(ii) \(A\cap (B\cup C)\)
(iii) \((A\cup B)\cap C\)
(iv) \((A\cap B)\cup C\)

If A = {-2,0,1,3,5}, B = {-1,0,2,5,6} and C = {-1,2,5,6,7} then show that A-(BUC) = (A-B)∩(A-C).

If A = {2,5,6,7} and B = {3,5,7,8}, then verify the commutative property of union sets

If A = {2,5,6,7} and B = {3,5,7,8}, then verify the commulative property of intersection of sets

Express the following decimal expression into rational numbers. 0.86

Draw Venn diagram and shade the region representing the following sets
(A – B)′

Find A∪B, A∩B, A–B and B–A for the following sets.
A = Set of all letters in the word “mathematics” and
B = Set of all letters in the word “geometry”

In a class of 50 students, each of the students passed either in mathematics or in science or in both. 10 students passed in both and 28 passed in science. Find how many students passed in mathematics only

Represent U= {1,2,3,4,5,6,7,8,9,10} A = {1,2,4,6,8,10} and B = {3,6,1,10} in venn-diagram, then find
(i) (A UB)'
(ii) (A ∩ B)'

Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
\(-{11\over 75}\)

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If U = {x : x\(\in \)N and x<10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A∪B)′] is  ________.

Which of the following is true?

\(n(A\cup B\cup C)\)=________

Which one of the following, regarding sum of two irrational numbers, is true?

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is ______________

In a town 30% like only coffee, 20% like only tea,10% like only like,15% like only any two of them, 5% only like all the three. What is the percentage of people who like none them.

\(\left( A\cup B\cup C \right) \cup \left( A\cup BC \right) ^{ ' }\)=_______

For any three sets, P,Q,R\(\left( P\cap Q \right) ^{ ' }\)

If A = {x, y, z} then the number of non - empty subsets of A is ________.

In a town 30% like only coffee, 20% like only tea,10% like only like,15% like only any two of them, 5% only like all the three. What is the percentage of people who like none them.

If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

\(\frac { \sqrt [ 3 ]{ 18 } }{ \sqrt [ 3 ]{ 2 } } \) is same as _____________

The GCD of a^k, a^k+1, a^k+5 where, k∈N _________

Which of the following is correct?

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

Sets having the same number of elements are called ___________

The number of elements of the set {x : x ∈ Z, x² = I} is ________

For any three sets A, B and C, (A−B)∩(B −C) is equal to ________.

If A∪B = A∩B, then ________.

From the adjacent diagram n[P(AΔB)] is ________.

The set does not have a proper subset is __________

\(\left[ n\left( A\cup B\cup C \right) ^{ ' } \right] \)=_______

\(n(A\cup B\cup C)\)=________

The shaded region in the adjacent diagram represents ______________

If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is ______________

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

The set does not have a proper subset is __________

If A,B,C are non-overlapping sets, then n \(\left( A\cap B\cap C \right) \) is ___________

Which of the following is correct?

The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is ________.

If U = {x : x\(\in \)W and x < 20}, A = {2,4,6,8}, B = {6,8,12,14} then\(\left[ n\left( A\cup B^{ ' } \right) \right] \)

For any three sets, P,Q,R\(\left( P\cap Q \right) ^{ ' }\)

The set does not have a proper subset is __________

The number of elements of the set {x : x ∈ Z, x² = I} is ________

If A is a proper subset of B, then A ∩ B = __________

For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is ________.

If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is ________.

If A∪B = A∩B, then ________.

The number of elements of the set {x : x ∈ Z, x² = I} is ________

If n(A \(\cup \) B \(\cup \) C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A\(\cap \)B) = 12, n(B\(\cap \)C) = 18 and n(A\(\cap \)C) = 15 , then n(A\(\cap \)B\(\cap \)C) is ___________

Which of the following is true?

\(n(A\cup B\cup C)\)=________

If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is ______________

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

Sets having the same number of elements are called ___________

The set of (A U B) - (A ก B) is ____________

If n(A \(\cup \) B \(\cup \) C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A\(\cap \)B) = 12, n(B\(\cap \)C) = 18 and n(A\(\cap \)C) = 15 , then n(A\(\cap \)B\(\cap \)C) is ___________

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

\(\left[ n\left( A\cup B\cup C \right) ^{ ' } \right] \)=_______

\(\frac { \sqrt [ 3 ]{ 18 } }{ \sqrt [ 3 ]{ 2 } } \) is same as _____________

\(\sqrt [ 3 ]{ 192 } +\sqrt [ 3 ]{ 24 } \)

The value of the polynomial f(x) = 6x - 3x²+9 when x = -1 is _____________________

The shaded region in the adjacent diagram represents ______________

Sets having the same number of elements are called ___________

Which one of the following is an irrational number.

Rationalising the denominator \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)  ___________

The Auto fare is found as minimum Rs. 25 for 3 kilometer and thereafter Rs. 12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

If n(A \(\cup \) B \(\cup \) C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A\(\cap \)B) = 12, n(B\(\cap \)C) = 18 and n(A\(\cap \)C) = 15 , then n(A\(\cap \)B\(\cap \)C) is ___________

In a town 30% like only coffee, 20% like only tea,10% like only like,15% like only any two of them, 5% only like all the three. What is the percentage of people who like none them.

The length and breadth of a rectangular plot are 5 \(\times\) 10⁵ and 4 \(\times\) 10⁴ metres respectively. Its area is ______.

In simple form,\(\sqrt [ 3 ]{ 54 } \) is ?

x³ – x² is a …………..

If B ⊆ A then n(A∩B) is –––––––––.

If A is a proper subset of B, then A ∩ B = __________

What is 5.92 \(\times\)10^-3 written in decimal form?

The length of a square is 1.2\(\times\)10³ m. Its area is_______

The zero of the polynomial 2x+5 is _______.

From the adjacent diagram n[P(AΔB)] is ________.

If U = {x : x\(\in \)W and x < 20}, A = {2,4,6,8}, B = {6,8,12,14} then\(\left[ n\left( A\cup B^{ ' } \right) \right] \)

Which one of the following is an irrational number.

Which of the following is not an irrational number?

The type of the polynomial 4–3x³ is  ________.

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

The set (A - B) U(B - A) is ___________

The length and breadth of a rectangular plot are 5 \(\times\) 10⁵ and 4 \(\times\) 10⁴ metres respectively. Its area is ______.

Rationalising the denominator \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)  ___________

The value of the polynomial f(x) = 6x - 3x²+9 when x = -1 is _____________________

If n(A \(\cup \) B \(\cup \) C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A\(\cap \)B) = 12, n(B\(\cap \)C) = 18 and n(A\(\cap \)C) = 15 , then n(A\(\cap \)B\(\cap \)C) is ___________

\(\left[ n\left( A\cup B\cup C \right) ^{ ' } \right] \)=_______

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

\(\sqrt [ 4 ]{ 405 } =h\sqrt [ 4 ]{ 5 } \), then h = ____________

If x⁵¹ + 51 is divided by x + 1, then the remainder is _______.

Let A = {∅} and B = P(A), then A∩B is ________.

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

The set (A - B) U(B - A) is ___________

The shade region with adjoint diagram represents ___________

For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is ________.

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

The number of elements of the set {x : x ∈ Z, x² = I} is ________

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

The type of the polynomial 4–3x³ is  ________.

If A, B and C are overlapping sets, then draw Venn diagram for the following sets:
(i) (A-B)\(\cap \)C
(ii) (A\(\cup \)C)-B
(iii) A-(A\(\cap \)C)
(iv) (B\(\cup \)C)-A
(v) A\(\cap \)B\(\cap \)C

Verify \(n\left( A\cup B\cup C \right) =n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\)for the following sets.
(i) A = {a, c, e, f , h} , B = {c, d, e, f } and C = {a, b, c, f }
(ii) A = {1, 3, 5} , B = {2, 3, 5, 6} and C = {1, 5, 6, 7}

A soap company interviewed 800 people in a city. It was found out that \(\frac{3}{8}\) use brand A soap, \(\frac{1}{5}\)use brand B soap, 70 use brand A and B soap, 55 use brand B and C soap, 60 use brand A and C soap and \(\frac{1}{40}\) use all the three brands Find,
(i) Number of people who use exactly two branded soaps,
(ii) Number of people who use atleast one branded soap,
(iii) Number of people who do not use any one of these brands.

Verify \(n\left( A\cup B\cup C \right) \) = n(A) + n(B) +n(C) - \(n\left( A\cap B \right) -n\left( B\cap C \right) -n\left( A\cap C \right) -n\left( A\cap C \right) +\left( A\cap B\cap C \right) \) for the following A = {1,3,5,6,8} C = {1,2,3,6}

In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who
(i) like both tea and coffee.
(ii) do not like Tea.
(iii) do not like coffee

Insert the appropriate symbol ∈ (belongs to) or ∉ (does not belong to) in the blanks.

In a class there are 40 students. 26 have opted for Mathematics and 24 have opted for Science. How many student have opted for Mathematics and Science.

Verify \(A-(B\cap C)=(A-B)\cup (A-C)\)using Venn diagrams.

In a residential area with 600 families \(\frac{3}{5}\) owned scooter, \(\frac{1}{3}\) owned car, \(\frac{1}{4}\) owned bicycle, 120 families owned scooter and car, 86 owned car and bicylce while 90 families owned scooter and bicylce. If \(\frac{1}{15}\) of families owned all the three types of vehicles, then find
(i) the number of families owned atleast two types of vehicle.
(ii) the number of families owned no vehicle.

Express the following decimal expression into rational numbers -\(21.21\overline {37}\)

Write the set of letters of the following words in Roster form
PRINCIPAL

If A = {–3, –2, 1, 4} and B = {0, 1, 2, 4}, find
(i) A – B
(ii) B – A.

Draw Venn diagram and shade the region representing the following sets
(i) A′

List the set of letters of the following words in Roster form.
PARALLELOGRAM

Find A∪B, A∩B, A–B and B–A for the following sets.
A = {a, b, c, e, u} and B = {a, e, i, o, u}

Which one of the following has terminating decimal expansion?

Irrational number has a________________ .

\(\sqrt [ 3 ]{ 192 } +\sqrt [ 3 ]{ 24 } \)

When \(\left( 2\sqrt { 3 } -\sqrt { 5 } \right) ^{ 2 }\) is simplified, we get __________

The length of a square is 1.2\(\times\)10³ m. Its area is_______

In a parallelogram \(\angle{A}:\angle{B}=1:2\) Then ㄥA ............

Which of the following is a formula to find the sum of interior angles of a quadrilateral of n-sides?

The angle subtend by equal chords of a circle at the centre is________

The distance between the longest chord of a circle and the centre is________

The perpendicular line from the centre of the circle to the chord divided the chord in the ratio________

On which quadrant does the point (- 4, 3) lie?

A point on the y-axis is ________________

The centre of a circle is (0, 0). One end point of a diameter is (5, -1), then ______________

The point (0, -3) lies on _______________

The diagonal of a square formed by the points (1, 0), (0, 1), (-1, 0) and (0, - 1) is_______________

The algebraic sum of the deviations of a set of n values from their mean is ___________

The mean of a, b, c, d and e is 28. If the mean of a, c and e is 24, then mean of b and d is _______________

The mean of the first 10 prime number is _______________

The mean of the first 10 whole number is

Find the mean of the prime factors of 165 _____________

If tan \(\theta\) cot 37⁰ , then the value of \(\theta\) is ________.

If 2 sin 2\(\theta\) = \(\sqrt { 3 } \) , them the value of \(\theta\) is ________.

The value of 2tan30° tan60° is

The value of cosec(70⁰ + \(\theta\)) - sec(20⁰ - \(\theta\)) + tan(65⁰ + \(\theta\)) - cot(25⁰ - \(\theta\)) is ________.

The value of \(\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' } \) is

A number between 0 and 1 that is used to measure uncertainty is called _______.

Probability lies between _______.

The probability based on the concept of relative frequency theory is called _______.

The probability of an event cannot be _______.

A random experiment contains

The sum of \({ 5x }^{ 2 };-7x^{ 2 };8x^{ 2 };11x^{ 2 }\ and\ -9x^{ 2 }\) is ___________ 

The area of a rectangle with length \(2l^{ 2 }m\) and breadth \(3l^{ 2 }m\) is_______________________

The value of the polynomial f(x) = 6x - 3x²+9 when x = -1 is _____________________

Divide x³-4x²+6x by "x" the result is _____________________

Degree of the linear polynomial is ________

The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is _______.

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is _______.

The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is _______.

If the ratio of the sides of two cubes are 2:3, then ratio of their surface areas will be _______.

The number of bricks each measuring 50 cm × 30 cm × 20 cm that will be required to build a wall whose dimensions are 5 m × 3 m × 2 m is _______.

The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

The number of elements of the set {x : x ∈ Z, x² = I} is ________

The shaded region in the venn diagram is ___________

If A,B,C are non-overlapping sets, then n \(\left( A\cap B\cap C \right) \) is ___________

For any three sets, P,Q,R\(\left( P\cap Q \right) ^{ ' }\)

From the adjacent diagram n[P(AΔB)] is ________.

The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is ____________

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

A number between 0 and 1 that is used to measure uncertainty is called _______.

The probability of an event cannot be _______.

The probability of all possible outcomes of a random experiment is always equal to _______.

If A is any event in S and its complement is A' then, P(A′) is equal to _______.

Which of the following cannot be taken as probability of an event?

The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is _______.

The lateral surface area of a cube of side 12 cm is _______.

The total surface area of a cuboid with dimension 10 cm × 6 cm × 5 cm is _______.

The capacity of a water tank of dimensions 10 m × 5 m × 1.5 m is _______.

The number of bricks each measuring 50 cm × 30 cm × 20 cm that will be required to build a wall whose dimensions are 5 m × 3 m × 2 m is _______.

(Graphing made easier!) Draw the graph of the line given by the equation y = 4x – 3.

Draw the graph for the following
(i) y = 3x - 1
(ii) \(y=\left( \frac { 2 }{ 3 } \right) x+3\)

Use graphical method to solve the following system of equations x + y = 5; 2x – y = 4.

Use graphical method to solve the following system of equations 3x + 2y = 6; 6x + 4y = 8

Solve graphically
 x + y = 7; x − y = 3

The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure.

In the class, weight of students is measured for the class records. Caculate mean weight of the students using direct method.

Calculate the mean of the following distribution using Assumed Mean Method

Find the Arithmetic Mean of the following data using Step Deviation Method

The following are the scored by the students in the Summative Assessment exam

Find the length of a chord which is at a distance of 2 \(\sqrt{11}\) cm from the centre of a circle of radius 12cm.

In the concentric circles, chord AB of the outer circle cuts the inner circle at C and D as shown in the diagram. Prove that, AB−CD = 2AC

Find the value of x° in the following figures:

Find the value of x° in the following figures:

If PQRS is a cyclic quadrilateral in which ㄥPSR=70° and ㄥQPR = 40°, then find ㄥPRQ.

Evaluate the following by using identities:
(i) 98³
(ii) 1001³

Simplify: \(\left[ \frac { ({ x }^{ 2 }-{ y }^{ 2 })^{ 3 }+({ y }^{ 2 }-{ z }^{ 2 })^{ 3 }+({ z }^{ 2 }-{ x }^{ 2 })^{ 3 } }{ (x-y)^{ 3 }+(y-z)^{ 3 }+(z-x)^{ 3 } } \right] \) by using identity

If a = 4, b = 5 and c = 6 , then find the value of \(\left[ \frac { (ab+bc+ca-{ a }^{ 2 }-{ b }^{ 2 }-{ c }^{ 2 }) }{ (3abc-{ a }^{ 3 }-{ b }^{ 3 }-{ c }^{ 3 }) } \right] \).

Factorise 2x²-15x+27

Factorise 2x² + 15x - 27

Find the 5^th root of 32

Find the 5^th root of 243.

Find the 5^th root of 100000

Find the 5^th root of \(\frac{1024}{3125}\)

Simplify the following using addition and subtraction properties of surds:
(i) 5\(\sqrt{3}\) + 18\(\sqrt{3}\)-2\(\sqrt{3}\)
(ii) \(4\sqrt [ 3 ]{ 5 } +2\sqrt [ 3 ]{ 5 } -3\sqrt [ 3 ]{ 5 } \)
(iii) 3\(\sqrt{75}\)+5\(\sqrt{48}\)-\(\sqrt{243}\)
(iv) \(5\sqrt [ 3 ]{ 40 } +2\sqrt [ 3 ]{ 625 } -3\sqrt [ 3 ]{ 320 } \)

if sin 30⁰ = x and cos 60⁰ = y, then x²  + y² is________.

If tan \(\theta\) cot 37⁰ , then the value of \(\theta\) is ________.

The value of tan72° tan18° is ________.

The value of \(\frac { tan15° }{ cot75° } \) is

if sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and \(\alpha\) is a cute, then (3 cos\(\alpha\) - 4cos³ \(\alpha\)) is equal to

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3) ______.

The ratio in which the x-axis divides the line segment joining the points A(a₁, b₁) and B(a₂, b₂ ) is ______.

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are ______.

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.

Using the adjacent Venn diagram, find the following sets:
(i) A-B
(ii) B-C
(iii) A'\(\cup \)B')
(iii) A'\(\cap \)B'
(iv) (B\(\cup \)C)'
(vi) A-(B\(\cup \)C)
(vii) A-(B\(\cap \)C)

If A, B and C are overlapping sets, then draw Venn diagram for the following sets:
(i) (A-B)\(\cap \)C
(ii) (A\(\cup \)C)-B
(iii) A-(A\(\cap \)C)
(iv) (B\(\cup \)C)-A
(v) A\(\cap \)B\(\cap \)C

If A = {x : x = 6n, n\(\in \)W and n < 6}, B = {x : x = 2n, n \(\in \)N and 2 < n ≤ 9} and C = {x : x = 3n, n\(\in \)N and 4n ≤ n < 10}, then show that \(A-(B\cap C)=(A-B)\cup (A-C)\).

If A = {y : y =\(\frac { a+1 }{ 2 } \), a \(\in \) W and a ≤ 5}, B = {y : y =\(\frac { 2n-1 }{ 2 } \), n\(\in \)W and n < 5} and C =\(\left\{ -1,-\frac { 1 }{ 2 } ,1,\frac { 3 }{ 2 } ,2 \right\} \), then show that \(A-(B\cup C)=(A-B)\cap (A-C)\).

Verify \(n\left( A\cup B\cup C \right) =n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)\)for the following sets.
(i) A = {a, c, e, f , h} , B = {c, d, e, f } and C = {a, b, c, f }
(ii) A = {1, 3, 5} , B = {2, 3, 5, 6} and C = {1, 5, 6, 7}

Which of the following statement is true for the equation 2x + 3y = 15

Which of the following is a solution of the equation 2x − y = 6.

Which condition does not satisfy the linear equation ax + by + c = 0.

The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is  _______.  

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { { c }_{ 1 } }{ { c }_{ 2 } } \) where a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 then the given pair of linear equation has _________ solution(s)

Data available in an unorganized form is called __________ data

A particular observation which occurs maximum number of times in a given data is called its _______.

The algebraic sum of the deviations of a set of n values from their mean is _______.

The mean of 5, 9, x, 17, and 21 is 13, then find the value of x _______.

The mean of a set of numbers is \(\bar X\). If each number is multiplied by z, the mean is _______.

Show that the points A(7,10), B(-2, 5), C(3, -4) are the vertices of a right angled triangle.

Prove that the points A(3, 5), B(6, 2), C(3,-1), and D(0, 2) taken in order are the vertices of a square.

Let A(2, 2), B(8, –4) be two given points in a plane. If a point P lies on the X- axis (in positive side), and divides AB in the ratio 1: 2, then find the coordinates of P.

Show that (4, 3) is the centre of the circle passing through the points (9, 3), (7, –1), (–1, 3). Find the radius.

Find the value of ‘a’ such that PQ = QR where P, Q, and R are the points whose coordinates are (6, –1), (1, 3) and (a, 8) respectively

ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°, ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent.

ABCD is a parallelogram Fig such that ∠BAD = 120^o and AC bisects ∠BAD show that ABCD is a rhombus.

In a quadrilateral ABCD, ∠A = 72° and ∠C is the supplementary of ∠A. The other two angles are 2x–10 and x + 4. Find the value of x and the measure of all the angles.

Show that the bisectors of angles of a parallelogram form a rectangle.

Diagonal AC of a parallelogram ABCD bisects ㄥA. Show that
(i) it bisects ㄥC also
(ii) ABCD is a rhombus.

The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x =10, y =5 find the amount paid by him.

The length of a rectangle is (3x+2) units and it’s breadth is (3x–2) units. Find its area in terms of x. What will be the area if x = 20 units.

If two polynomials 2x³ + ax² + 4x – 12 and x³ + x² –2x+ a leave the same remainder when divided by (x – 3), find the value of a and also find the remainder.

If the polynomials f(x) = ax³ + 4x² + 3x –4 and g(x) = x³ – 4x + a leave the same remainder when divided by x–3, find the value of a. Also find the remainder.

Classify the following polynomials.

Represent the following irrational numbers on the number line \(\sqrt { 3 } \)

Represent the following irrational numbers on the number line \(\sqrt { 4.7 } \)

Find any two irrational numbers between 0.3010011000111…. and 0.3020020002….

Represent 4.863 on the number line.

Represent \(3.4\bar { 5 } \) on the number line Upto 4 decimal places

PQ and RS are two equal chords of a circle with centre O such that ㄥPOQ = 70°, then ㄥORS = ________.

In a cyclic quadrilaterals ABCD, ㄥA = 4x, ㄥC = 2x the value of x is ________.

In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ㄥQRS = 100°, then ㄥTVS = ______.

If one angle of a cyclic quadrilateral is 75° , then the opposite angle is ________.

AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24cm then the distance of AB from the centre of the circle is ______.

If p(a)= 0 then (x-a) is a _____ of p(x).

Zeros of (2-3x) is ______.

If x - 3 is a factor of p(x), then the remainder is _______.

In an expression ax²+bx c the sum and product of the factors respectively____________

Cubic polynomial may have maximum of ________ linear factors.

If n is a natural number then \(\sqrt { n } \) is ________.

Which one of the following, regarding sum of two irrational numbers, is true?

The number \(0.\bar { 3 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

\(0.\overline { 34 } +0.3\bar { 4 } \) = ________.

Which one of the following has terminating decimal expansion?

If U = {x : x\(\in \)N and x<10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A∪B)′] is  ________.

Which of the following is true?

If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is ________.

If A and B are two non-empty sets, then (A-B)U(A⋂B) is _____________

For any three A, B and C, \(A-\left( B\cup C \right) \) ________

What is the probability of throwing an even number with a single standard dice of six faces?

There are 24 balls in a pot. If 3 of them are Red, 5 of them are Blue and the remaining are Green then, what is the probability of picking out
(i) a Blue ball 
(ii) a Red ball and
(iii) a Green ball?

Frame two problems in calculating probability, based on the spinner shown here.

A company manufactures 10000 Laptops in 6 months. In that 25 of them are found to be defective. When you choose one Laptop from the manufactured, what is the probability that selected Laptop is a good one.

If a probability of a player winning a particular tennis match is 0.72. What is the probability of the player loosing the match?

The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of Rs. 20 per m².

Find the area of an equilateral triangle whose perimeter is 180 cm.

A park is in the shape of a quadrilateral. The sides of the park are 15 m, 20 m, 26 m and 17 m and the angle between the first two sides is a right angle. Find the area of the park.

The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes.

Find the volume of a cube each of whose side is
(i) 5 cm
(ii) 3.5 m
(iii) 21 cm

From the given figure, find all the trigonometric ratios of angle B.

From the given figure, find the values of 
(i) sin B
(ii) sec B
(iii) cot B  
(iv) cos C
(v) tan C
(vi) cosec C

If cos A = \(\frac { 2x }{ 1+{ x }^{ 2 } } \) then find the values of sinA and tan A in terms of x.

If sin \(\theta\)  = \(\frac { a }{ \sqrt { { a }^{ 2 }+{ b }^{ 2 } } } \) then show that b sin \(\theta\) = a cos \(\theta\)

Verify 3 cos A = 4 cos³ A - 3 cosA , when A = 30⁰

If the mid-point (x, y) of the line joining (3, 4) and (p, 7) lies on 2x + 2y +1 = 0 , then what will be the value of p?

The mid-point of the sides of a triangle are (2, 4), (−2, 3) and (5, 2). Find the coordinates of the vertices of the triangle.

A(−3,2), B(3,2) and C(−3,−2) are the vertices of the right triangle, right angled at A. Show that the mid-point of the hypotenuse is equidistant from the vertices.

Show that the line segment joining the mid-points of two sides of a triangle is half of the third side
(Hint: Place triangle ABC in a clever way such that A is (0, 0), B is (2a, 0) and C to be (2b, 2c). Now consider the line segment joining the mid-points of AC and BC. This will make calculations simpler).

The vertices of a triangle are (1, 2), (h, −3) and (−4, k). If the centroid of the triangle is at the point (5, −1) then find the value of \(\sqrt { { (h+k) }^{ 2 }+{ (h+3k) }^{ 2 } } \)

Give any two examples for linear equations in one variable.

Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

Raman’s age is three times the sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman.

Five years ago, a man was seven times as old as his son, while five year hence, the man will be four times as old as his son. Find their present age.

Akshaya has 2 rupee coins and 5 rupee coins in her purse. If in all she has 80 coins totalling Rs. 220, how many coins of each kind does she have.

In a rice mill, seven labours are receiving the daily wages of Rs. 500, Rs. 600, Rs. 600, Rs. 800, Rs. 800, Rs. 800 and Rs. 1000, find the modal wage

Find the mode for the set of values 17, 18, 20, 20, 21, 21, 22, 22.

A set of numbers consists of five 4’s, four 5’s, nine 6’s,and six 9’s. What is the mode.

In a week, temperature of a certain place is measured during winter are as follows 26^oC, 24^oC, 28^oC, 31^oC, 30^oC, 26^oC, 24^oC. Find the mean temperature of the week.

The mean weight of 4 members of a family is 60 kg. Three of them have the weight 56kg, 68kg and 72 kg respectively. Find the weight of the fourth member.

The radius of the circle is 25cm and the length of one of its chord is 40cm. Find the distance of the chord from the centre

The chord of length 30 cm is drawn at the distance of 8cm from the centre of the circle. Find the radius of the circle

In a circle, AB and CD are two parallel chords with centre O and radius 10 cm such that AB = 16 cm and CD = 12 cm determine the distance between the two chords?

In the given figure, AC is the diameter of the circle with centre O. If ㄥADE = 30°; ㄥDAC = 35° and ㄥCAB = 40°. Find
(i) ㄥACD 
(ii) ㄥACB 
(iii) ㄥDAE

Find all the angles of the given cyclic quadrilateral ABCD in the figure.

Expand the following using identities: (5x+4y)(5x-4y)

Expand (a -b +c)²

Expand (2x +3y+ 4z)²

Find the product of (2x+3y+4z)(4x²+9y²+16z²- 6xy -12yz - 8zx)

Evaluate 10³-15³+5³

Use a fractional index to write: \(\sqrt{5}\)

Use a fractional index to write: \(\left( \sqrt [ 3 ]{ 49 } \right) ^{ 5 }\)

Use a fractional index to write: \(\left( \frac { 1 }{ \sqrt [ 3 ]{ 100 } } \right) ^{ 7 }\)

Given \(\sqrt{2}\) = 1.414, find the value of \(\frac { 8-5\sqrt { 2 } }{ 3-2\sqrt { 2 } } \)  (to 3 places of decimals).

Simplify: \( \left(8.41 \times 10^{4}\right) \div\left(4.3 \times 10^{5}\right) \)

If A = {2, 3, 4, 5}, B = {2, 3, 5, 7} and C = {1, 3, 5}, then verify \(A\cup (B\cup C)=(A\cup B)\cup C\).

If A =\(\left\{ -\frac { 1 }{ 2 } ,0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2 \right\} \), B =\(\left\{ 0,\frac { 1 }{ 4 } ,\frac { 3 }{ 4 } ,2,\frac { 5 }{ 2 } \right\} \) and C =\(\left\{ -\frac { 1 }{ 2 } .\frac { 1 }{ 4 } ,1,2,\frac { 5 }{ 2 } \right\} \), then verify \(A\cap (B\cap C)=(A\cap B)\cap C\) .

If P = {1,2,5,7,9}, Q = {2, 3, 5, 9, 11}, R = {3, 4,5 7, 9} and S = {2, 3, 4, 5, 8}, then find
(i) \((P\cup Q)\cup R\)
(ii) \((P\cap Q)\cap S\)
(iii) \((Q\cap S)\cap R\)

Test for the commutative property of union and intersection of the sets
P = { x : x is a real number between 2 and 7} and
Q = { x : x is an rational number between 2 and 7}.

If A = {p, q, r, s}, B = {m, n, q, s, t} and C = {m, n, p, q, s}, then verify the associative property of union of sets.

In which quadrant does the following points lie? (3,–8)

In which quadrant does the following points lie?(–1,–3)

In which quadrant does the following points lie?(2, 5)

In which quadrant does the following points lie?(–7, 3)

Plot the following points in the coordinate system and identify the quadrants
P(–7, 6), Q(7, –2), R(–6, –7), S(3, 5) and T(3, 9)

If A∪B = A∩B, then ________.

Which one of the following has a terminating decimal expansion?

The zero of the polynomial 2x+5 is _______.

ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles with vertex O are ________.

If ( x+2, 4) = (5, y–2), then the coordinates (x,y) are _____.

Find the value of x

Find the value of x

Draw the circumcircle for, An equilateral triangle of side 7 cm.

Draw the circumcircle for, An isosceles right triangle having 6 cm as the length of the equal sides.

Which ones are not quadrilaterals?

Find the Zeros of the following polynomials. f(x) = 3x – 5

Find the roots of the following polynomial equations: 5x – 3 = 0

Find the zeros of the polynomial in each of the following: p(x) = 2x + 5.

Find the zeros of the polynomial in each of the following: q(y) = 2y-3.

Find the roots of the polynomial equations: 9x – 4 = 0

Express the following in the form  \({p\over q},\)  where p and q are integers and q \(\ne\) 0.
\(0.2\overline{45}\)

Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
\({17\over 200}\)

Express the following in the form 3ⁿ: 243

Use a fractional index to write \(\left( 5\sqrt { 125 } \right) ^{ 7 }\)

Express the surds in the simple form \(\sqrt { 27 } \)

Write the set of letters of the following words in Roster form
PRINCIPAL

Find the number of subsets and the number of proper subsets of a set X = {a, b, c, x, y, z}.

If U = {c, d, e, f, g, h, i, j} and A = { c, d, g, j} , find A′.

Represent A Δ B through Venn diagram.

Verify whether A = {20, 22, 23, 24} and B = {25, 30, 40, 45} are disjoint sets.

In a party of 45 people, each one likes tea or coffee or both. 35 people like tea and 20 people like coffee. Find the number of people who
(i) like both tea and coffee.
(ii) do not like Tea.
(iii) do not like coffee

A and B are two sets such that n(A – B) = 32 + x, n(B – A) = 5x and n(A∩B) = x. Illustrate the information by means of a Venn diagram. Given that n(A) = n(B), calculate the value of x.

Find any two irrational numbers between\(\frac { 6 }{ 7 } \) and \(\frac { 12 }{ 13 } \)

The cost of a chocolate is Rs. (x + y) and Amir bought (x + y) chocolates. Find the total amount paid by him in terms of x and y. If x =10, y =5 find the amount paid by him.

Construct ΔABC with AB = 5 cm ㄥB = 100⁰ and BC = 6 cm. Also locate its circumcentre draw circumcircle.

A number between 0 and 1 that is used to measure uncertainty is called _______.

A random experiment contains

The probability of all possible outcomes of a random experiment is always equal to _______.

If A is any event in S and its complement is A' then, P(A′) is equal to _______.

Which of the following cannot be taken as probability of an event?

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is _______.

The lateral surface area of a cube of side 12 cm is _______.

If the lateral surface area of a cube is 600 cm², then the total surface area is _______.

The volume of a cuboid is 660 cm³ and the area of the base is 33 cm². Its height is _______.

The number of bricks each measuring 50 cm × 30 cm × 20 cm that will be required to build a wall whose dimensions are 5 m × 3 m × 2 m is _______.

if sin 30⁰ = x and cos 60⁰ = y, then x²  + y² is________.

The value of 2tan30° tan60° is

The value of tan 1° tan 2° tan 3°...tan 89° is ________.

Given that sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and cos \(\beta\) = \(\frac { 1 }{ 2 } \), then the value of \(\alpha\) + \(\beta\) is ________.

The value of \(\frac { sin{ 29 }^{ 0 }31' }{ cos{ 60 }^{ 0 }29' } \) is

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.

If (1,−2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is ______.

The centroid of the triangle with vertices (−1, −6), (−2, 12) and (9, 3) is

Which of the following statement is true for the equation 2x + 3y = 15

Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = −2 .

The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is  _______.  

A pair of linear equations has no solution then the graphical representation is _______.

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { { c }_{ 1 } }{ { c }_{ 2 } } \) where a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 then the given pair of linear equation has _________ solution(s)

Data available in an unorganized form is called __________ data

Let m be the mid point and b be the upper limit of a class in a continuous frequency distribution. The lower limit of the class is _______.

The algebraic sum of the deviations of a set of n values from their mean is _______.

If the mean of five observations x, x+2, x+4, x+6, x+8, is 11, then the mean of first three observations is _______.

Find the mode for the set of values 17, 18, 20, 20, 21, 21, 22, 22.

In a cyclic quadrilaterals ABCD, ㄥA = 4x, ㄥC = 2x the value of x is ________.

In the figure, PQRS and PTVS are two cyclic quadrilaterals, If ㄥQRS = 100°, then ㄥTVS = ______.

If one angle of a cyclic quadrilateral is 75° , then the opposite angle is ________.

AD is a diameter of a circle and AB is a chord If AD = 30 cm and AB = 24cm then the distance of AB from the centre of the circle is ______.

Distance from the centre to any point on the circumference of the circle is called ____

If p(a)= 0 then (x-a) is a _____ of p(x).

Which of the following has x -1 as a factor?

If x - 3 is a factor of p(x), then the remainder is _______.

If (x + 5) and (x - 3) are the factors of ax²+bx+c, then values of a, b and c are _______.

Cubic polynomial may have maximum of ________ linear factors.

Which of the following statement is false?

\(\left( 0.000729 \right) ^{ \frac { -3 }{ 4 } }\times \left( 0.09 \right) ^{ \frac { -3 }{ 4 } }\) = ______.

Which is the best example of a number written in scientific notation?

What is 5.92 \(\times\)10^-3 written in decimal form?

The length and breadth of a rectangular plot are 5 \(\times\) 10⁵ and 4 \(\times\) 10⁴ metres respectively. Its area is ______.

If U = {x : x\(\in \)N and x<10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A∪B)′] is  ________.

Which of the following is true?

If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ⋂ L is ________.

If A and B are two non-empty sets, then (A-B)U(A⋂B) is _____________

In a city, 40% people like only one fruit, 35% people like only two fruits, 20% people like all the three fruits. How many percentage of people do not like any one of the above three fruits?

Point (–3, 5) lie in the ________ quadrant

The point M lies in the IV quadrant. The coordinates of M is _______

On plotting the points O(0, 0), A(3, – 4), B(3, 4) and C(0, 4) and joining OA, AB, BC and CO, which of the following figure is obtained?

If P( –1, 1), Q( 3, -4), R( 1,  -1), S(-2, -3) and T( -4, 4) are plotted on a graph paper, then the points in the fourth quadrant are ______.

The point whose ordinate is 4 and which lies on the y-axis is ______.

If x³ + 6x² + kx + 6 is exactly divisible by (x + 2), then k= ?

The type of the polynomial 4–3x³ is  ________.

The sum of the polynomials p(x) = x³ – x² – 2, q(x) = x²–3x+ 1 _______.

The remainder when p(x) = x³ – ax² + 6x – a is divided by (x – a) is ______________

Degree of the polynomial (y³–2)(y³ + 1) is _______.

It is not possible to construct a triangle when its sides are ____________

In the given figure CE || DB then the value of x⁰ is  ________.

If the diagonal of a rhombus are equal, then the rhombus is a ________.

The interior angle made by the side in a parallelogram is 90° then the parallelogram is a ________.

The angles of the triangle are 3x–40, x+20 and 2x–10 then the value of x is ________.

If n is a natural number then \(\sqrt { n } \) is ________.

An irrational number between 2 and 2.5 is ________.

The number \(0.\bar { 3 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is ____________

Find the odd one out of the following.

If B ⊆ A then n(A∩B) is –––––––––.

If A = {x, y, z} then the number of non - empty subsets of A is ________.

If B - A is B, then A∩B is ________.

Consider the following sets A = {0, 3, 5, 8}, B = {2, 4, 6, 10} and C = {12, 14,18, 20}.
3\(\in \) ______ 

Consider the following sets A = {0, 3, 5, 8}, B = {2, 4, 6, 10} and C = {12, 14,18, 20}.
14\(\in \) _______ 

PQ and RS are two equal chords of a circle with centre O such that ㄥPOQ = 70°, then ㄥORS = ________.

A chord is at a distance of 15 cm from the centre of the circle of radius 25 cm. The length of the chord is ________.

In the figure, O is the centre of the circle and ㄥACB = 40° then ㄥAOB = ________.

In a cyclic quadrilaterals ABCD, ㄥA = 4x, ㄥC = 2x the value of x is ________.

In the figure, O is the centre of a circle and diameter AB bisects the chord CD at a point E such that CE = ED = 8 cm and EB = 4 cm. The radius of the circle is ________.

If p(a)= 0 then (x-a) is a _____ of p(x).

Zeros of (2-3x) is ______.

Which of the following has x -1 as a factor?

If x - 3 is a factor of p(x), then the remainder is _______.

(x+y)(x²−xy+y²) is equal to_______.

If n is a natural number then \(\sqrt { n } \) is ________.

Which of the following is not true?

Irrational number has a________________ .

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

Which of the following are not rational numbers?

It is not possible to construct a triangle when its sides are ____________

The exterior angle of a triangle is equal to the sum of two ________.

If the diagonal of a rhombus are equal, then the rhombus is a ________.

What is the name of a regular polygon of six sides?

One angle of a parallelogram is a right angle. The name of the quadrilateral is ______

Point (–3, 5) lie in the ________ quadrant

Signs of the abscissa and ordinate of a point in the fourth quadrant are respectively

On which quadrant does the point (- 4, 3) lie?

The point whose abscissa is 5 and lies on the x-axis is__________

A point which lies in the III quadrant is__________________

If U = {x : x\(\in \)N and x<10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A∪B)′] is  ________.

For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is ________.

For any three sets A, B and C, (A−B)∩(B −C) is equal to ________.

If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ⋂ L is ________.

If A and B are two non-empty sets, then (A-B)U(A⋂B) is _____________

The root of the polynomial equation 2x + 3 = 0 is ________.

The sum of the polynomials p(x) = x³ – x² – 2, q(x) = x²–3x+ 1 _______.

The product of the polynomials p(x) = 4x –3 q(x) = 4x + 3 ____________

The remainder when p(x) = x³ – ax² + 6x – a is divided by (x – a) is ______________

Degree of the polynomial (y³–2)(y³ + 1) is _______.

If n is a natural number then \(\sqrt { n } \) is ________.

Which of the following is not true?

Which one of the following, regarding sum of two irrational numbers, is true?

Which one of the following has a terminating decimal expansion?

Which one of the following is an irrational number.

Which of the following is correct?

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If B - A is B, then A∩B is ________.

If n(A) = 10 and n(B) = 15, then the minimum and maximum number of elements in A ∩ B is ________.

The set does not have a proper subset is __________

If U = {x : x\(\in \)N and x<10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A∪B)′] is  ________.

If J = Set of three sided shapes, K = Set of shapes with two equal sides and L = Set of shapes with right angle, then J ∩ K ⋂ L is ________.

If A,B,C are non-overlapping sets, then n \(\left( A\cap B\cap C \right) \) is ___________

\(\left( A\cup B\cup C \right) \cup \left( A\cup BC \right) ^{ ' }\)=_______

\(n(A\cup B\cup C)\)=________

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

If B - A is B, then A∩B is ________.

Which one of the following is an irrational number.

x³ – x² is a …………..

Degree of the polynomial (y³–2)(y³ + 1) is _______.

Which of the following is correct?

If B - A is B, then A∩B is ________.

An irrational number between 2 and 2.5 is ________.

x³ – x² is a …………..

The exterior angle of a triangle is equal to the sum of two ________.

In a village of 100 families, 65 families buy Tamil newspapers and 55 families buy English newspapers. Find the number of families who buy
(i) Both Tamil and English newspapers.
(ii) Tamil newspapers only
(iii) English newspapers only.

A and B are two sets such that n(A – B) = 32 + x, n(B – A) = 5x and n(A∩B) = x. Illustrate the information by means of a Venn diagram. Given that n(A) = n(B), calculate the value of x.

Find any two irrational numbers between\(\frac { 6 }{ 7 } \) and \(\frac { 12 }{ 13 } \)

 Express\(\frac { 1 }{ 13 } \) in decimal form. Find the length of the period of decimals

Classify the numbers as rational or irrational
(i) \(\sqrt { 10 } \)
(ii) \(\sqrt { 49 } \)
(iii) 0.025
(iv) \(0.7\overline { 6 } \)
(v) 2.505500555...
(vi) \(\frac { \sqrt { 2 } }{ 2 } \)

Write the set of letters of the following words in Roster form
ASSESSMENT

If A = {1,2,3,4,5,7,9,11}, find n(A).

Write all the subsets of A = {a, b}.

If A = {1, 2, 6} and B = {2, 3, 4} , find A∪B.

If A = {6, 7, 8, 9} and B = {8, 10, 12}, find A Δ B.

Which of the following is correct?

If A∪B = A∩B, then ________.

Sets having the same number of elements are called ___________

The shade region with adjoint diagram represents ___________

Which one of the following has a terminating decimal expansion?

Point (–3, 5) lie in the ________ quadrant

Point (–10, 0) lies ___________

The point M lies in the IV quadrant. The coordinates of M is _______

On plotting the points O(0, 0), A(3, – 4), B(3, 4) and C(0, 4) and joining OA, AB, BC and CO, which of the following figure is obtained?

The point whose ordinate is 4 and which lies on the y-axis is ______.

It is not possible to construct a triangle when its sides are ____________

In the quadrilateral ABCD, AB = BC and AD = DC Measure of ∠BCD is ________.

In the given figure CE || DB then the value of x⁰ is  ________.

The correct statement out of the following is ________.

The interior angle made by the side in a parallelogram is 90° then the parallelogram is a ________.

If x³ + 6x² + kx + 6 is exactly divisible by (x + 2), then k= ?

The type of the polynomial 4–3x³ is  ________.

The sum of the polynomials p(x) = x³ – x² – 2, q(x) = x²–3x+ 1 _______.

The product of the polynomials p(x) = 4x –3 q(x) = 4x + 3 ____________

The Auto fare is found as minimum Rs. 25 for 3 kilometer and thereafter Rs. 12 for per kilometer. Which of the following equations represents the relationship between the total cost ‘c’ in rupees and the number of kilometers n?

If n is a natural number then \(\sqrt { n } \) is ________.

Which one of the following, regarding sum of two irrational numbers, is true?

An irrational number between 2 and 2.5 is ________.

The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is ____________

\(0.\overline { 34 } +0.3\bar { 4 } \) = ________.

Which of the following is correct?

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If B ⊆ A then n(A∩B) is –––––––––.

If A = {x, y, z} then the number of non - empty subsets of A is ________.

If B ⊆ A then n(A∩B) is –––––––––.

If B - A is B, then A∩B is ________.

If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is ______________

In a class of 50 boys, 35 boys play Carrom and 20 boys play Chess then the number of boys play both games is________.

If A is a proper subset of B, then A ∩ B = __________

Which of the following is a solution of the equation 2x − y = 6.

Which condition does not satisfy the linear equation ax + by + c = 0.

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

The centroid of the triangle with vertices (−1, −6), (−2, 12) and (9, 3) is

if sin \(\alpha\) = \(\frac { 1 }{ 2 } \) and \(\alpha\) is a cute, then (3 cos\(\alpha\) - 4cos³ \(\alpha\)) is equal to

If (2,3) is a solution of linear equation 2x + 3y = k then, the value of k is _______.

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } \neq \frac { { b }_{ 1 } }{ { b }_{ 2 } } \) where a₁x + b₁y + c₁ = 0 and a₂x + b₂ y + c₂ = 0 then the given pair of linear equation has _______ solution(s)

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are ______.

The value of tan72° tan18° is ________.

A number between 0 and 1 that is used to measure uncertainty is called _______.

Probability lies between _______.

The probability based on the concept of relative frequency theory is called _______.

The probability of an event cannot be _______.

A random experiment contains

The area of a triangle whose sides are a, b and c is ________

The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is _______.

If the sides of a triangle are 3 cm, 4 cm and 5 cm, then the area is _______.

The total surface area of a cuboid is ______________

The lateral surface area of a cube of side 12 cm is _______.

if sin 30⁰ = x and cos 60⁰ = y, then x²  + y² is________.

If tan \(\theta\) cot 37⁰ , then the value of \(\theta\) is ________.

The value of tan72° tan18° is ________.

The value of \(\frac { tan15° }{ cot75° } \) is

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

The coordinates of the point C dividing the line segment joining the points P(2, 4) and Q(5, 7) internally in the ratio 2:1 is______.

If \(P(\frac{a}{3},\frac{b}{2})\)is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is ______.

In what ratio does the point Q(1, 6) divide the line segment joining the points P(2, 7) and R(−2, 3) ______.

The ratio in which the x-axis divides the line segment joining the points A(a₁, b₁) and B(a₂, b₂ ) is ______.

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.

Give any two examples for linear equations in one variable.

Two cars are 100 miles apart. If they drive towards each other they will meet in 1 hour. If they drive in the same direction they will meet in 2 hours. Find their speed by using graphical method.

Raman’s age is three times the sum of the ages of his two sons. After 5 years his age will be twice the sum of the ages of his two sons. Find the age of Raman.

The monthly income of A and B are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs. 5,000 per month, find the monthly income of each.

It takes 24 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 8 hours and the pipe of the smaller diameter is used for 18 hours. Only half of the pool is filled. How long would each pipe take to fill the swimming pool.

Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = −2 .

Which of the following is a solution of the equation 2x − y = 6.

Which of the following is not a linear equation in two variable.

The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is  _______.  

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 } } =\frac { { b }_{ 1 } }{ { b }_{ 2 } } \neq \frac { { c }_{ 1 } }{ { c }_{ 2 } } \) where a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 then the given pair of linear equation has _________ solution(s)

Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = −2 .

Which of the following is a solution of the equation 2x − y = 6.

A pair of linear equations has no solution then the graphical representation is _______.

If \(P(\frac{a}{3},\frac{b}{2})\)is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is ______.

The ratio in which the x-axis divides the line segment joining the points A(a₁, b₁) and B(a₂, b₂ ) is ______.

The linear equation in one variable is __________

The value of k for which the pair of linear equations 4x + 6y −1 = 0 and 2x + ky − 7 = 0 represents parallel lines is  _______.  

If \(P(\frac{a}{3},\frac{b}{2})\)is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is ______.

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

Which of the following is not a linear equation in two variable.

A pair of linear equations has no solution then the graphical representation is _______.

If \(P(\frac{a}{3},\frac{b}{2})\)is the mid-point of the line segment joining A(−4, 3) and B(−2, 4) then (a, b) is ______.

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are ______.

The value of \(\frac { 2tan\ 30° }{ 1-{ tan }^{ 2 }30° } \) is equal to ________.

For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is ________.

Which of the following is true?

If A and B are two non-empty sets, then (A-B)U(A⋂B) is _____________

When (2\(\sqrt{5}\)-\(\sqrt{2}\))² is simplified, we get ________.

\(\frac { \sqrt [ 3 ]{ 18 } }{ \sqrt [ 3 ]{ 2 } } \) is same as _____________

For any three sets P, Q and R, P-(Q\(\\ \cap \)R) is ________.

Which of the following is true?

If n(A \(\cup \) B \(\cup \) C) = 40, n(A) = 30, n(B) = 25, n(C) = 20, n(A\(\cap \)B) = 12, n(B\(\cap \)C) = 18 and n(A\(\cap \)C) = 15 , then n(A\(\cap \)B\(\cap \)C) is ___________

In simplest form, \(\sqrt{640}\) is ____________

When written with a rational denominator, the expression \(\frac { 2\sqrt { 3 } }{ 3\sqrt { 2 } } \) can be simplified as ________.

If A∪B = A∩B, then ________.

If X = {x : x = 4(n – 1), n ∈ N} and Y = {y : y = 3n – 2n – 1, n ∈ N}, then X∪Y is ______________

Sets having the same number of elements are called ___________

Which one of the following has terminating decimal expansion?

Let the polynomials be
(A) –13q⁵ + 4q² + 12q
(B) (x² +4 )(x² + 9)
(C) 4q⁸ – q⁶ + 2
(D) -\(\frac {5}{7}\)y¹²+y³+y⁵
Then ascending order of their degree is _______.

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

Sets having the same number of elements are called ___________

The shade region with adjoint diagram represents ___________

If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

Which of the following are irrational numbers?
\(\sqrt { 2+\sqrt { 3 } } \)
\(\sqrt [ 3 ]{ 5+\sqrt { 7 } } \)
\(\sqrt { 8-\sqrt [ 3 ]{ 8 } } \)
\(\sqrt { 4+\sqrt { 25 } } \)

Write the set of letters of the following words in Roster form
ASSESSMENT

If A = {1,2,3,4,5,7,9,11}, find n(A).

If A = {6, 7, 8, 9} and B = {8, 10, 12}, find A Δ B.

Draw Venn diagram and shade the region representing the following sets
(A ∪ B)′

In a class, all students take part in either music or drama or both. 25 students take part in music, 30 students take part in drama and 8 students take part in both music and drama. Find
(i) The number of students who take part in only music.
(ii) The number of students who take part in only drama.
(iii) The total number of students in the class.

if \(\frac { 1 }{ 7 } \) = \(0.\overline { 142857 } \) then the value of \(\frac { 5 }{ 7 } \) ________.

Find the odd one out of the following.

It is not possible to construct a triangle when its sides are ____________

Point (–3, 5) lie in the ________ quadrant

Point (0, –7) lies ________

If A = {x, y, z} then the number of non - empty subsets of A is ________.

Which of the following is correct?

If A∪B = A∩B, then ________.

If B - A is B, then A∩B is ________.

The shaded region in the adjacent diagram represents ______________

Which of the following is correct?

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If B ⊆ A then n(A∩B) is –––––––––.

If A = {x, y, z} then the number of non - empty subsets of A is ________.

Which of the following is correct?

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

The shade region with adjoint diagram represents ___________

If n is a natural number then \(\sqrt { n } \) is ________.

Point (–3, 5) lie in the ________ quadrant

Signs of the abscissa and ordinate of a point in the fourth quadrant are respectively

On plotting the points O(0, 0), A(3, – 4), B(3, 4) and C(0, 4) and joining OA, AB, BC and CO, which of the following figure is obtained?

If P( –1, 1), Q( 3, -4), R( 1,  -1), S(-2, -3) and T( -4, 4) are plotted on a graph paper, then the points in the fourth quadrant are ______.

The point whose ordinate is 4 and which lies on the y-axis is ______.

It is not possible to construct a triangle when its sides are ____________

The exterior angle of a triangle is equal to the sum of two ________.

ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles with vertex O are ________.

In the given figure CE || DB then the value of x⁰ is  ________.

The correct statement out of the following is ________.

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

If U = {x | x ∈ N, x < 10} and A = {x | x ∈ N, 2 ≤ x < 6} then (A′)′ is –––––––––.

If B ⊆ A then n(A∩B) is –––––––––.

If A = {x, y, z} then the number of non - empty subsets of A is ________.

Which of the following is correct?

If x³ + 6x² + kx + 6 is exactly divisible by (x + 2), then k= ?

The root of the polynomial equation 2x + 3 = 0 is ________.

The type of the polynomial 4–3x³ is  ________.

x³ – x² is a …………..

If x⁵¹ + 51 is divided by x + 1, then the remainder is _______.

If n is a natural number then \(\sqrt { n } \) is ________.

Which of the following is not true?

Which one of the following, regarding sum of two irrational numbers, is true?

Which one of the following has a terminating decimal expansion?

Find the odd one out of the following.

The set P = {x | x ∈ Z , –1 < x < 1} is a –––––––––.

Number of subsets in set A = {1,2,3} is ________

The set {x: x ∈ A, x ∈ B, x ∉ A ∩ B} is___________.

Which one of the following has a terminating decimal expansion?

Which one of the following has terminating decimal expansion?

If A = {x, y, z} then the number of non - empty subsets of A is ________.

If A∪B = A∩B, then ________.

The shaded region in the adjacent diagram represents ______________

A = {set of odd natural numbers}, B = {set of even natural numbers}, then A and B are ___________

Sets having the same number of elements are called ___________