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.