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

(a)

(A x C) ⊂ (B x D)

(b)

(B x D) ⊂ (A x C)

(c)

(A x B) ⊂ (A x D)

(d)

(D x A) ⊂ (B x A)

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

(a)

3

(b)

2

(c)

4

(d)

8

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

(a)

x² + 2

(b)

\({ x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \)

(c)

x²- 2

(d)

\({ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } \)

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

(a)

4

(b)

2

(c)

1

(d)

3

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

(a)

1

(b)

2

(c)

3

(d)

4

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

(a)

b

(b)

a

(c)

ab

(d)

\(\frac { a }{ b } \)

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

(a)

3

(b)

5

(c)

6

(d)

8

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

(a)

\(\frac {9y}{7}\)

(b)

\(\frac {9y^{2}}{(21y - 21)}\)

(c)

\(\frac {21y^2 - 42y + 21}{3y^{2}}\)

(d)

\(\frac {7(y^{2} - 2y + 1)}{y^{2}}\)

Graphically an infinite number of solutions represents ___________

(a)

three planes with no point in common

(b)

three planes intersecting at a single point

(c)

three planes intersecting in a line or coinciding with one another

(d)

None

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

(a)

2.5 cm

(b)

5 cm

(c)

10 cm

(d)

\(5\sqrt { 2 } \)cm

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

(a)

25 : 4

(b)

25 : 7

(c)

25 : 11

(d)

25 : 13

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

(a)

\(x=\frac { ay }{ b+a } \)

(b)

\(x=\frac { a+b }{ ay } \)

(c)

\(x=\frac { ay }{ b-a } \)

(d)

\(\frac { x }{ y } =\frac { a }{ b } \)

The straight line given by the equation x = 11 is

(a)

parallel to X axis

(b)

parallel to Y axis

(c)

passing through the origin

(d)

passing through the point (0,11)

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

(a)

3

(b)

6

(c)

9

(d)

12

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

(a)

a = b

(b)

a + b

(c)

ab = 0

(d)

a ≠ b

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

(a)

2a

(b)

3a

(c)

0

(d)

2ab

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

(a)

25

(b)

\(\frac { 1 }{ 25 } \)

(c)

5

(d)

1

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

(a)

\(\sqrt{3}\)

(b)

\(\frac{1}{\sqrt{3}}\)

(c)

\(\frac{\sqrt{3}}{2}\)

(d)

1

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

(a)

12 cm

(b)

10 cm

(c)

13 cm

(d)

5 cm

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

(a)

1:2

(b)

1:4

(c)

1:6

(d)

1:8

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

(a)

S₁ = S₂

(b)

S₁ > S₂

(c)

S₁ < S₂

(d)

S₁ = 2S₂

The sum of all deviations of the data from its mean is

(a)

Always positive

(b)

always negative

(c)

zero

(d)

non-zero integer

The mean of 100 observations is 40 and their standard deviation is 3. The sum of squares of all observations is

(a)

40000

(b)

160900

(c)

160000

(d)

30000

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

(a)

91%

(b)

8%

(c)

92%

(d)

80%

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

(a)

0

(b)

1

(c)

\(\frac{1}{2}\)

(d)

\(\frac{1}{9}\)