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

(a)

1

(b)

2

(c)

3

(d)

6

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

(a)

linear

(b)

cubic

(c)

reciprocal

(d)

quadratic

If f : R⟶R is defined by (x) = x² + 2, then the preimage 27 are _________

(a)

0.5

(b)

5, -5

(c)

5, 0

(d)

\(\sqrt { 5 } ,-\sqrt { 5 } \)

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

(a)

-1

(b)

-3

(c)

1

(d)

0

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

(a)

1 < r < b

(b)

0 < r < b

(c)

0 \(\le\) r < b

(d)

0 < r \(\le\) b

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

(a)

14400

(b)

14200

(c)

14280

(d)

14520

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

(a)

na

(b)

(2n - 1)a

(c)

n² - a

(d)

n²a²

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

(a)

a G.P

(b)

an A.P

(c)

a constant sequence

(d)

neither an A.P nor a G.P

If A is a 2 x 3 matrix and B is a 3 x 4 matrix, how many columns does AB have

(a)

3

(b)

4

(c)

2

(d)

5

If number of columns and rows are not equal in a matrix then it is said to be a

(a)

diagonal matrix

(b)

rectangular matrix

(c)

square matrix

(d)

identity matrix

A Quadratic polynomial whose one zero is 5 and sum of the zeroes is 0 is given by ___________

(a)

x²-25

(b)

x²-5

(c)

x²-5x

(d)

x²-5x+5

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

(a)

\(\angle B=\angle E\)

(b)

\(\angle A=\angle D\)

(c)

\(\angle B=\angle D\)

(d)

\(\angle A=\angle F\)

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

(a)

120^o

(b)

100°

(c)

110°

(d)

90°

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

(a)

3

(b)

6

(c)

9

(d)

12

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

(a)

0 sq.units

(b)

25 sq.units

(c)

5 sq.units

(d)

none of these

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

(a)

x - y - 3 = 0; 3x - y - 7 = 0

(b)

x + y = 3; 3x + y = 7

(c)

3x + y = 3; x + y = 7

(d)

x + 3y - 3 = 0; x - y - 7 = 0

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

(a)

7:2

(b)

3:4

(c)

2:7

(d)

5:3

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

(a)

 \(ta{ n }^{ 2 }\theta \)

(b)

1

(c)

\(cot^{ 2 }\theta \)

(d)

0

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

(a)

9

(b)

7

(c)

5

(d)

3

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

(a)

-1

(b)

0

(c)

1

(d)

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

If A is an assets angle of Δ ABC, right angle at 3, then the value of sin A T cos A is ___________

(a)

=1

(b)

>1

(c)

<1

(d)

=2

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

(a)

60\(\pi\) cm²

(b)

68\(\pi\) cm²

(c)

120\(\pi\) cm²

(d)

136\(\pi\) cm²

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

(a)

1:2:3

(b)

2:1:3

(c)

1:3:2

(d)

3:1:2

Which of the following is not a measure of dispersion?

(a)

Range

(b)

Standard deviation

(c)

Arithmetic mean

(d)

Variance

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

(a)

\(\frac{1}{5}\)

(b)

\(\frac{3}{10}\)

(c)

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

(d)

\(\frac{4}{5}\)