If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by "x is greater than y". The range of R is __________

(a)

{1, 4, 6, 9}

(b)

{4, 6, 9}

(c)

{1}

(d)

None of these

If f(x) = |x - 2| + |x + 2|, x ∈ R, then

(a)

\(f(x)=\left\{\begin{array}{lll} -2 x & \text { if } & x \in(-\infty,-2] \\ 4 & \text { if } & x \in(-2,2] \\ 2 x & \text { if } & x \in(2, \infty) \end{array}\right.\)

(b)

\(f(x)=\begin{cases}2x\ if\ x∈(-∞,-2] \\4x\ if \ x∈(-2,2]\\ - 2x\ if\ x∈(2,∞)\end{cases}\)

(c)

\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\-4x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

(d)

\(f(x)=\begin{cases}-2x\ if\ x∈(-∞,-2] \\2x\ if \ x∈(-2,2]\\ 2x\ if\ x∈(2,∞)\end{cases}\)

Let S = (1, 2, 3), R be (1, 1) (1, 2) (2, 2) (1, 3) (3, 1), what are the elements to-be included to make R reflexive ___________

(a)

(3, 3)

(b)

(2, 3)

(c)

(3, 2)

(d)

none of these

If \({ log }_{ \sqrt { x } }\) 0.25 = 4, then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

\((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to ___________

(a)

1

(b)

3

(c)

23

(d)

21

Logarithm of 144 to the base 2\(\sqrt{3}\) is ___________

(a)

2

(b)

3

(c)

4

(d)

5

If cosec x + cot x = \(\frac { 11 }{ 2 } \) then tan x = ___________

(a)

\(\frac { 21 }{ 22 } \)

(b)

\(\frac { 15 }{ 16 } \)

(c)

\(\frac { 44 }{ 117 } \)

(d)

\(\frac { 117 }{ 44 } \)

If tan θ = \(\frac{-4}{3}\), then sin θ is _____________ 

(a)

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

(b)

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

(c)

\(\frac{-4}{5}\quad or\quad \frac{4}{5}\)

(d)

None

If sin θ = sin \(\alpha\), then the angles θ and \(\alpha\) are related by _______________

(a)

\(\theta=n\pi\pm\alpha\)

(b)

\(\theta=2n\pi+(-1)^n\alpha\)

(c)

\(\alpha=n\pi\pm(-1)^n\theta\)

(d)

\(\theta=(2n+1)\pi+\alpha\)

Choose the incorrect pair:

(a)

sinx - x ∈ R

(b)

cos x - x ∈ R

(c)

log x x > 0

(d)

e^-x - x > 0

Find the incorrect pair

(a)

\(\\ \frac { a }{ sin\ A } =\frac { b }{ sin\ B } =\frac { C }{ sin\ C } \) - 2R

(b)

\(\frac { { b }^{ 2 }+{ c }^{ 2 }-{ a }^{ 2 } }{ 2bc } \) - cos A

(c)

\(\frac { a-b }{ a+b } cot\frac { c }{ 2 } \) - tan\(\frac{A-B}{2}\)

(d)

\(\frac { { a }^{ 2 }+{ c }^{ 2 }-{ b }^{ 2 } }{ 2ac } \) - cos C

The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

The product of r consecutive positive integers is divisible by _________

(a)

r!

(b)

r!+1

(c)

(r+1)

(d)

none of these

There are 10 lamps in a hall. Each one of them can be switched on independently. The number of ways in which the hall can be illuminated is  _________

(a)

10²

(b)

10²³

(c)

2¹⁰

(d)

10!

The number of ways of disturbing 7 identical balls in 3 distinct boxes, so that no box is empty is  _________

(a)

7

(b)

6

(c)

35

(d)

15

If \(\frac { 1 }{ 7! } +\frac { 1 }{ 8! } =\frac { A }{ 9! } ,\) then the value of A is _________

(a)

7²

(b)

8²

(c)

9

(d)

9²

Assertion (A): Every body in a room shakes hands with everybody else. The total number of persons in the room is n. The number of hand shakes is \(\frac{n(n-1)}{2}\)
Reason (R): The number of handshakes is nC₂

(a)

Both A and R are true and R is the correct explanation of A

(b)

Both A and R are true but R is not the correct explantion of A

(c)

A is true R is false

(d)

is false R is true

The coefficient of x⁵ in the series e^-2x is

(a)

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

(b)

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

(c)

\(\frac { -4 }{ 15 } \)

(d)

\(\frac { 4 }{ 15 } \)

The series for log \(\left( \frac { 1+x }{ 1-x } \right) is\) ______________

(a)

\(x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \)

(b)

\(2\left[ x+\frac { { x }^{ 3 } }{ 3 } +\frac { { x }^{ 5 } }{ 5 } +...+\infty \right] \)

(c)

\(\frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 4 } }{ 4 } +\frac { { x }^{ 6 } }{ 6 } +...+\infty \)

(d)

\(2\left[ \frac { { x }^{ 2 } }{ 2 } +\frac { { x }^{ 4 } }{ 4 } +\frac { { x }^{ 6 } }{ 6 } +...+\infty \right] \)

The first and last term of an A. P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be ______________

(a)

5

(b)

6

(c)

7

(d)

8

The equation of the line with slope 2 and the length of the perpendicular from the origin equal to \(\sqrt5\) is

(a)

x - 2y = \(\sqrt5\)

(b)

2x - y =\(\sqrt5\)

(c)

2x - y = 5

(d)

x - 2y - 5 = 0

If the lines x + q = 0, y - 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be ______________

(a)

2

(b)

2

(c)

3

(d)

5

The lines x cos \(\alpha\) + y sin \(\alpha\) = p and xcos\(\beta\) + y sin\(\beta\) = q will be perpendicular if ______________

(a)

\(\alpha =\beta\)

(b)

\(\alpha-\beta=\frac{\pi}{2}\)

(c)

\(|\alpha-\beta|=\frac{\pi}{2}\)

(d)

\(\alpha-\beta=0\)

Separate equation of lines for a pair of lines whose equation is x²+ xy -12y² = 0 are ______________

(a)

x + 4y = 0 and x + 3y = 0

(b)

2x - 3y = 0 and x - 4y = 0

(c)

x - 6y = 0 and x - 3y = 0

(d)

x + 4y = 0 and x - 3y = 0

The locus of a point which is collinear with the points (a, 0) and (0, b) is ______________

(a)

x + y = 1

(b)

\(\frac{x}{a}+\frac{y}{b}=1\)

(c)

x + y = ab

(d)

\(\frac{x}{a}-\frac{y}{b}=1\)