If A = {(x,y) : y = e^x, x∈R} and B = {(x,y) : y = e^-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

0

(c)

1

(d)

2

If the roots of x²-bx + c = 0 are two consecutive integer,then b²- 4c is ___________

(a)

0

(b)

1

(c)

2

(d)

none of these

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

(a)

2

(b)

3

(c)

4

(d)

5

The value of \(\sqrt [ 4 ]{ { (-2) }^{ 4 } } =\) _______.

(a)

2

(b)

-2

(c)

4

(d)

-4

cos 6x - cos 8x = _______________

(a)

2 sin 7x sin x

(b)

sin 7x sin x

(c)

\(\frac { 1 }{ 2 } \)sin 7x + sin x

(d)

\(\sqrt { 2 } \) sin7x sin x

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)

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

The value of x, for which the matrix A = \(\begin{bmatrix} e^{x-2}& e^{7+x} \\ e^{2+x} & e^{2x+3} \end{bmatrix}\) is singular

(a)

9

(b)

8

(c)

7

(d)

6

\(\int \frac{x^2+\cos ^2 x}{x^2+1} \operatorname{cosec}^2 x d x\) is

(a)

cot x + sin ^-1x + c

(b)

-cot x + tan^-1x + c

(c)

-tan x + cot^-1x + c

(d)

-cot x - tan^-1x + c

\(\int x^2 e^{\frac{x}{2}} d x\) is

(a)

\( x^2e^{x\over2}-4xe^{x\over2}-8e^{x\over2}+c\)

(b)

\( 2x^2e^{x\over2}-8xe^{x\over2}-16e^{x\over2}+c\)

(c)

\( 2x^2e^{x\over2}-8xe^{x\over2}+16e^{x\over2}+c\)

(d)

\( x^2{e^{x\over2}\over 2}-{xe^{x\over2}\over 4}+{e^{x\over2}\over 8}+c\)

If a and b are chosen randomly from the set {1,2,3,4} with replacement, then the probability of the real roots of the equation \(x^2+ax+b=0\) is

(a)

\({3\over 16}\)

(b)

\({5\over 16}\)

(c)

\({7\over 16}\)

(d)

\({11\over 16}\)