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The value of $\sin^{-1}\left(\frac{1}{2}\right)+\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is

$\cos^{-1}\left(\frac{1}{2}\right)$

$\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

$\cos^{-1}\left(-\frac{1}{2}\right)$

$\sin^{-1}\left(-\frac{1}{2}\right)$

If $f(x)=\frac{2x+3}{3x-2},x\neq\frac{2}{3}$ , then the function f of is

A) a constant function

B) an exponential function

C) an even function

D) an identity function

If $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4$ , then $\frac{dy}{dx}=$

$\frac{7y-x}{y-7x}$

$\frac{y-7x}{7x-y}$

$\frac{y+7x}{7y-x}$

$\frac{7x+y}{x-7y}$

The symbolic form of the following circuit is (where p,q represents switches S₁ and S₂ closed respectively )

$(p\wedge q)\wedge (\sim p\wedge \sim q)=l$

$(p\wedge [q\wedge (\sim p\wedge \sim q)=l$

$(p\vee q)\vee (\sim p\wedge \sim q)=l$

$(p\vee [q\wedge (\sim p\wedge \sim q)=l$

If A = {x,y,z}, B= {1,2} , then the total number of relations from set A to set B are

A) 8

B) 64

C) 32

D) 16

The value of

$\tan^{-1}\left(\frac{1}{3}\right)+\tan^{-1}\left(\frac{1}{5}\right)+\tan^{-1}\left(\frac{1}{7}\right)+\tan^{-1}\left(\frac{1}{8}\right)$ is

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{12}$

The negation of the statement ' he is poor but happy ' is

A) He is poor but not happy

B) He is neither poor nor happy

C) He is not poor and not happy

D) He is not poor or not happy

$\int\frac{dx}{\cos 2x-\cos^{2}x}=$

A) - tan x+c

B) cot x+ c

C) tan x+c

D) - cot x+c

If the line $r= (\hat{i}-2\hat{j}+3\hat{k})+\lambda (2\hat{i}+\hat{j}+2\hat{k})$ is parallel to the plane

$r. (3\hat{i}-2\hat{j}+m\hat{k})=10$ , then the value of m is

A) -2

B) 3

C) 2

D) -3

tan A+2tan 2A+4 tan 4A+8 cot 8A=

A) tan A

B) tan 2A

C) cot 2A

D) cot A

The c.d. f F(x) associated with p.d.f.

$f(x) =3(1-2x^{2})$ . If 0 < x <1. is $k\left( x-\frac{2x^{3}}{k}\right)$ , then value of k is

A) 3

$\frac{1}{3}$

C) 1

$\frac{1}{6}$

$\int \frac{dx}{x^{2}+4x+13}=$

$\frac{1}{3}\tan^{-1}\left(\frac{x+2}{3}\right)+C$

$\frac{1}{6}\tan^{-1}\left(\frac{x-1}{x+5}\right)+C$

$3\tan^{-1}\left(\frac{x+2}{3}\right)+C$

$\frac{1}{6}\tan^{-1}\left(\frac{x+2}{3}\right)+C$

The principal solutions of $\cot x=\sqrt{3}$ are

$\frac{\pi}{6},\frac{7\pi}{6}$

$\frac{\pi}{3},\frac{7\pi}{3}$

$\frac{\pi}{4},\frac{5\pi}{4}$

$\frac{\pi}{6},\frac{5\pi}{6}$

The cofactors of the elements of the first column of the matrix

$A=\begin{bmatrix}2 & 0 &-1\\3 & 1&2\\ -1 &1 & 2 \end{bmatrix}$ are

A) 0,-7,2

B) -1,3,-2

C) 0,-8,4

D) 0,-1, 1

The equation of the directrix of the parabola 3x²=16y is

A) 3y-4=0

B) 3y+4=0

C) 3x+4=0

D) 3x-4=0

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