1 The p.d.f of c.r.v X is given by $f(x)=\frac{x+2}{18}$ , if -2 < x < 4=0, otherwise =0, then P[|x| <1]= A) $\frac{2}{9}$ B) $\frac{4}{9}$ C) $\frac{1}{9}$ D) $\frac{1}{18}$
2 If $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4$, then $\frac{dy}{dx}=$ A) $\frac{7y-x}{y-7x}$ B) $\frac{y-7x}{7x-y}$ C) $\frac{y+7x}{7y-x}$ D) $\frac{7x+y}{x-7y}$
3 The symbolic form of the following circuit is (where p,q represents switches S1 and S2 closed respectively ) A) $(p\wedge q)\wedge (\sim p\wedge \sim q)=l$ B) $(p\wedge [q\wedge (\sim p\wedge \sim q)=l$ C) $(p\vee q)\vee (\sim p\wedge \sim q)=l$ D) $(p\vee [q\wedge (\sim p\wedge \sim q)=l$
4 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
5 The points of discontinuity of the function $f(x)= \frac{1}{x-1}, if 0\leq x\leq2$ $= \frac{x+5}{x+3}, if 2< x\leq4$ in its domain are A) x=1,x=2 B) x=0, x=2 C) x=2 only D) x=4 only
6 If the equation ax2+2hxy+by2+2gx+2fy=0 has one line as the bisector of the angle between co-ordinate axes, then A) $(a+b)^{2}=4(h^{2}+f^{2})$ B) $(a+b)^{2}=4(h^{2}+g^{2}+f^{2})$ C) $(a+b)^{2}=4h^{2}$ D) $(a+b)^{2}=4(h^{2}+g^{2})$
7 The eccentricity of the ellipse y2+4x2-12x+6y+14=0 is A) $\frac{1}{\sqrt{2}}$ B) $\frac{1}{2}$ C) $\frac{\sqrt{3}}{2}$ D) $\frac{1}{\sqrt{3}}$
8 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 A) $\frac{\pi}{6}$ B) $\frac{\pi}{3}$ C) $\frac{\pi}{4}$ D) $\frac{\pi}{12}$
10 The angle between the lines $\frac{x-1}{4}=\frac{y-3}{1}=\frac{z}{8}$ and $\frac{x-2}{2}=\frac{y+1}{2}=\frac{z-4}{1}$ A) $\cos^{-1}\left(\frac{2}{3}\right)$ B) $\cos^{-1}\left(\frac{1}{2}\right)$ C) $\cos^{-1}\left(\frac{3}{4}\right)$ D) $\cos^{-1}\left(\frac{1}{3}\right)$
11 The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is A) $x^{2}+68x+256=0$ B) $x^{2}+68x-256=0$ C) $x^{2}-68x+256=0$ D) $x^{2}-68x-256=0$
12 The negation of the statement pattern $\sim p \vee (q\rightarrow\sim r)$ is A) $p\wedge (q\wedge r)$ B) $\sim p\wedge (q\wedge r)$ C) $p \vee (q\wedge r)$ D) $p \rightarrow (q\wedge \sim r)$
13 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 B) $\frac{1}{3}$ C) 1 D) $\frac{1}{6}$
14 The principal solutions of $\cot x=\sqrt{3}$ are A) $\frac{\pi}{6},\frac{7\pi}{6}$ B) $\frac{\pi}{3},\frac{7\pi}{3}$ C) $\frac{\pi}{4},\frac{5\pi}{4}$ D) $\frac{\pi}{6},\frac{5\pi}{6}$
15 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
