1 If $\frac{x}{\sqrt{1+x}}+\frac{y}{\sqrt{1+y}}=0, x\neq y,$ then $ (1+x)^{2}\frac{dy}{dx}=$ A) 1 B) $\frac{1}{2}$ C) -1 D) 0
2 The value of $\sin^{-1}\left(\frac{1}{2}\right)+\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is A) $\cos^{-1}\left(\frac{1}{2}\right)$ B) $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ C) $\cos^{-1}\left(-\frac{1}{2}\right)$ D) $\sin^{-1}\left(-\frac{1}{2}\right)$
3 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) $\frac{1}{18}$
4 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) $(p\vee [q\wedge (\sim p\wedge \sim q)=l$
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 The radius of the circle passing through the points (5,7),(2,-2) and (-2,0) is A) 2 units B) 5 units C) 3 units D) 4 units
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) $\frac{\pi}{12}$
9 If $A=\begin{bmatrix}2 & 3 \\1 & 2 \end{bmatrix}$ , $B=\begin{bmatrix}1 & 0 \\3 & 1\end{bmatrix}$ , then B-1 A-1 = A) $\begin{bmatrix}-2 &- 3 \\-7 & 11 \end{bmatrix}$ B) $\begin{bmatrix}2 &- 3 \\-7 & 11 \end{bmatrix}$ C) $\begin{bmatrix}2 &3 \\7 & 11 \end{bmatrix}$ D) $\begin{bmatrix}-2 &- 3 \\-7 & -11 \end{bmatrix}$
10 With usual notations, if the angles A,B,C of a $\triangle$ABC are in AP and b:c= $\sqrt{3}:\sqrt{2}$ A) $75^{0}$ B) $55^{0}$ C) $35^{0}$ D) $45^{0}$
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 equation of planes parallel to the plane x+2y+2z+8=0 , which are at a distance of 2 units from the point (1,1,2) are A) x+2y+2z-5=0 or x+2y+2z-3=0 B) x+2y+2z-6=0 or x+2y+2z-7=0 C) x+2y+2z-13=0 or x+2y+2z-1=0 D) x+2y+2z+3=0 or x+2y+2z-5=0
13 $\int \frac{dx}{x^{2}+4x+13}=$ A) $\frac{1}{3}\tan^{-1}\left(\frac{x+2}{3}\right)+C$ B) $\frac{1}{6}\tan^{-1}\left(\frac{x-1}{x+5}\right)+C$ C) $3\tan^{-1}\left(\frac{x+2}{3}\right)+C$ D) $\frac{1}{6}\tan^{-1}\left(\frac{x+2}{3}\right)+C$
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) $\frac{\pi}{6},\frac{5\pi}{6}$
