1 The minimum value of Z=5x+8y subject to $x+y\geq 5,0\leq x\leq4,y\geq2,x\geq0, y\geq0$ is A) 40 B) 36 C) 20 D) 31
2 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) $\frac{1}{18}$
3 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
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 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 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
12 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) $45^{0}$
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) $\frac{\pi}{6},\frac{5\pi}{6}$
