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 $\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4$, then $\frac{dy}{dx}=$ A) $\frac{7y-x}{y-7x}$ B) $\frac{y-7x}{7x-y}$ C) $\frac{y+7x}{7y-x}$ D) $\frac{7x+y}{x-7y}$
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 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
9 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) $\cos^{-1}\left(\frac{1}{3}\right)$
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) $45^{0}$
12 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) $x^{2}-68x-256=0$
13 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) $p \rightarrow (q\wedge \sim r)$
14 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) $\frac{1}{6}$
15 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) $\frac{\pi}{6},\frac{5\pi}{6}$
