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 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
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 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 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) $(a+b)^{2}=4(h^{2}+g^{2})$
8 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
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) $45^{0}$
14 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) $x^{2}-68x-256=0$
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
