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 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 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 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) $\cos^{-1}\left(\frac{1}{3}\right)$
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) $\begin{bmatrix}-2 &- 3 \\-7 & -11 \end{bmatrix}$
11 For any non-zero vectors a and b , [b a x b a]= A) a xb B) $|a \times b|^{2}$ C) 0 D) $|a \times b|^{}$
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 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