1 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) $\sin^{-1}\left(-\frac{1}{2}\right)$
2 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) $(p\vee [q\wedge (\sim p\wedge \sim q)=l$
3 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
4 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
5 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) $\frac{1}{\sqrt{3}}$
6 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) $\frac{\pi}{12}$
7 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) $\cos^{-1}\left(\frac{1}{3}\right)$
8 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
10 For any non-zero vectors a and b , [b a x b a]= A) a xb B) $|a \times b|^{2}$ C) 0 D) $|a \times b|^{}$
11 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 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) $p \rightarrow (q\wedge \sim r)$
13 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) $\frac{1}{6}$
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
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
