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 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) $\frac{7x+y}{x-7y}$
3 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) $(p\vee [q\wedge (\sim p\wedge \sim q)=l$
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 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
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 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) $45^{0}$
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 $\int \frac{dx}{x^{2}+4x+13}=$ 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) $\frac{1}{6}\tan^{-1}\left(\frac{x+2}{3}\right)+C$
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