1 If $\frac{x}{\sqrt{1+x}}+\frac{y}{\sqrt{1+y}}=0, x\neq y,$ then $ (1+x)^{2}\frac{dy}{dx}=$ A) 1 B) $\frac{1}{2}$ C) -1 D) 0
2 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
3 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) $\sin^{-1}\left(-\frac{1}{2}\right)$
4 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
5 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) $\frac{7x+y}{x-7y}$
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 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 $A=\begin{bmatrix}2 & 3 \\1 & 2 \end{bmatrix}$ , $B=\begin{bmatrix}1 & 0 \\3 & 1\end{bmatrix}$ , 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) $\begin{bmatrix}-2 &- 3 \\-7 & -11 \end{bmatrix}$
9 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) $|a \times b|^{}$
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 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) $\frac{\pi}{6},\frac{5\pi}{6}$
