1 If $z=x+iy, z^{1/3} = a - ib,$ then $\frac{x}{a}-\frac{y}{b} = k(a^{2}-b^{2})$ where k is equal to A) 1 B) 2 C) 3 D) 4
2 If the coordinates at one end of the diameter of the circle x2 + y2 - 8x- 4y+ c = 0 are (-3, 2), then the coordinates at the other end are A) (5,3) B) (6,2) C) (1,-8) D) (11,2)
3 The system of linear equations : x + y+ z = 0, 2x + y - z = 0, 3x +2y = 0 has: A) no solution B) a unique solution C) an infinitely many solution D) None of these
4 If the lines 3x -4y + 4 = 0 and 6x- 8y-7 = 0 are tangents to a circle, then radius of the circle is A) 3/4 B) 2/3 C) 1/4 D) 5/2
5 The position vector of A and B are $2\hat{i}+2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}+4\hat{k}$. The length of the internal bisector of <BOA triangle AOB is A) $\sqrt{\frac{136}{9}}$ B) $\frac{\sqrt{136}}{9}$ C) $\frac{20}{3}$ D) $\sqrt{\frac{217}{9}}$
6 If y = $\tan^{-1}\frac{4x}{1+5x^{2}}+\tan^{-1}\frac{2+3x}{3-2x}$ then $\frac{dy}{dx}$ = A) $\frac{1}{1+25x^{2}}+\frac{2}{1+x^{2}}$ B) $\frac{5}{1+25x^{2}}+\frac{2}{1+x^{2}}$ C) $\frac{5}{1+25x^{2}}$ D) $\frac{1}{1+25x^{2}}$
7 The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. The rate of change of the volume of the cylinder, in cm3/min, when the radius is 2 cm and the height is 3 cm is A) $-2\pi$ B) -$\frac{-8\pi}{5}$ C) $\frac{-3\pi}{5}$ D) $\frac{2\pi}{5}$
8 If a, b, c are in A. P, then the value of $\begin{vmatrix}x+1& x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c \end{vmatrix}$ is? A) 3 B) -3 C) 0 D) Noneof these
9 If sin y = x sin(a+y), then $\frac{dy}{dx}$ is equal to A) $\frac{\sin\sqrt{a}}{\sin\left(a+y\right)}$ B) $\frac{\sin^{2} (a+y)}{\sin a}$ C) $\sin(a+y)$ D) None of these
10 $\int_{}^{} (27e^{9x}+e^{12x})^{1/3}dx $ is equal to A) $(1/4)(27+e^{3x})^{1/3}+C$ B) $(1/4)(27+e^{3x})^{2/3}+C$ C) $(1/3)(27+e^{3x})^{4/3}+C$ D) $(1/4)(27+e^{3x})^{4/3}+C$
11 The area under the curve y = |cos x - sin x|, 0≤x≤$\frac{\pi}{2}$ A) $2\sqrt{2}$ B) $2\sqrt{2}-2$ C) $2\sqrt{2}+2$ D) 0
12 If $\int_{}^{}\frac{\sin x}{\sin (x - \alpha)}dx = Ax + B\log_{}{\sin (x - \alpha)}+C$ then value of (A,B) is A) $(-\cos\alpha,\sin\alpha)$ B) $(\cos\alpha,\sin\alpha)$ C) $(-\sin\alpha,\cos\alpha)$ D) $(\sin\alpha,\cos\alpha)$
13 If f(x) = $x^{3}+bx^{2}+cx+d$ and 0<b2<c, then in (-∞, ∞) A) f(x) is a strictly increasing function B) f(x) has local maxima C) f(x) is a strictly decreasing function D) f(x) is bounded
14 The solution of the differential equation $\left\{1+x\sqrt{(x^{2}+y^{2})}\right\}dx + \left\{\sqrt{(x^{2}+y^{2})}-1\right\}ydy = 0 is ? A) $x^{2}+\frac{y^{2}}{2}+\frac{1}{3}(x^{2}+y^{2})^{3/2}$=C B) $x-\frac{y^{2}}{3}+\frac{1}{2}(x^{2}+y^{2})^{1/2}$=C C) $x-\frac{y^{2}}{2}+\frac{1}{3}(x^{2}+y^{2})^{3/2}$=C D) None of these