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\omega =\frac{-1 + \sqrt{3i}}{2} $ then $ (3+\omega+\omega^{2})^4$ is A) 16 B) -16 C) $16\omega$ D) $16\omega^{2}$
5 At how many points between the interval (-∞, ∞) is the function f (x): sin x is not differentiable A) 0 B) 7 C) 9 D) 3
6 If vector equation of the line $\frac{x-2}{2}=\frac{2y-5}{-3} = z+1,$ is $\overrightarrow{r}$= $(2\hat{i}+\frac{5}{2}\hat{j}-\hat{k})+\lambda\left(2\hat{i}-\frac{3}{2}\hat{j}+p\hat{k}\right)$ then p is equal to A) 0 B) 1 C) 2 D) 3
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 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
9 If $(\overrightarrow{a}\times\overrightarrow{b})^{2}+(\overrightarrow{a}.\overrightarrow{b})^{2}$= 676 |$\overrightarrow{b}$| = 2 then |$\overrightarrow{a}$| is equal to A) 13 B) 26 C) 39 D) None of these
10 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) $(\sin\alpha,\cos\alpha)$
11 Value of $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{1}{1+\sqrt{\cot x}}dx $ is A) $\frac{\pi}{6}$ B) $\frac{\pi}{12}$ C) $\frac{12}{\pi}$ D) None of these
12 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
14 It is given that the events A and B are such that P(A) = 1/4 , P(A/B) = 1/2 and P(B/A) = 2/3 then P(B) is? A) $\frac{1}{6}$ B) $\frac{1}{3}$ C) $\frac{2}{3}$ D) $\frac{1}{2}$
15 Let f: R→ R, g : R→ R be two functions such that f(x) = 2x - 3, g(x) = x3 + 5. The function (fog)-1(x) is equal to A) $\left(\frac{x+7}{2}\right)^{1/3}$ B) $\left(x-\frac{7}{2}\right)^{1/3}$ C) $\left(\frac{x-2}{7}\right)^{1/3}$ D) $\left(\frac{x-7}{2}\right)^{1/3}$