1 If tan θ = √n for some non-square natural number n, then sec 2θ is : A) a rational number B) an irrational number C) a positive number D) none of the above
2 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
3 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)
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 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) $\frac{2\pi}{5}$
6 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
7 $\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) $(1/4)(27+e^{3x})^{4/3}+C$
8 The equation of the plane which bisects the angle between the planes 3x - 6y + 2z + 5 = 0 and 4x - 12y + 3z- 3 = 0 which contains the origin is A) 33x - 13y + 32z + 45 = 0 B) x - 3Y + z - 5 = 0 C) 33x + 13y + 32z + 45 = 0 D) None of these
9 A wire 34 cm long is to be bent in the form of a quadrilateral of which each angle is 90°. What is the maximum area which can be enclosed inside the quadrilateral? A) $68cm^{2}$ B) $70cm^{2}$ C) $71.25cm^{2}$ D) $72.25cm^{2}$
10 The domain of the function f(x) = $\sqrt{\frac{1}{|x-2|-(x-2)}}$ is: A) $(-\infty,2)$ B) $(2,\infty)$ C) $(-\infty,2)$ D) $(2,\infty)$
11 Let f be the function defined by f(x) = $\begin{cases}\frac{x^{2}-1}{x^{2}-2|x-1|-1} & x \neq 1\\1/2 & x = 1\end{cases}$ A) The function is continuous for all values of x B) The function is continuous only for x > 1 C) The function is continuous at x=1 D) The function is not continuous at x =1
13 The value of x in the interval [4,9] at which the function f(x) = √x satisfies the mean value theorem is A) 13/4 B) 17/4 C) 21/4 D) 25/4
15 Let a, b, c, be in A.P. with a common difference d.Then $e^{1/c}, e^{b/ac},e^{1/a}$ are in : A) GP. with common ratio $e^{d}$ B) GP. with common ratio $e^{1/d}$ C) GP. with common ratio $e^{d/(b^{2}-d^{2})}$ D) A.P