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 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
4 Evaluate $\lim_{x \rightarrow 2}\frac{\sqrt{(x+7)}-3\sqrt{(2x-3)}}{\sqrt[3]{(x+6)}-2\sqrt[3]{(3x-5)}}$ A) $\frac{17}{9}$ B) $\frac{17}{18}$ C) $\frac{34}{23}$ D) $\frac{26}{7}$
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 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
7 The equation $y^{2}+3=2(2x+y)$ represents a parabola with the vertex at A) (1/2,1) and axis parallel to y-axis B) (1,1/2) and axis parallel to x-axis C) (1/2,1) and focus at (3/2,1) D) (1,1/2) and focus at (3/2,1)
8 The conic represented by x = 2 (cos t + sin t), y = 5 (cos t - sin t) is A) a circle B) a parabola C) an ellipse D) a hyperbola
9 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
10 The equation of the chord of the hyperbola 25x2 - 16y2 = 400, that is bisected at point (5,3) is: A) 135 x - 48y = 481 B) 125x - 48y = 481 C) 125 x - 4y = 48 D) None of these
11 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) $(2,\infty)$
12 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
14 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) $\left(\frac{x-7}{2}\right)^{1/3}$
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