1 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
2 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
3 A circle has a radius of 3 and its center lies on the line y = x - 1. The equation of the circle, if it passes through (7, 3), is A) $ x^{2} +y^{2} +8x-6y+16=0$ B) $x^{2} +y^{2} -8x+6y+16=0$ C) $x^{2} +y^{2} -8x-6y-16=0$ D) $x^{2} +y^{2} -8x-6y+16=0$
4 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
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 The solution of sin x = $-\frac{\sqrt{3}}{2}$ is A) $x = n\pi+ (-1)^{n}\frac{4\pi}{3}, n \epsilon Z$ B) x = n\pi+ (-1)^{n}\frac{2\pi}{3}, n \epsilon Z C) $x = n\pi+ (-1)^{n}\frac{3\pi}{3}, n \epsilon Z$ D) None of 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 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 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 Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is A) 20 B) 9 C) 120 D) 40
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
15 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
