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 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
5 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
6 If A = $\begin{bmatrix}0 & c & -b \\-c & 0 & a \\b & -a & 0 \end{bmatrix}$ and B =$\begin{bmatrix}a^{2} & ab & ac \\ab & b^{2} & bc \\ac & bc & c^{2} \end{bmatrix}$ then AB is equal to A) B B) A C) 0 D) I
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 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
9 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
10 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
11 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
12 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
13 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 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
