If vectors $a\hat{i} +\hat{j}+\hat{k},\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i} +\hat{j}+c\hat{k}$ (a ≠ b ≠ c ≠ 1) are coplanar, then find $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$

A) 0

B) 1

C) -1

D) 2


The angle between a pair of tangants drawn from a point T to the circle

$x^{2}+y^{2}+4x-6y+9\sin^{2} \alpha+13\cos^{2} \alpha =0$  is  2α

The equation of the locus of the point T is

A) $x^{2}+y^{2}+4x-6y+4=0$

B) $x^{2}+y^{2}+4x-6y-9=0$

C) $x^{2}+y^{2}+4x-6y-4=0$

D) $x^{2}+y^{2}+4x-6y+9=0$


If matrix         $A=\begin{bmatrix}3 & -2 & 4 \\1 & 2 & -1\\0 & 1 & 1 \end{bmatrix}$       and

$A^{-1}=\frac{1}{k}adj\left(A\right)$,   then k is


A) 7

B) -7

C) 15

D) -11


The volume V and depth x of water in a vessel are connected by the relation $V=5x-\frac{x^{2}}{6}$ and the volume of water is increasing, at the rate of 5 cm3/sec, when x=2 cm. The rate at which the depth of water is increasing is

A) $\frac{5}{18}cm/sec$

B) $\frac{1}{4}cm/sec$

C) $\frac{5}{16}cm/sec$

D) None of these


The set of points of discontinuity of the function

$f(x)=\lim_{n \rightarrow \alpha}\frac{(2\sin x)^{2n}}{3^{n}-(2\cos x)^{2n}}$  is given by

A) R

B) ${n\pi\pm\frac{\pi}{3},n\epsilon I}$

C) ${n\pi\pm\frac{\pi}{6},n\epsilon I}$

D) None of these