12345>>
1.

If A and B are events having probabilities P(A)=0.6 , P(B)=0.4  and  $P(A\cap B)=0$ , then probability that neither  A nor B occurs is

A) $\frac{1}{4}$

B) 1

C) $\frac{1}{2}$

D) 0

2.

If the line x-y=-4K is a tangent  to the parabola $y^{2}=8x$ at P, then the perpendicular distance of normal at P from (K,2K) is

A) $\frac{5}{2\sqrt{2}}$

B) $\frac{7}{2\sqrt{2}}$

C) $\frac{9}{2\sqrt{2}}$

D) $\frac{1}{2\sqrt{2}}$

3.

The lengths of the sides  of a triangle are13,14 and 15. If R and r repectively  denote circumradius and inradius of that  triangle , then  8R+r=

A) 84

B) $\frac{65}{8}$

C) 4

D) 69

4.

The number of solutions of $\cos 2 \theta=\sin \theta$ in $(0,2\pi)$ is

A) 4

B) 3

C) 2

D) 5

5.

If the pair of straight  lines xy-x-y+1=0  and the line x+ay-3=0 are concurrent, then the acute angle between  the pair of lines

$ax^{2}-13xy-7y^{2}+x+23y-6=0$ is

A) $\cos^{-1}\left(\frac{5}{\sqrt{218}}\right)$

B) $\cos^{-1}\left(\frac{1}{\sqrt{10}}\right)$

C) $\cos^{-1}\left(\frac{5}{\sqrt{173}}\right)$

D) $\cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$

12345>>