The c.d. f  F(x) associated  with p.d.f.

$f(x) =3(1-2x^{2})$. If  0 < x <1. is  $k\left( x-\frac{2x^{3}}{k}\right)$  , then value of k is 

A) 3

B) $\frac{1}{3}$

C) 1

D) $\frac{1}{6}$


 The negation of the statement pattern $\sim p \vee (q\rightarrow\sim r)$  is

A) $p\wedge (q\wedge r)$

B) $\sim p\wedge (q\wedge r)$

C) $p \vee (q\wedge r)$

D) $p \rightarrow (q\wedge \sim r)$


 The quadratic  equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is

A) $x^{2}+68x+256=0$

B) $x^{2}+68x-256=0$

C) $x^{2}-68x+256=0$

D) $x^{2}-68x-256=0$


$\int_{0}^{1} \tan^{-1}\left(\frac{2x-1}{1+x-x^{2}}\right)dx=$

A) 2

B) 1

C) 0

D) 4


 With usual notations, if the angles A,B,C of a  $\triangle$ABC  are in AP  and b:c= $\sqrt{3}:\sqrt{2}$

A) $75^{0}$

B) $55^{0}$

C) $35^{0}$

D) $45^{0}$