question_answer

Match the statements of Column I with values of Column II:

Column I		Column II
a.	The number of polynomials f(x) with non-negative integer coefficients of degree \[\le \] 2, satisfying\[f(0)=0\,\,and\,\,\int\limits_{0}^{1}{f(x)\,\,dx=1}\]is _____.	p.	8
b.	The number of points in the interval \[\left[ -\sqrt{13},\sqrt{13} \right]\] at which \[f(x)=sin({{x}^{2}})+cos({{x}^{2}})\] attains, its maximum value is ________.	q.	2
c.	\[\int\limits_{-2}^{2}{\left( \frac{3{{x}^{2}}}{1+{{e}^{x}}} \right)}\,\,dx\] equals to ______.	r.	4
d.	\[\frac{\int\limits_{-1/2}^{1/2}{\cos 2x\,\,\log \left( \frac{1+x}{1-x} \right)\,\,dx}}{\int\limits_{0}^{1/2}{\cos 2x\,\,\log \left( \frac{1+x}{1-x} \right)}\,\,dx}\] equals to _______.	s.	0

Codes:

A)  \[a-p,\,\,b-r,\,\,c-q,\,\,d-s\]

B)  \[a-q,\,\,b-r,\,\,c-s,\,\,d-p\]

C)  \[a-r,\,\,b-q,\,\,c-s,\,\,d-p\]

D)  \[a-r,\,\,b-q,\,\,c-p,\,\,d-s\]

E)  None of these