Mathematics

Problem

Match List I with List II. List I: A. The number of polynomials

f(x)

with non-negative integer coefficients of degree

\le 2

, satisfying

f(0)=0

and

\int_{0}^{1} f(x)\,dx = 1

, is B. The number of points in the interval

[-\sqrt{13}, \sqrt{13}]

at which

f(x)=\sin(x^2)+\cos(x^2)

attains its maximum value, is C.

\int_{-2}^{2} \frac{3x^2}{1+e^x}\,dx

equals D.

\left(\frac{\int_{-1/2}^{1/2} \cos 2x \log\left(\frac{1+x}{1-x}\right)\,dx}{\int_{0}^{1/2} \cos 2x \log\left(\frac{1+x}{1-x}\right)\,dx}\right)

equals List II: p. 8 q. 2 r. 4 s. 0 a. A-r, B-q, C-s, D-p b. A-q, B-r, C-s, D-p c. A-r, B-q, C-p, D-s d. A-q, B-r, C-p, D-s