P. The number of polynomials $f(x)$ with non-negative integer coefficients of degree $\leq 2$, satisfying $f(0) = 0$ and $\int_{0}^{1} f(x)\,dx = 1$, is
1. 8
Q. 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
2. 2
R. $\int_{-2}^{2} \frac{3x^2}{1+e^x}\,dx$ equals
3. 4
S. $\dfrac{\displaystyle\int_{-\frac{1}{2}}^{\frac{1}{2}} \cos 2x \log\left(\frac{1+x}{1-x}\right)dx}{\displaystyle\int_{0}^{\frac{1}{2}} \cos 2x \log\left(\frac{1+x}{1-x}\right)dx}$ equals
4. 0
P Q R S (A) 3241 (B) 2341 (C) 3214 (D) 2314
\begin{center}
\begin{tabular}{|l|l|}
\hline
List I & List II \\
\hline
P. The number of polynomials $f(x)$ with non-negative integer coefficients of degree $\leq 2$, satisfying $f(0) = 0$ and $\int_{0}^{1} f(x)\,dx = 1$, is & 1. 8 \\
\hline
Q. 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 & 2. 2 \\
\hline
R. $\int_{-2}^{2} \frac{3x^2}{1+e^x}\,dx$ equals & 3. 4 \\
\hline
S. $\dfrac{\displaystyle\int_{-\frac{1}{2}}^{\frac{1}{2}} \cos 2x \log\left(\frac{1+x}{1-x}\right)dx}{\displaystyle\int_{0}^{\frac{1}{2}} \cos 2x \log\left(\frac{1+x}{1-x}\right)dx}$ equals & 4. 0 \\
\hline
\end{tabular}
\end{center}
P Q R S\\
(A) 3241\\
(B) 2341\\
(C) 3214\\
(D) 2314