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List-I \( \quad \) List-II
P. The number of polynomials \( \mathrm{f}(\mathrm{x}) \) with non-negative integer
\( 1.8 \)
coefficients of degree \( \leq 2 \), satisfying \( f(0)=0 \) and \( \int_{0}^{1} f(x) d x=1 \), is
Q. The number of points in the interval \( [-\sqrt{13}, \sqrt{13}] \) at which
2. 2 \( f(x)=\sin \left(x^{2}\right)+\cos \left(x^{2}\right) \) attains its maximum value, is
R. \( \quad \int_{-2}^{2} \frac{3 x^{2}}{\left(1+\mathrm{e}^{\mathrm{x}}\right)} \mathrm{dx} \) equals
3. 4
\( \mathrm{S} \). \( \frac{\left(\int_{\frac{-1}{2}}^{\frac{1}{2}} \cos 2 x \log \left(\frac{1+x}{1-x}\right) d x\right)}{\left(\int_{0}^{\frac{1}{2}} \cos 2 x \log \left(\frac{1+x}{1-x}\right) d x\right)} \) equals
Codes:
(C) \( \begin{array}{lllll}3 & 2 & 1 & 4\end{array} \)
(D) \( \begin{array}{llll}3 & 3 & 1 & 4\end{array} \)
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