List IList IIP.The number of polynomials f(x) with non-negative integer coefficients of degree ≤2, satisfying f(0)=0 and 1∫0f(x) dx=1, is 1.8Q.The number of points in the interval [−√13,√13] at which f(x)=sin(x2)+cos(x2) attains its maximum value, is2.2R.2∫−23x21+ex dx equals 3.4S.⎛⎜⎜⎝ 1/2∫−1/2cos2xlog(1+x1−x) dx⎞⎟⎟⎠⎛⎜⎝ 1/2∫0cos2xlog(1+x1−x) dx⎞⎟⎠ equals 4.0Which of the following option is correct?

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1.	List IList IIP.The number of polynomials f(x) with non-negative integer coefficients of degree ≤2, satisfying f(0)=0 and 1∫0f(x) dx=1, is 1.8Q.The number of points in the interval [−√13,√13] at which f(x)=sin(x2)+cos(x2) attains its maximum value, is2.2R.2∫−23x21+ex dx equals 3.4S.⎛⎜⎜⎝ 1/2∫−1/2cos2xlog(1+x1−x) dx⎞⎟⎟⎠⎛⎜⎝ 1/2∫0cos2xlog(1+x1−x) dx⎞⎟⎠ equals 4.0Which of the following option is correct?
Answer» $\begin{matrix} L i s t I & L i s t I I P . & The number of polynomials f (x) with non-negative integer coefficients of degree \leq 2, satisfying f (0) = 0 and 1 \int 0 f (x) d x = 1, is & 1. & 8 Q . & The number of points in the interval [- \sqrt{13}, \sqrt{13}] at which f (x) = sin (x^{2}) + cos (x^{2}) attains its maximum value, is & 2. & 2 R . & 2 \int - 2 \frac{3 x^{2}}{1 + e^{x}} d x equals & 3. & 4 S . & \frac{⎛ ⎜⎜ ⎝ 1 / 2 \int - 1 / 2 cos 2 x log (\frac{1 + x}{1 - x}) d x ⎞ ⎟⎟ ⎠}{⎛ ⎜ ⎝ 1 / 2 \int 0 cos 2 x log (\frac{1 + x}{1 - x}) d x ⎞ ⎟ ⎠} equals & 4. & 0 \end{matrix}$ Which of the following option is correct?