JEE Advanced 2014 Paper 2 Mathematics Q18

Mathematics

Problem

Match List I with List II and select the correct option. Column I — P: The number of polynomials f(x)f(x) with non-negative integer coefficients of degree ≤2\le2, satisfying f(0)=0f(0)=0 and ∫01f(x) dx=1\int_0^1f(x)\,dx=1, is; Q: The number of points in [−13,13][-\sqrt{13},\sqrt{13}] at which f(x)=sin⁡(x2)+cos⁡(x2)f(x)=\sin(x^2)+\cos(x^2) attains its maximum value, is; R: ∫−223x21+ex dx\displaystyle\int_{-2}^{2}\frac{3x^2}{1+e^x}\,dx equals; S: ∫−1/21/2cos⁡2xlog⁡(1+x1−x) dx∫01/2cos⁡2xlog⁡(1+x1−x) dx\displaystyle\frac{\int_{-1/2}^{1/2}\cos2x\log\left(\frac{1+x}{1-x}\right)\,dx}{\int_0^{1/2}\cos2x\log\left(\frac{1+x}{1-x}\right)\,dx} equals Column Ii — 1: 88; 2: 22; 3: 44; 4: 00

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