Q37 / 60 · JEE Advanced 2014 (Paper 2) · Mathematics

Match the following.
 
  List – I   List – II
(A) The number of polynomials f(x) with non – negative integer coefficients of degree ≤2, satisfying f(0) =0 and ∫01fxdx=1, is (P) 8
(B) The number of point in the interval - 13, 13 at which fx=sin⁡x2+cos⁡x2 attains its maximum value, is (Q) 2
(C) ∫-223x21+exdx  equals (R) 4
(D) ∫-1212cos⁡2x .log⁡1+x1-xdx∫012cos⁡2x .log⁡1+x1-xdx (S) 0

  • A
    a-r;b-p;c-s;d-q;
  • Correct answer
    B
    a-q;b-r;c-p;d-s;
  • C
    a-p;b-r;c-q;d-s;
  • D
    a-q;b-p;c-s;d-r;

Solution

P   fx=ax2+bx, ∫01fx dx=1
⇒   2a+3b=6
⇒   a, b≡0, 2 and 3, 0
Q  fx=2cos⁡x2-π4 
For maximum value, x2-π4=2nπ
⇒   x2=2nπ+π4
⇒   x=± π4, ± 9π4 as x ϵ -3, 13
R  ∫023x21+ex+3x21+e-xdx=∫023x2dx=8
S   ∫-1212cos⁡2x In 1+x1-xdx=0 as it is an odd function.

Hence, the correct answer is option: 'B'.

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