List I P. Let y(x) = (3 ^ -1 x), x ∈ [−1, 1], x 3 2 . Then 1 y(x) (x^2 - 1) d^2y(x) dx^2 + x dy(x) dx equals...

Question

List I P. Let y(x) = (3 ^ -1 x), x ∈ [−1, 1], x 3 2 . Then 1 y(x) (x^2 - 1) d^2y(x) dx^2 + x dy(x) dx equals Q. Let A_1, A_2, , A_n (n > 2) be the vertices of a regular polygon of n sides with its centre at the origin. Let a_k be the position vector of the point A_k, k = 1, 2, …, n. If | _ k=1 ^ n-1 ( a_k a_ k+1 ) | = | _ k=1 ^ n-1 ( a_k a_ k+1 ) |, then the minimum value of n is R. If the normal from the point P(h, 1) on the ellipse x^2 6 + y^2 3 = 1 is perpendicular to the line x + y = 8, then the value of h is S. Number of positive solutions satisfying the equation ^ -1 ( 1 2x + 1 ) + ^ -1 ( 1 4x + 1 ) = ^ -1 ( 2 x^2 ) is List II 1. 1 2. 2 3. 8 4. 9

Accepted Answer

(A)

JEE Advanced 2014 Mathematics question

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