List I List II P. Let y(x) = cos(3 cos –1 x), x ∈ [–1,1], x ≠ ± 2 3 . Then ) x ( y 1 ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + dx ) x ( dy x dx ) x ( y d ) 1 – x ( 2 2 2 equals 1. 1 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 → k a be the positi

Question

List I List II P. Let y(x) = cos(3 cos –1 x), x ∈ [–1,1], x ≠ ± 2 3 . Then ) x ( y 1 ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ + dx ) x ( dy x dx ) x ( y d ) 1 – x ( 2 2 2 equals 1. 1 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 → k a be the position vector of the point A k , k = 1,2, …, n. If ∑ = → −− + → ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × 1 – n 1 k 1 k k a a = ∑ = → −− + → ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ 1 – n 1 k 1 k k a a , then the minimum value of n is 2. 2 R. If the normal from the point P(h, 1) on the ellipse 6 x 2 + 3 y 2 = 1 is perpendicular to the line x + y = 8, then the value of h is 3. 8 S. Number of positive solutions satisfying the equation tan –1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + 1 x 2 1 + tan –1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + 1 x 4 1 = tan –1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 x 2 is 4. 9 P Q R S

Accepted Answer

4 3 2 1

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