Match the following: List-I List-II (P) Let y(x)=\cos(3cos^{-2}x),x∊[-1,1],x\neq\pm \sqrt3/2 Then1/{y(x)}\{(x^2-1)\frac{d^2y(x)}{dx^2}+x\frac{dy(x)}{dx}\}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 center at the origin, Let a_k^{-} be the position vector of the point A_k,k=1,2,...n.If |\sum^{n-1}_{k=1}(a_k^{-}\timesa^{-}_{k+1})|=|\sum^{n-1}_{k=1}(a_k^{-}·a^{-}_{k+1})|,then the minimum value of n is (2) 2 (R) If the normal form 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 (3) 8 (S) Number of positive solution satisfying the equation \tan^{-1}(1/{2x+1})+\tan^{-1}(1/{4x+1})=\tan^{-1}(2/x^2) is (4) 9 [JEE Adv 2014 P2]

Inverse Trigonometric Functions

Section: Mathematics

Question : 10 of 14

Marks: +1, -0

Match the following:

List-I

List-II

(P)

Let y(x)=cos(3cos−2x),x∊[−1,1],x≠±

√3

Then

y(x)

{(x2−1)

d2y(x)

dx2

dy(x)

}equals

(1)

(Q)

Let A1,A2,...An(n>2) be the vertices of a regular polygon of n sides with its center at the origin, Let

−

be the position vector of the point Ak,k=1,2,...n.If |∑k=1n−1(

−

k+1)|=|∑k=1n−1(

−

k+1)|,then the minimum value of n is

(2)

(R)

If the normal form the point P(h,1) on the ellipse

=1 is perpendicular to the line x+y=8, then the value of h is

(3)

(S)

Number of positive solution satisfying the equation tan−1(

2x+1

)+tan−1(

4x+1

)=tan−1(

) is

(4)

[JEE Adv 2014 P2]

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