Page 62 - ISC-12

4Jai Baba Ki ISC Mathematics – Class XII by Gupta–Bansal

4. Match the following two lists:

List-I List-II
√
3
−1
(P) Let y(x) = cos (3 cos x), x ∈ [−1, 1], x 6= ± . Then (1) 1
2
2
1 d y dy
2
(x − 1) + x equals
y(x) dx 2 dx

(Q) Let A 1 , A 2 , . . ., A n (n > 2) be the vertices of a regular (2) 2
− →
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

n−1 n−1
P − → −−→ P − → −−→
(a k × a k+1 ) = (a k · a k+1 ) , then the minimum

k=1 k=1
value of n is
(R) If the normal from the point P(h, 1) on the ellipse (3) 8
x 2 y 2
+ = 1 is perpendicular to the line x + y = 8, then
6 3
the value of h is

(S) Number of positive solutions satisfying the equation (4) 9

1 1 2
tan −1 + tan −1 = tan −1 is
2x + 1 4x + 1 x 2

(P) (Q) (R) (S)
(A) (4) (3) (2) (1)
(B) (2) (4) (3) (1)
(C) (4) (3) (1) (2)
(D) (2) (4) (1) (3)

[JEE 2014]