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# IIT-JEE-Mathematics-Paper2-2008

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8.     Let

.

Then, for an arbitrary constant C, the value of J - I equals.

9.     Let g(x)&nbs    Let g(x)  = log f(x) where f(x) is a twice differentiable positive function on (0, ∞) such that f(x + 1) = x f(x). Then, for N = 1, 2, 3, ......,

10. Suppose four distinct positive numbers a1, a2, a3, a4 are in G.P. Let
b1 = a1, b2 = b1 + a2, b3 = b2 + a3 and b4 = b3 + a4.

STATEMENT-1: The numbers b1, b2, b3, b4 are neither in A.P. nor in G.P.

and

STATEMENT-2: The numbers b1, b2, b3, b4 are in H.P.

(A)    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1.

(B)    Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for statement-1.

(C)    Statement-1 is True, Statement-2 is False

(D)    Statement-1 is False, Statement-2 is True

11.    Let a, b, c, p, q be real numbers. Suppose α, β are the roots of the equation x2 + 2px + q = 0 and α, 1/β are the roots of the equation ax2 + 2bx + c = 0, where β2 is not belongs to {-1, 0, 1}.

STATEMENT-1: (p2 - q)(b2 - ac) > 0

and

STATEMENT-2: b ¹ pa or c ¹ qa

(A)    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1.

(B)    Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for statement-1.

(C)    Statement-1 is True, Statement-2 is False

(D)    Statement-1 is False, Statement-2 is True

12.    Consider

L1 : 2x + 3y + p - 3 = 0

L2 : 2x + 3y + p + 3 = 0

where p is a real number, and C : x2 + y2 + 6x + 10y + 30 = 0

STATEMENT-1: If line L1 is a chord of circle C, then line L2 is not always a diameter of circle C.

and

STATEMENT-2: If line L1 is a diameter of circle C, then line L2 is not a chord of circle C.

(A)    Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1.

(B)    Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for statement-1.

(C)    Statement-1 is True, Statement-2 is False

(D)    Statement-1 is False, Statement-2 is True