IIT-JEE Exam

Let the straight line x = b divides the area enclosed by y = (1 - x)^2, y = 0 and x = 0 into two parts R1(0 £ x
£ b) and R2(b £ x £ 1) such that R1 - R2 =1/4 then b equals

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IIT-JEE Other Question

A straight line L through the point (3, -2) is inclined at an angle 60° to the line sqrt(3x) + y = 1. If L also
intersects the x-axis, then the equation of L is Let f: R ® R be a function such that f(x + y) = f(x) + f(y), " x, y Î R. If f(x) is differentiable at x = 0, then
(A) f(x) is differentiable only in a finite interval containing zero
(B) f(x) is continuous " x Î R
(C) f¢(x) is constant " x Î R
(D) f(x) is differentiable except at finitely many points