Wbjee

Let f : [a, b] → R be such that f is differentiable in (a, b), f is continuous at x = a and x = b and moreover f(a) = 0 = f(b). Then 

(A) there exists at least one point c in (a, b) such that f'(c) = f(c) 

(B) f'(x) = f(x) does not hold at any point in (a, b) 

(C) at every point of (a, b), f'(x) > f(x) 

(D) at every point of (a, b), f'(x) < f(x)

A compound formed by elements X and Y crystallizes in the cubic structure, where X atoms are at the corners of a cube and Y atoms are at the centres of the body. The formula of the compound is : 

(A) XY 

(B) XY₂ 

(C) X₂Y₃ 

(D) XY₃

Let f : [a, b] → R be differentiable on [a, b] and k ∈ R. Let f(a) = 0 = f(b). Also let J(x) = f'(x) + kf(x). Then 

(A) J(x) > 0 for all x ∈ [a, b] 

(B) J(x) < 0 for all x ∈ [a, b] 

(C) J(x) = 0 has at least one root in (a, b) 

(D) J(x) = 0 through (a, b)

How the linear velocity ‘v’ of an electron in the Bohr orbit is related to its quantum number ‘n’?

(A) v ∝ 1/n

(B) v ∝ 1/n²

(C) v ∝ 1/√n

(D) v ∝ n

The intensity of a sound appears to an observer to be periodic. Which of the following can be the cause of it? 

(A) The intensity of the source is periodic. 

(B) The source is moving towards the observer. 

(C) The observer is moving away from the source. 

(D) The source is producing a sound composed of two nearby frequencies.

Which of the following is present in maximum amount in ‘acid rain’?

(A) HNO₃ 

(B) H₂SO₄ 

(C) HCl 

(D) H₂CO₃