Let f : R → R be a twice continuously differentiable function such that f(0) = f(1) = f'(0) = 0. Then

(A) f”(0) = 0

(B) f”(c) = 0 for some c ∈ R

(C) if c ≠ 0, then f ”(c) ≠ 0

(D) f'(x) > 0 for all x ≠ 0

From a collection of 20 consecutive natural numbers, four are selected such that they are not consecutive. The number of such selections is 

(A) 284 × 17 

(B) 285 × 17 

(C) 284 × 16 

(D) 285 × 16

The number (101)¹⁰⁰ – 1 is divisible by 

(A) 10⁴ 

(B) 10⁶ 

(C) 10⁸ 

(D) 10¹²

Which of the following statement(s) is/are true ? “Internal energy of an ideal gas ………………” 

(A) decreases in an isobaric process. 

(B) remains constant in an isothermal process. 

(C) increases in an isobaric process. 

(D) decreases in an isobaric expansion.

There is a small air bubble at the centre of a solid glass sphere of radius ‘r’ and refractive index ‘Ω‘. What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

(A) r

(B) r/μ

(C) r(1 – 1/μ)

(D) Zero

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

(A) HNO₃ 

(B) H₂SO₄ 

(C) HCl 

(D) H₂CO₃

On the occasion of Dipawali festival each student of a class sends greeting cards to others. If there are 20 students in the class, the number of cards send by students is 

(A) ²⁰C₂ 

(B) ²⁰P₂ 

(C) 2 × ²⁰C₂ 

(D) 2 × ²⁰P₂

Which of the set of oxides are arranged in the proper order of basic, amphoteric, acidic?

(A) SO₂, P₂O₅, CO 

(B) BaO, Al₂O₃, SO₂ 

(C) CaO, SiO₂, Al₂O₃ 

(D) CO₂, Al₂O₃, CO

On R, a relation ρ is defined by xρy if and only if x – y is zero or irrational. Then 

(A) ρ is equivalence relation 

(B) ρ is reflexive but neither symmetric nor transitive

(C) ρ is reflexive & symmetric but not transitive 

(D) ρ is symmetric & transitive but not reflexive

Which one of the following is a condensation polymer? 

(A) PVC 

(B) Teflon 

(C) Dacron 

(D) Polystyrene