Wbjee

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)

The number of selection of n objects from 2n objects of which n are identical and the rest are different is 

(A) 2ⁿ 

(B) 2^{n – 1} 

(C) 2^{n – 1} 

(D) 2^{n –1} + 1

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

Let ρ be a relation defined on N, the set of natural numbers, as ρ = {(x, y) ∈ N × N : 2x + y = 41} Then 

(A) ρ is an equivalence relation 

(B) ρ is only reflexive relation 

(C) ρ is only symmetric relation 

(D) ρ is not transitive

Silver chloride dissolves in excess of ammonium hydroxide solution. The cation present in the resulting solution is 

(A) [Ag(NH₃)₆]⁺ 

(B) [Ag(NH₃)₄]⁺ 

(C) Ag⁺ 

(D) [Ag(NH₃)₂]⁺

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

The main reason that SiCl₄ is easily hydrolysed as compared to CCl₄ is that 

(A) Si-Cl bond is weaker than C-Cl bond. 

(B) SiCl₄ can form hydrogen bonds. 

(C) SiCl₄ is covalent. 

(D) Si can extend its coordination number beyond four.

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

(A) HNO₃ 

(B) H₂SO₄ 

(C) HCl 

(D) H₂CO₃

The correct order of reactivity for the addition reaction of the following carbonyl compounds with ethylmagnesium iodide is

(A) I > III > II > IV 

(B) IV > III > II > I 

(C) I > II > IV > III 

(D) III > II > I > IV

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