Related InterviewSolutions

• 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)
• 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)
• 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
• 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
• If Young's double slit experiment is done with white light, which of the following statements will be true? (A) All the bright fringes will be coloured. (B) All the bright fringes will be white. (C) The central fringe will be white. (D) No stable interference pattern will be white.
• 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
• 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]+
• 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.
• The number (101)100 – 1 is divisible by (A) 104 (B) 106 (C) 108 (D) 1012
• If (2 ≤ r ≤ n), then nCr + 2.nCr+ 1 + nCr + 2 is equal to (A) 2. nCr + 2 (B) n+1Cr + 1 (C) n+2Cr + 2 (D) n+1C