26 + Interview Questions in GENERAL QA IN WBJEE Page 1 InterviewSolution

1.	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)
Answer» The correct option (A) there exists at least one point c in (a, b) such that f'(c) = f(c) Explanation: Let h(x) = e^–xf(x) h(a) = 0, h(b) = 0 h(x) is continuous and diff. by rolles theorem h'(c) = 0, c ∈ (a, b) e^–xf(x) + (–e^–x)f(x) = 0 e^–cf'(c) = e^–cf(c) f'(c) = f(c)

1.

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)

Answer»

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

Explanation:

Let h(x) = e^–xf(x) h(a) = 0,

h(b) = 0 h(x) is continuous and diff. by rolles theorem

h'(c) = 0, c ∈ (a, b)

e^–xf(x) + (–e^–x)f(x) = 0

e^–cf'(c) = e^–cf(c)

f'(c) = f(c)

Discussion

2.	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)
Answer» The correct option (C) J(x) = 0 has at least one root in (a, b) Explanation: Let g(x) = e^kx f(x) f(a) = 0 = f(b) by rolles theorem g'(c) = 0, c ∈ (a, b) g'(x) = e^kxf'(x) + ke^kxf(x) g'(c) = 0 e^kc(f'(c) + kf(c) = 0 ⇒ f'(c) + kf(c) = 0 for at least one c in (a, b)

2.

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)

Answer»

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

Explanation:

Let g(x) = e^kx f(x)

f(a) = 0 = f(b)

by rolles theorem

g'(c) = 0, c ∈ (a, b)

g'(x) = e^kxf'(x) + ke^kxf(x)

g'(c) = 0

e^kc(f'(c) + kf(c) = 0

⇒ f'(c) + kf(c) = 0 for at least one c in (a, b)

Discussion

3.	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
Answer» The correct option (D) Zero Explanation: All incident rays are normal to surface, therefore there will be no deviation in the refracting ray.

3.

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

Answer»

The correct option (D) Zero

Explanation:

All incident rays are normal to surface, therefore there will be no deviation in the refracting ray.

Discussion

4.	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
Answer» The correct option (A) v ∝ 1/n Explanation: v = ze²/2∈₀nh

4.

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

Answer»

The correct option (A) v ∝ 1/n

Explanation:

v = ze²/2∈₀nh

Discussion

5.	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.
Answer» The correct option (C) The central fringe will be white. Explanation: Δx = 0 at centre for all wavelengths.

5.

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.

Answer»

The correct option (C) The central fringe will be white.

Explanation:

Δx = 0 at centre for all wavelengths.

Discussion

6.	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
Answer» The correct option (B) ²⁰P₂ (C) 2 × ²⁰C₂ Explanation: Number of ways = ²⁰C₂× 2! = ²⁰P₂

6.

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

Answer»

The correct option (B) ²⁰P₂

(C) 2 × ²⁰C₂

Explanation:

Number of ways = ²⁰C₂× 2!

= ²⁰P₂

Discussion

7.	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]+
Answer» The correct option (D) [Ag(NH₃)₂]⁺ Explanation: Ag⁺ + NH₃ → [Ag(NH₃)₂]⁺ excess

7.

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]+

Answer»

The correct option (D) [Ag(NH₃)₂]⁺

Explanation:

Ag⁺ + NH₃ → [Ag(NH₃)₂]⁺

excess

Discussion

8.	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.
Answer» The correct option (D) Si can extend its coordination number beyond four. Explanation: In SiCl₄ vacant d–orbitals are present. So hydrolysed by co–ordination bond formation and Si expand its valency.

8.

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.

Answer»

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

Explanation:

In SiCl₄ vacant d–orbitals are present. So hydrolysed by co–ordination bond formation and Si expand its valency.

Discussion

9.	The number (101)100 – 1 is divisible by (A) 104 (B) 106 (C) 108 (D) 1012
Answer» The correct option (A) 10⁴ Explanation: (101)¹⁰⁰ – 1 = (100 + 1)¹⁰⁰– 1 = ¹⁰⁰C₀ . 100¹⁰⁰ + ¹⁰⁰C₁ . 100⁹⁹+ ..... + ¹⁰⁰C₉₉ . 100 + ¹⁰⁰C₁₀₀ . 1 – 1 = 10⁴ (¹⁰⁰C₀ . 100⁹⁶+ ...... + 1)

9.

The number (101)100 – 1 is divisible by (A) 104 (B) 106 (C) 108 (D) 1012

Answer»

The correct option (A) 10⁴

Explanation:

(101)¹⁰⁰ – 1

= (100 + 1)¹⁰⁰– 1

= ¹⁰⁰C₀ . 100¹⁰⁰ + ¹⁰⁰C₁ . 100⁹⁹+ ..... + ¹⁰⁰C₉₉ . 100 + ¹⁰⁰C₁₀₀ . 1 – 1

= 10⁴ (¹⁰⁰C₀ . 100⁹⁶+ ...... + 1)

Discussion

10.	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
Answer» The correct option (C) ⁿ⁺²C_{r + 2} Explanation: ⁿC_r+ ⁿC_r+1 + ⁿC_r+1 + ⁿC_r+2 = ⁿ⁺¹C_r+1 + ⁿ⁺¹C_r+2 = ⁿ⁺²C_r+2

10.

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

Answer»

The correct option (C) ⁿ⁺²C_{r + 2}

Explanation:

ⁿC_r+ ⁿC_r+1 + ⁿC_r+1 + ⁿC_r+2 = ⁿ⁺¹C_r+1 + ⁿ⁺¹C_r+2 = ⁿ⁺²C_r+2

Discussion

11.	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.
Answer» The correct option (B) remains constant in an isothermal process. Explanation: In isothermal process ΔU = 0 In isobaric expansion V ∝ T so ΔU increases.

11.

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.

Answer»

The correct option (B) remains constant in an isothermal process.

Explanation:

In isothermal process ΔU = 0

In isobaric expansion V ∝ T so ΔU increases.

Discussion

12.	The number of selection of n objects from 2n objects of which n are identical and the rest are different is (A) 2n (B) 2n – 1 (C) 2n – 1 (D) 2n –1 + 1
Answer» The correct option (A) 2ⁿ Explanation: ⁿC₀ + ⁿC₁ + ⁿC₂ …… + ⁿC_n = 2ⁿ

12.

The number of selection of n objects from 2n objects of which n are identical and the rest are different is (A) 2n (B) 2n – 1 (C) 2n – 1 (D) 2n –1 + 1

Answer»

The correct option (A) 2ⁿ

Explanation:

ⁿC₀ + ⁿC₁ + ⁿC₂ …… + ⁿC_n

= 2ⁿ

Discussion

13.	A proton of mass 'm' moving with a speed v (<< c, velocity of light in vacuum) completes a circular orbit in time 'T' in a uniform magnetic field. If the speed of the proton is increased to 2v, what will be time needed to complete the circular orbit?(A) √2T(B) T(C) T/√2(D) T/2
Answer» The correct option (B) T Explanation: T = 2mπ/qB T is independent of v.

13.

A proton of mass 'm' moving with a speed v (<< c, velocity of light in vacuum) completes a circular orbit in time 'T' in a uniform magnetic field. If the speed of the proton is increased to 2v, what will be time needed to complete the circular orbit?(A) √2T(B) T(C) T/√2(D) T/2

Answer»

The correct option (B) T

Explanation:

T = 2mπ/qB

T is independent of v.

Discussion

14.	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
Answer» The correct option (D) ρ is not transitive Explanation: ρ = {(x, y) ∈ N × N, 2x + y = 41} for reflexive relation x R x ⇒ 2x + x = 41 ⇒ x = 41/3 ∈ N for symmetric ⇒ x R y ⇒ 2x + y = 41 ≠ y R x (Not symmetric) for transitive xRy ⇒ 2x + y = 41 and yRz ⇒ 2y + z = 41, xRz (not transitive )

14.

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

Answer»

The correct option (D) ρ is not transitive

Explanation:

ρ = {(x, y) ∈ N × N, 2x + y = 41}

for reflexive relation x R x ⇒ 2x + x = 41 ⇒ x = 41/3 ∈ N

for symmetric ⇒ x R y ⇒ 2x + y = 41 ≠ y R x (Not symmetric)

for transitive xRy ⇒ 2x + y = 41 and yRz ⇒ 2y + z = 41, xRz (not transitive )

Discussion

15.	Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 – 4x – 6y + 9 = 0 changes to (A) x2 + y2 + 4 = 0 (B) x2 + y2 = 4 (C) x2 + y2 – 8x – 12y + 48 = 0 (D) x2 + y2 = 9
Answer» The correct option (B) x² + y² = 4 Explanation: x → x + 2, y → y + 3 ∴ (x + 2)² + (y + 3)² – 4(x + 2) – 6(y + 3) + 9 = 0 ⇒ x² + 4x + 4 + y² + 6y + 9 – 4x – 8 – 6y – 18 + 9 = 0 ⇒ x² + y² – 4 = 0

15.

Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 – 4x – 6y + 9 = 0 changes to (A) x2 + y2 + 4 = 0 (B) x2 + y2 = 4 (C) x2 + y2 – 8x – 12y + 48 = 0 (D) x2 + y2 = 9

Answer»

The correct option (B) x² + y² = 4

Explanation:

x → x + 2, y → y + 3

∴ (x + 2)² + (y + 3)² – 4(x + 2) – 6(y + 3) + 9 = 0

⇒ x² + 4x + 4 + y² + 6y + 9 – 4x – 8 – 6y – 18 + 9 = 0

⇒ x² + y² – 4 = 0

Discussion

16.	Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?(A) (n –1)d8ns2 (B) (n –1)d5ns2 (C) (n –1)d3ns2 (D) (n –1)d5ns1
Answer» The correct option (B) (n –1) d⁵ns² Explanation: (n – 1)d⁵ns² → [Mn] Mn show highest Oxidation state = +7

16.

Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?(A) (n –1)d8ns2 (B) (n –1)d5ns2 (C) (n –1)d3ns2 (D) (n –1)d5ns1

Answer»

The correct option (B) (n –1) d⁵ns²

Explanation:

(n – 1)d⁵ns² → [Mn]

Mn show highest Oxidation state = +7

Discussion

17.	Which one of the following is a condensation polymer? (A) PVC (B) Teflon (C) Dacron (D) Polystyrene
Answer» The correct option (C) Dacron Explanation: Dacron is a condensation of polymer of terephthalic acid and ethylene glycol.

17.

Which one of the following is a condensation polymer? (A) PVC (B) Teflon (C) Dacron (D) Polystyrene

Answer»

The correct option (C) Dacron

Explanation:

Dacron is a condensation of polymer of terephthalic acid and ethylene glycol.

Discussion

18.

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

Answer»

The correct option (B) BaO, Al₂O₃, SO₂

Explanation:

Basic	Amphoteric	acidic
BaO	Al₂O₃	SO₂

Discussion

19.	Which of the following is present in maximum amount in 'acid rain'?(A) HNO3 (B) H2SO4 (C) HCl (D) H2CO3
Answer» The correct option (B) H₂SO₄ Explanation: 2SO₂(g) + O₂(g) + 2H₂O(l) → H₂SO₄(aq.)

19.

Which of the following is present in maximum amount in 'acid rain'?(A) HNO3 (B) H2SO4 (C) HCl (D) H2CO3

Answer»

The correct option (B) H₂SO₄

Explanation:

2SO₂(g) + O₂(g) + 2H₂O(l) → H₂SO₄(aq.)

Discussion

20.	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
Answer» The correct option (C) ρ is reflexive & symmetric but not transitive Explanation: xRy ⇒ x – y is zero or irrational xRx ⇒ 0 ∴ reflective if xRy ⇒ x – y is zero or irrational ⇒ y – x is zero or irrational ∴ yRx symmetric xRy ⇒ x – y is 0 or irrational yRz ⇒ y – z is 0 or irrational then (x – y) + (y – z) = x – z may be rational ∴ it is not transitive

20.

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

Answer»

The correct option (C) ρ is reflexive & symmetric but not transitive

Explanation:

xRy ⇒ x – y is zero or irrational

xRx ⇒ 0 ∴ reflective

if xRy ⇒ x – y is zero or irrational

⇒ y – x is zero or irrational

∴ yRx symmetric xRy

⇒ x – y is 0 or irrational yRz

⇒ y – z is 0 or irrational then (x – y) + (y – z) = x – z may be rational

∴ it is not transitive

Discussion

21.	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
Answer» The correct option (B) f''(c) = 0 for some c ∈ R Explanation: f(x) is continuous and differentiable f(0) = f(1) = 0 ⇒ by rolles theorem f'(a) = 0 , a ∈ (0, 1) given f'(0) = 0 by rolles theorem f''(0) = 0 for some c, c ∈ (0, a)

21.

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

Answer»

The correct option (B) f''(c) = 0 for some c ∈ R

Explanation:

f(x) is continuous and differentiable

f(0) = f(1) = 0 ⇒ by rolles theorem

f'(a) = 0 , a ∈ (0, 1)

given f'(0) = 0 by rolles theorem

f''(0) = 0 for some c, c ∈ (0, a)

Discussion

22.	If f : R → R be defined by f(x) = ex and g : R → R be defined by g(x) = x2. The mapping gof : R → R be defined by (gof)(x) = g[f(x)] ∀ x ∈ R, Then (A) gof is bijective but f is not injective (B) gof is injective and g is injective (C) gof is injective but g is not bijective (D) gof is surjective and g is surjective
Answer» The correct option (C) gof is injective but g is not bijective Explanation: f(x) = e^x : R → R g(x) = x² : R → R g(f(x)) = g(e^x) = (e^x)² = e^2x ∀ x ∈ R clearly g(f(x)) is injective and g(x) is not injective

22.

If f : R → R be defined by f(x) = ex and g : R → R be defined by g(x) = x2. The mapping gof : R → R be defined by (gof)(x) = g[f(x)] ∀ x ∈ R, Then (A) gof is bijective but f is not injective (B) gof is injective and g is injective (C) gof is injective but g is not bijective (D) gof is surjective and g is surjective

Answer»

The correct option (C) gof is injective but g is not bijective

Explanation:

f(x) = e^x : R → R g(x) = x² : R → R

g(f(x)) = g(e^x) = (e^x)² = e^2x ∀ x ∈ R

clearly g(f(x)) is injective and g(x) is not injective

Discussion

23.	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
Answer» The correct option (A) I > III > II > IV Explanation: Reactivity order for nucleophilic addition reaction is H–CHO > CH₃–CHO > (CH₃)₂CO > [C(CH₃)₃]₂CO Reactivit ∝ 1/Steric crowding

23.

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

Answer»

The correct option (A) I > III > II > IV

Explanation:

Reactivity order for nucleophilic addition reaction is

H–CHO > CH₃–CHO > (CH₃)₂CO > [C(CH₃)₃]₂CO

Reactivit ∝ 1/Steric crowding

Discussion

24.	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.
Answer» The correct option (A) The intensity of the source is periodic. (D) The source is producing a sound composed of two nearby frequencies.

24.

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.

Answer»

The correct option

(A) The intensity of the source is periodic.

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

Discussion

25.	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
Answer» The correct option (A) 284 × 17 Explanation: 1, 2, 3, 4, .................. 20 there are 17 way for four consecutive number number ways = ²⁰C₄ – 17 = 285 × 17 – 17 = 284 × 17

25.

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

Answer»

The correct option (A) 284 × 17

Explanation:

1, 2, 3, 4, .................. 20

there are 17 way for four consecutive

number number ways = ²⁰C₄ – 17

= 285 × 17 – 17

= 284 × 17

Discussion

26.	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
Answer» The correct option (A) XY Explanation: X = 8 x 1/8 = 1 (at corner) Y = 1 × 1 = 1 (at body center) So formula of compound = XY

26.

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

Answer»

The correct option (A) XY

Explanation:

X = 8 x 1/8 = 1 (at corner)

Y = 1 × 1 = 1 (at body center)

So formula of compound = XY

Discussion

Explore topic-wise InterviewSolutions in .

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) &gt; 0 for all x ∈ [a, b] (B) J(x) &lt; 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

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.

The number of selection of n objects from 2n objects of which n are identical and the rest are different is (A) 2n (B) 2n – 1 (C) 2n – 1 (D) 2n –1 + 1

A proton of mass 'm' moving with a speed v (&lt;&lt; c, velocity of light in vacuum) completes a circular orbit in time 'T' in a uniform magnetic field. If the speed of the proton is increased to 2v, what will be time needed to complete the circular orbit?(A) √2T(B) T(C) T/√2(D) T/2

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

Without changing the direction of the axes, the origin is transferred to the point (2, 3). Then the equation x2 + y2 – 4x – 6y + 9 = 0 changes to (A) x2 + y2 + 4 = 0 (B) x2 + y2 = 4 (C) x2 + y2 – 8x – 12y + 48 = 0 (D) x2 + y2 = 9

Out of the following outer electronic configurations of atoms, the highest oxidation state is achieved by which one?(A) (n –1)d8ns2 (B) (n –1)d5ns2 (C) (n –1)d3ns2 (D) (n –1)d5ns1

Which one of the following is a condensation polymer? (A) PVC (B) Teflon (C) Dacron (D) Polystyrene

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

Which of the following is present in maximum amount in 'acid rain'?(A) HNO3 (B) H2SO4 (C) HCl (D) H2CO3

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 &amp; symmetric but not transitive (D) ρ is symmetric &amp; transitive but not reflexive

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) &gt; 0 for all x ≠ 0

The correct order of reactivity for the addition reaction of the following carbonyl compounds with ethylmagnesium iodide is(A) I &gt; III &gt; II &gt; IV (B) IV &gt; III &gt; II &gt; I (C) I &gt; II &gt; IV &gt; III (D) III &gt; II &gt; I &gt; IV

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

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)

A proton of mass 'm' moving with a speed v (<< c, velocity of light in vacuum) completes a circular orbit in time 'T' in a uniform magnetic field. If the speed of the proton is increased to 2v, what will be time needed to complete the circular orbit?(A) √2T(B) T(C) T/√2(D) T/2

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

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

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