Archives

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then

a) 18 > x b) x > 54 c) 54 > x > 36 d) 36 > x >18 Answer: b) x > 54 Solution: For the first... View Article

If the equation of transverse wave is y = 2sin (kx – 2t ), then the maximum particle velocity is

a) 4 unit b) 2 unit c) zero d) 6 unit Answer: a) 4 unit Solution: Given, y=2sin(kx−2t) Comparing with the standard... View Article

Two points on a travelling wave having frequency 600 Hz and velocity 300 ms^-1 are 60° out of phase, then the minimum distance between the two points is

a) 0.3 b) 0.17 c) 0.25 d) 0.4 Answer: b) 0.17 Solution: Velocity(V)= frequency(f) x wavelength(λ) λ = V/f = 300/600 =... View Article

The equation of a progressive wave is given by y =20 sin (600πt – 0.02πx). The frequency of the wave is

a) 330 Hz b) 342 Hz c) 365 Hz d) 660 Hz Answer: a) 330 Hz Solution: y=15 sin (660πt−0.02πx) Comparing with the... View Article

The speed of sound in gas of density ρ at a pressure p is proportional to

a) (p/ρ)2 b)(p/ρ)3/2 c) √(ρ/p) d) √(p/ρ) e) (ρ/p)2 Answer: c) √(ρ/p) Solution: The speed of the sound, v = √(γp/ρ) v ∝ √(p/ρ) p =... View Article

If a sound absorber attenuates the sound level by 20 dB. The factor by which the intensity decreases is

a) 1000 b) 10000 c) 10 d) 100 Answer: d) 100 Solution: Let the intensity of sound be l and l' Loudness of sound initially... View Article

A stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points P and Q are at a distance of 4 m and 9 m respectively from the source

The ratio of amplitudes of the waves at P and Q is a) 3/2 b) 4/9 c) 2/3 d) 9/4 Answer: 9/4 Solution: For an isotropic point source... View Article

In a 12 – storey house ten people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 and 5 people at different storeys. The number of ways they can do so if the lift does not stop at the second storey is

(a) 78 (b) 112 (c) 720 (d) 132 Solution: Leaving the ground floor and the second floor, there are 10 floors in which... View Article

Find the number of ways in which 16 identical things can be distributed among 4 persons, if each person gets at least 3 things.

(a) 15 (b) 25 (c) 35 (d) 40 Solution: Let a,b,c,d be the numbers of things distributed to each person such that... View Article

How many numbers with no more than three digits can be formed using only the digits 1 through 7 with no digit used more than once in a given number?

(a) 259 (b) 249 (c) 257 (d) 252 Solution: Numbers can be with 1 digit, 2 digits and 3 digits formed by 1, 2, 3, 4, 5,... View Article

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :

(a) 40 (b) 41 (c) 16 (d) 32 Solution: The committee should include at least 1 lady. at least 1 old man and at most 2 young men.... View Article

Four couples (husband and wife) decide to form a committee of four members. Find the number of different committees that can be formed in which no couple finds a place.

(a) 12 (b) 14 (c) 16 (d) 24 Solution: The number of committees of 4 gentlemen = 4C4 = 1 The number of committees of... View Article

There are three men and seven women taking a dance class. Number of different ways in which each man is paired with a woman partner, and the four remaining women are paired into two pairs each of two is

(a) 105 (b) 315 (c) 630 (d) 450 Solution: 3 women can be selected in 7C3 ways and can be paired with 3 men in 3!... View Article

Three boys and three girls are to be seated around a table, in a circle. Among them, the boy X does not want any girl neighbour and the girls Y does not want any boy neighbour. The number of such arrangements possible is

(a) 4 (b) 6 (c) 8 (d) None of these Solution: Consider the figure. 1, 2 and X are the three boys and 3, 4 and Y are three girls, Boy X will... View Article

The graph of the function y = f(x) is symmetrical about the line x = 2, then

(a) f(x) = -f(-x) (b) f(2+x) = f(2-x) (c) f(x) = f(-x) (d) f(x+2) = f(x-2) Solution: Consider a graph symmetric with respect to line x = 2... View Article

Which of the following statements is incorrect.

(a) x sgn x = |x| (b) |x| sgn x = x (c) x (sgn x) (sgn x) = x (d) |x| (sgn x)3 = |x| Solution: The signum function gives the sign for... View Article

Let f(x) = x/(1- x) and ‘a’ be a real number. If x₀ = a, x₁ = f(x₀), x₂ = f(x₁), x₃ = f(x₂)……. If x₂₀₀₉= 1, then the value of a is

(a) 0 (b) 2009/2010 (c) 1/2009 (d) 1/2010 Solution: Given f(x) = x/(1- x) x0 = a, x1 = f(x0) = f(a) = a/(1-a) x2 = f(x1) =... View Article

If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of F(x) = f(x) g(x/5) – g(x) f(x/3)

(a) 177 (b) 222 (c) 433 (d) 1155 Solution: Given F(x) = f(x) g(x/5) - g(x) f(x/3) Period of f(x) = 7 Therefore... View Article

Let f(x) = [x], where [x] denotes the greatest integer less than or equal to x. If a = √(2011²+2012), then the value of f(a) is equal to

If f and g are two functions defined as f(x) = x + 2, x ≤ 0; g (x) = 3, x ≥0, then the domain of f + g is

(a) {0} (b) [0, ∞) (c) (-∞, ∞) (d) (-∞, 0) Solution: f(x) = x + 2, x ≤ 0 g(x) = 3, x... View Article