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The ratio of frequencies of two waves travelling through the same medium is 2: 5. The ratio of their wavelengths will be ………

1) 2 : 5 2) 5 : 2 3) 3 : 5 4) 5 : 3 Answer: 2) 5: 2 Solution: Frequency ∝ 1/Wavelength (f1/f2) =... View Article

From a point source, if the amplitude of waves at a distance r is A, its amplitude at a distance 2r will be

1) A 2) 2A 3) A/2 4) A/4 Answer: 3) A/2 Solution: Intensity = Power/Area = P/ 4πr2 Therefore, Intensity ∝ 1/r2... View Article

A uniform wire of length L, diameter D and density p is stretched under a tension T. The correct relation between its fundamental frequency f, the length Land the diameter D is

1) f ∝ (1/LD) 2)f ∝ (1/L√D) 3) f ∝ (1/D2) 4) f ∝ (1/LD2) Answer: 1) f ∝ (1/LD) Solution: f =... View Article

The angle of elevation of the top of a tower from two places situated at distances 21m. and x m. from the base of the tower are 45⁰ and 60⁰ respectively. What is the value of x?

(a) 7 √3 (b) 7- √3 (c) 7+ √3 (d) 14 Solution: Consider triangle ABD. tan 45 = AD/BD 1 = AD/21 => AD = 21 tan 60 = AD/x => √3 =... View Article

The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances 49 m and 36 m are 43⁰ and 47⁰respectively. What is the height of the tower?

(a) 40 m (b) 42 m (c) 45 m (d) 47 m Solution: Let height of the tower AB be h. BD = 36 m BC = 49 m ∠D = 470 ∠C = 430 In triangle ABD,... View Article

A person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is 60⁰. When he retreats 20 feet from the bank, he finds the angle to be 30⁰. The breadth of the river in feet is

(a) 15 (b) 15√3 (c) 10√3 (d) 10 Solution: Let h be the height of tree PQ and breadth of river PS be x ft. Angle of elevation subtended by... View Article

A vertical pole consists of two parts, the lower part being one-third of the whole. At a point in the horizontal plane through the base of the pole and distance 20 meters from it, the upper part of the pole subtends an angle whose tangent is 1/2. The possible heights of the pole are

(a) 20 m and 20 3 m (b) 20 m and 60 m (c) 16 m and 48 m (d) None of these Solution: Let H be the height of the pole. tan α = H/60 tan θ... View Article

The maximum area of a right-angled triangle with hypotenuse h is

(a) h2/2√2 (b) h2/2 (c) h2/√2 (d) h2/4 Solution: Given that the hypotenuse of right-angled triangle is h. Let base = b... View Article

The distance of the point on y = x⁴ + 3x² + 2x which is nearest to the line y = 2x – 1 is

(a) 2/√5 (b) √5 (c) 1/√5 (d) 5√5 Solution: Given y = x4 + 3x2 + 2x dy/dx = 4x3 + 6x + 2 Slope of line y =... View Article

An experiment consists of flipping a coin and then flipping it a second time if head occurs. If a tail occurs on the first flip, then a six-faced die is tossed once. Assuming that the outcomes are equally likely, what is the probability of getting one head and one tail?

(a) 1/4 (b) 1/36 (c) 1/6 (d) 1/8 Solution: When a coin is tossed, we get head (H) or tail (T). If the head occurs, the... View Article

It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternately, is

(a) 5/12 (b) 5/36 (c) 19/27 (d) 5/27 Solution: Probability of A winning = 6/12 = 1/2 Probability of B winning = 4/12 =... View Article

In an examination, the probability of a candidate solving a question is 1/2. Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions?

(a) 1/64 (b) 3/16 (c) 1/2 (d) 13/16 Solution: The probability of a candidate solving a question = 1/2 Required probability =... View Article

The probabilities of two events A and B are given as P (A) = 0.8 and P (B) = 0.7. What is the minimum value of P(A⋂B)?

(a) 0 (b) 0.1 (c) 0.5 (d) 1 Solution: P(A) = 0.8 P(B) = 0.7 P(A) + P(B) - P(A⋂B) ≤ 1 0.8 + 0.7 -... View Article

Seven people seat themselves indiscriminately at round table. The probability that two distinguished persons will be next to each other is

(a) 1/3 (b) 1/2 (c) 1/4 (d) 2/3 Solution: We know that number of ways n people can be seated around a round table = (n-1)! 7 people... View Article

A coin is tossed. If a head is observed, a number is randomly selected from the set {1, 2, 3} and if a tail is observed, a number is randomly selected from the set {2, 3, 4, 5}. If the selected number be denoted by X, what is the probability that X = 3?

(a) 2/7 (b) 1/5 (c) 1/6 (d) 7/24 Solution: Probability of getting head = 1/2 Probability of getting tail = 1/2... View Article

When sound is produced in an aeroplane moving with a velocity of 200 ms^-1 horizontal, its echo is heard after 10√5s. If the velocity of sound in air is 300 ms^-1, the elevation of aircraft is

1) 250 m 2) 250√5 3) 12.50 m 4) 2500 m Answer: 2500 m Solution: V1 = 200 ms-1 V2 = 300 ms-1 t... View Article

Two strings A and B of lengths, L_A = 80cm and L_B=x cm respectively are used separately in a sonometer. The ratio of their densities (d_A /d_B ) is 0.81. The diameter of B is one-half that of A. If the strings have the same tension and fundamental frequency, the value of x is

1) 33 2) 102 3) 144 4) 130 Answer: 3) 144 Solution: f = (1/2l) √(T/μ) T = tension in the string μ = mass... View Article

Which of the following functions represent a wave?

1) (x – v t)2 2) In (x + v t) 3) 4) 1/(x + vt) Answer: 3) Solution: Option 3 is correct because its value is... View Article

Fundamental frequency of a sonometer wire is n. If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is

1) 2n/√2 2)n/2√2 3) √2n 4) n/4 Answer: 4) n/4 Solution: Fundamental frequency of a sonometer wire is given by... View Article

A pipe closed at one end produces a fundamental note of 412 hz. It is cut into two pieces of equal length. The fundamental frequencies produced in the two pieces are

1) 206 hz,412 hz 2) 824 hz, 1648 hz 3) 412 hz, 824 hz 4) 206 hz, 824 hz Answer: 2) 824 hz, 1648 hz Solution: As the pipe... View Article