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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... 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... 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... 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)... 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... 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 =... 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... 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... View Article

Which of the following functions represent a wave?

1) (x – v t)2 2) In (x + v t) 3) \(\begin{array}{l}e^{-(x-vt)^{2}}\end{array} \) 4) 1/(x + vt) Answer: 3) \(\begin{array}{l}e^{-(x-vt)^{2}}\end{array} \) Solution:... 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 F... 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)... View Article

Two parts of a sonometer wire divided by a movable bridge differ in length by 0.2 cm and produce one beat per second when sounded together. The total length of wire is one metre, then the frequencies are 100 cm

1) 250.5 and 249.5 Hz 2) 230.5 and 229.5 Hz 3) 220.5 and 219.5 Hz 4) 210.5 and 209.5 Hz... View Article

A 5.5 metre length of the string has a mass of 0.035 kg. if the tension in the string is 77 N, the speed of a wave on the string is

1) 110 ms -1 2) 165 ms -1 3) 77 ms -1 4) 102 ms -1 Answer: 1) 110 ms -1 Solution:... View Article

A tuning fork produces 5 beats/sec. with a sonometer wire of lengths 40 cm and 44 cm, other factors remaining unchanged. The frequency of the tuning fork is

1) 80 Hz 2) 88 Hz 3) 160 Hz 4) 105 Hz Answer: 4) 105 Hz Solution: The frequency of the... View Article

In a sonometer, the waves produced are

1) longitudinal progressive 2) transverse progressive 3) transverse, stationary and polarised 4) transverse, stationary and unpolarised Answer: 3) transverse, stationary and... View Article

If an integer q be chosen at random in the interval -10 ≤ q ≤ 10, then the probability that the roots of the equation x² + qx + (¾)q + 1 = 0 are real is

(a) 2/3 (b) 15/21 (c) 16/21 (d) 17/21 Solution: Given that q is an integer chosen at random in the... View Article

What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards? [A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]

(a) 6/4165 (b) 4/4165 (c) 3/4165 (d) None of these Solution: Number of ways of selecting 5 cards from 52... View Article

A bag contains an assortment of blue and red balls. If two balls are drawn at random, the probability of drawing two red balls is five times the probability of drawing two blue balls. Furthermore, the probability of drawing one ball of each color is six times the probability of drawing two blue balls. The number of red and blue balls in the bag is

(a) 6, 3 (b) 3, 6 (c) 2, 7 (d) None of these Solution: Let the number of red and... View Article

Two dice are thrown. What is the probability that the sum of the faces equals or exceeds 10?

(a) 1/12 (b) 1/4 (c) 1/3 (d) 1/6 Solution: Total number of events = 36 Favourable events = {(6, 4),... View Article

Two events A and B are such that P(not B) = 0.8, P(A⋃B) = 0.5 and P(A|B) = 0.4. Then P(A) is equal to

(a) 0.28 (b) 0.32 (c) 0.38 (d) None of the above Solution: Given P(not B) = 0.8, So P(B) =... View Article

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