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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 Answer: 1) 250.5 and 249.5 Hz Solution:... 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: μ = 0.035/5.5 T = 77 N v... 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 tuning fork is n As the frequency of... 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... 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 interval -10 ≤ q ≤ 10. Then... 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 cards = 52C5 =... 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 blue balls be r and b, respectively. ... 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), (5, 5), (4, 6),... 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) = 1-0.8 = 0.2 P(A⋃B) =... View Article

There is a five-volume dictionary among 50 books arranged on a shelf in random order. If the volumes are not necessarily kept side by side, the probability that they occur in increasing order from left to right is

(a) 1/5! (b) 1/550 (c) 1/505 (d) None of these Solution: The total number of arrangement of 50 books = 50! The number of ways of... View Article

A bag contains 50 tickets numbered 1, 2, 3, …., 50 of which five are drawn at random and arranged in ascending order of magnitude (x₁ < x₂ < x₃ < x₄ < x₅). The probability that x₃ = 30 is

(a) 20C2/ 50C5 (b) 2C2/ 50C5 (c) 20C2 ×29C2/ 50C5 (d) none of these Solution: The number of ways of selecting 5 tickets out of 50 =... View Article

From past experience it is known that an investor will invest in security A with a probability of 0.6, will invest in security B with a probability 0.3 and will invest in both A and B with a probability of 0.2. What is the probability that an investor will invest neither in A nor in B?

(a) 0.7 (b) 0.28 (c) 0.3 (d) 0.4 Solution: Given P(A) = 0.6 P(B) = 0.3 P(A⋂B) = 0.2 P(A⋃B) = P(A) + P(B) -... View Article

If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25?

(a) 0 (b) 1/2 (c) 1 (d) 1/1296 Solution: Maximum value on a die = 6 When 4 dice are thrown, maximum sum of numbers... View Article

Three digits are chosen at random from 1, 2, 3, 4, 5, 6, 7, 8, and 9 without repeating any digit. What is the probability that the product is odd?

(a) 2/3 (b) 7/48 (c) 5/42 (d) 5/108 Solution: Total number of 3-digit numbers = 9 ×8 ×7 = 504 For the product to be odd,... View Article

A box contains 10 identical electronic components of which 4 are defective. If 3 components are selected at random from the box in succession, without replacing the units already drawn, what is the probability that two of the selected components are defective?

(a) 1/5 (b) 5/24 (c) 3/10 (d) 1/40 Solution: Total number of ways of selecting 3 components out of 10 = 10C3 Number... View Article

Let A, B, C be three events. If the probability of occurring exactly one event out of A and B is 1-a, out of B and C and A is 1-a and that of occurring three events simultaneously is a², then the probability that at least one out of A, B, C will occur is

(a) 1/2 (b) Greater than 1/2 (c) Less than 1/2 (d) Greater than 3/4 Solution: P (exactly one event out of A and B... View Article

An aircraft has three engines A, B, and C. The aircraft crashes if all three engines fail. The probabilities of failure are 0.03, 0.02, and 0.05 for engines A, B, and C respectively. What is the probability that the aircraft will not crash?

(a) 0.00003 (b) 0.90 (c) 0.99997 (d) 0.90307 Solution: Let P(A), P(B) and P(C) denotes the probabilities of failure of A,... View Article

Two numbers are successively drawn from the set U = {1, 2, 3, 4, 5, 6, 7, 8}, the second being drawn without replacing the first. The number of elementary events in the sample is:

(a) 64 (b) 56 (c) 32 (d) 14 Solution: U = {1, 2, 3, 4, 5, 6, 7, 8} n(U) = 8 Number of ways of selecting first... View Article

A machine has three parts, A, B, and C, whose chances of being defective are 0.02, 0.10, and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?

(a) 0.06 (b) 0.16 (c) 0.84 (d) 0.94 Solution: Let P(A), P(B), P(C) be the probability of parts A, B and C working... View Article

x₁, x₂, x₃, ……., x₅₀ are fifty real numbers such that x_r <x_r+1 for r = 1, 2, 3, …., 49. Five numbers out of these are picked up at random. The probability that the five numbers have x₂₀ as the middle number, is

(a) 20C2 ×30C2/50C5 (b) 30C2 ×19C2/50C5 (c) 19C2 ×31C3/50C5 (d) none of these Solution: n(S) = 50C5 n(E) = 30C2... View Article