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, LA = 80cm and LB=x cm respectively are used separately in a sonometer. The ratio of their densities (dA /dB ) 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
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
