Practice Questions

Q80.Let 𝑆= {1, 2, 3, 4, 5, 6} . Then the probability that a randomly chosen onto function 𝑔 from 𝑆 to 𝑆 satisfies 𝑔3 = 2 𝑔1 is : 1 1 (1) (2) 15 5 (3) 1 (4) 1 30 10

Q80.Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is: (1) 5 (2) 1 8 8 (3) 5 (4) 1 16

Q80.A student appeared in an examination consisting of 8 true-false type questions. The student guesses the answers with equal probability. The smallest value of n, so that the probability of guessing at least n correct answers is less than 1 , is : 2 (1) 5 (2) 6 (3) 3 (4) 4

Q80.Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is : JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper 1 1 (1) (2) 9 7 (3) 2 (4) 1 7 18

Q80.Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 −k), the probability that exactly one of B and C occurs is (1 −2k), the probability that exactly one of C and A occurs is (1 −k) and the probability of all A, B and C occur simultaneously is k2, where 0 < k < 1. Then the probability that at least one of A, B and C occur is: (1) greater than 1 but less than 1 (2) greater than 1 8 4 2 (3) greater than 1 but less than 1 (4) exactly equal to 1 4 2 2 + −4 = 0, x > 0, is

Q80.Let A denote the event that a 6 -digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3 . Then probability of event A is equal to : (1) 9 (2) 4 56 9 (3) 3 (4) 11 7 27

Q80.When a missile is fired from a ship, the probability that it is intercepted is 1 and the probability that the 3 missile hits the target, given that it is not intercepted, is 3 . If three missiles are fired independently from the 4 ship, then the probability that all three hit the target, is: (1) 3 (2) 1 8 27 (3) 1 (4) 3 8 4 JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper

Q80.A fair die is tossed until six is obtained on it. Let X be the number of required tosses, then the conditional probability P(X ⩾5 ∣X > 2) is : (1) 25 (2) 5 36 6 (3) 11 (4) 125 36 216

Q80.Let the equation of the plane, that passes through the point (1, 4, −3) and contains the line of intersection of the planes 3 x −2 y + 4 z −7 = 0 and x + 5 y −2 z + 9 = 0, be αx + βy + γz + 3 = 0, then α + β + γ is equal to : (1) −15 (2) 15 (3) −23 (4) 23

Q80.The probability that a randomly selected 2− digit number belongs to the set {n ∈N : (2n −2) is a multiple of 3} is equal to (1) 1 (2) 2 6 3 (3) 1 (4) 1 2 3

Q80.When a certain biased die is rolled, a particular face occurs with probability 16 −x and its opposite face occurs with probability 61 + x. All other faces occur with probability 16 . Note that opposite faces sum to 7 in any die. If 0 < x < 61 , and the probability of obtaining total sum = 7, when such a die is rolled twice, is 9613 , then the value of x is JEE Main 2021 (27 Aug Shift 1) JEE Main Previous Year Paper (1) 161 (2) 121 (3) 81 (4) 19 Z is the set of ∈R : x −2 > B = C = ∈R : x −4

Q80.The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is: (1) 65 (2) 65 28 27 (3) 35 (4) 135 27 29

Q80.Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be 21 and probability of occurrence of 0 at the odd place be 31 . Then the probability that 10 is followed by 01 is equal to : (1) 1 (2) 1 18 3 (3) 1 (4) 1 6 9

Q80.Let X be a random variable such that the probability function of a distribution is given by P(X = 0) = 21 , P(X = j) = 3j1 (j = 1, 2, 3, … , ∞). Then the mean of the distribution and P(X is positive and even ) respectively, are: (1) 3 and 1 (2) 3 and 1 8 8 4 8 (3) 3 and 1 (4) 3 and 1 4 9 4 16

Q80.Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0. 4096 and 0. 2048 respectively. Then the probability of getting exactly 3 successes is equal to : (1) 32 (2) 80 625 243 (3) 40 (4) 128 243 625

Q80.A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is : (1) 3 (2) 52 4 867 (3) 39 (4) 22 50 425 ¯

Q80.A vector →a has components 3p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, →a has components p + 1 and √10, then a value of p is equal to: (1) 1 (2) −54 (3) 4 (4) −1 5 JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper

Q80.A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is (1) 15 (2) 15 213 214 (3) 15 (4) 15 212 28

Q80.Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is: JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper (1) 1 (2) 1 66 11 (3) 1 (4) 2 9 11

Q81.If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10, 000 is equal to __________.

Q81.The number of the real roots of the equation (x + 1)2 + x −5 = 274 is ________.

Q81.Let z1, z2 be the roots of the equation z2 + az + 12 = 0 and z1, z2 form an equilateral triangle with origin. Then, the value of |a| is

Q81.If the least and the largest real values of 𝛼, for which the equation 𝑧+ 𝛼𝑧- 1 + 2𝑖= 0 𝑧∈𝐶 and 𝑖= √-1 has a solution, are 𝑝 and 𝑞 respectively; then 4𝑝2 + 𝑞2 is equal to_______.

Q81.If (2021)3762 is divided by 17, then the remainder is _______.

Q81.The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is . JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper 7 9 13 19