Practice Questions

Q80.Two integers x and y are chosen with replacement from the set {0, 1, 2, 3, … . . , 10}. Then the probability that |x −y| > 5 is : (1) 30 (2) 62 121 121 (3) 60 (4) 31 121 121

Q80.If an unbiased dice is rolled thrice, then the probability of getting a greater number in the ith roll than the number obtained in the (i −1)th roll, i = 2, 3, is equal to (1) 3/54 (2) 2/54 (3) 1/54 (4) 5/54

Q80.A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is- 2 1 (1) (2) 9 9 (3) 2 (4) 1 27 27

Q80.A company has two plants A and B to manufacture motorcycles. 60% motorcycles are manufactured at plant A and the remaining are manufactured at plant B.80% of the motorcycles manufactured at plant A are rated of the standard quality, while 90% of the motorcycles manufactured at plant B are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If p is the probability that it was manufactured at plant B, then 126p is (1) 54 (2) 66 (3) 64 (4) 56

Q80.A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is (1) 5 (2) 1 6 6 (3) 5 (4) 6 11 11

Q80.Let the sum of two positive integers be 24 . If the probability, that their product is not less than 3 times their 4 greatest possible product, is m , where gcd(m, n) = 1, then n −m equals n (1) 10 (2) 9 (3) 11 (4) 8

Q80.Let P be the point of intersection of the lines x−21 = y−45 = z−21 and x−32 = y−23 = z−32 . Then, the shortest distance of P from the line 4x = 2y = z is (1) 5√14 (2) 3√14 7 7 (3) √14 (4) 6√14 7 7

Q80.There are three bags X, Y and Z . Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5 five-rupee coins and Bag Z contains 3 one-rupee coins and 6 five-rupee coins. A bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability, that it came from bag Y, is : (1) 1 (2) 1 4 2 (3) 5 (4) 1 12 3

Q80.A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is: (1) 2 (2) 2 5 7 1 1 (3) (4) 7 5

Q80.Bag 𝐴 contains 3 white, 7 red balls and bag 𝐵 contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn in white, is : 1 1 (1) (2) 4 9 (3) 1 (4) 3 3 10

Q80.An integer is chosen at random from the integers 1 , 2, 3, . . . . . , 50. The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is (1) 8 (2) 21 25 50 (3) 9 (4) 14 50 25 is equal to _______. +

Q80.The shortest distance between the lines x−34 = −11y+7 = z−15 and x−53 = y−9−6 = z+21 is: (1) 178 (2) 187 √563 √563 (3) 185 (4) 179 √563 √563

Q80.Let Ajay will not appear in JEE exam with probability 𝑝= 2 while both Ajay and Vijay will appear in the 7, exam with probability 𝑞= 15. Then the probability, that Ajay will appear in the exam and Vijay will not appear is: 9 18 (1) (2) 35 35 (3) 24 (4) 3 35 35

Q80.If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to exactly two addresses is: JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper (1) 18 (2) 12 25 25 (3) 6 (4) 4 25 25

Q80.Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is : (1) 5 (2) 5 18 16 (3) 4 (4) 7 17 18 1C0+1C1 2C0+2C1+2C2 3C0+3C1+3C2+3C3 , b = 1 +

Q80.The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are chosen from the set {1, 2, 3, 4, 5, 6, 7, 8} . The probability of this equation having repeated roots is : (1) 1 (2) 1 128 64 (3) 3 (4) 3 256 128

Q80.If the shortest distance between the lines x−41 = y+12 = −3z and x−λ2 = y+14 = z−2−5 is √56 , then the sum of all possible values of λ is : (1) 5 (2) 8 (3) 7 (4) 10

Q80.An urn contains 6 white and 9 black balls. Two successive draws of 4 balls are made without replacement. The probability, that the first draw gives all white balls and the second draw gives all black balls, is : (1) 5 (2) 5 256 715 3 3 (3) (4) 715 256 1

Q80.The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are from the set {1, 2, 3, 4, 5, 6}. If the probability of this equation having one real root bigger than the other is p, then 216 p equals : (1) 57 (2) 76 (3) 38 (4) 19

Q81.The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7 , when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to__________ JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper

Q81.Let x1, x2, x3, x4 be the solution of the equation 4x4 + 8x3 −17x2 −12x + 9 = 0 and (4 + x21) (4 + x22) (4 + x23) (4 + x24) = 12516 m. Then the value of m is

Q81.Let the set C = {(x, y) ∣x2 −2y = 2023, x, y ∈N}. Then ∑(x,y)∈C(x y)

Q81.Let 𝑃= 𝑧∈ℂ: 𝑧+ 2 −3𝑖≤1 and 𝑄= 𝑧∈ℂ: 𝑧1 + 𝑖+ ¯𝑧1 −𝑖≤−8. Let in 𝑃∩𝑄, 𝑧−3 + 2𝑖 be maximum and minimum at 𝑧1 and 𝑧2 respectively. If 𝑧12 + 2𝑧2 = 𝛼+ 𝛽√2, where 𝛼, 𝛽 are integers, then 𝛼+ 𝛽 equals __________

Q81.The number of real solutions of the equation \(x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0\) is ______.

Q81.The number of ways of getting a sum 16 on throwing a dice four times is______