Practice Questions

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.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.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.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.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.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.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

Q80.Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable 𝑥 to be the number of rotten apples in a draw of two apples, the variance of 𝑥 is 37 57 (1) (2) 153 153 47 40 (3) (4) 153 153

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.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.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.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.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.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.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

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 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 distinct real roots of the equation |x + 1||x + 3| −4|x + 2| + 5 = 0, is JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper

Q81.There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is _____

Q81.Let 𝑎, 𝑏, 𝑐 be the length of three sides of a triangle satisfying the condition 𝑎2 + 𝑏2𝑥2 −2𝑏𝑎+ 𝑐 𝑥+ 𝑏2 + 𝑐2 = 0. If the set of all possible values of 𝑥 is in the interval 𝛼, 𝛽, then 12𝛼2 + 𝛽2 is equal to _______.

Q81.Let α, β be the roots of the equation x2 −x + 2 = 0 with Im (α) >Im (β). Then α6 + α4 + β4 −5α2 is equal to

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

Q81.The sum of the square of the modulus of the elements in the set {z = a + ib : a, b ∈Z, z ∈C, |z −1| ≤1, |z −5| ≤|z −5i|} is ________