Practice Questions

Q79.Let (α, β, γ) be the image of the point (8, 5, 7) in the line x−12 = y+13 = z−25 . Then α + β + γ is equal to : (1) 16 (2) 20 (3) 14 (4) 18

Q79.Let the line L intersect the lines x −2 = −y = z −1, 2(x + 1) = 2(y −1) = z + 1 and be parallel to the line y−1 x−2 3 = 1 = z−22 . Then which of the following points lies on L? (1) (−13 , 1, −1) (2) (−13 , −1, 1) (3) (−13 , 1, 1) (4) (−13 , −1, −1)

Q79.Let 𝑃 and 𝑄 be the points on the line = = which are at a distance of 6 units from the point 8 2 2 𝑅( 1, 2, 3 ) . If the centroid of the triangle 𝑃𝑄𝑅 is 𝛼, 𝛽, 𝛾, then 𝛼2 + 𝛽2 + 𝛾2 is: (1) 26 (2) 36 (3) 18 (4) 24

Q79.Let d be the distance of the point of intersection of the lines x+63 = 2y = z+11 and x−74 = y−93 = z−42 from the point (7, 8, 9) . Then d2 + 6 is equal to : (1) 69 (2) 78 (3) 72 (4) 75

Q79.If the shortest distance between the lines x−λ 2 = y−43 = z−34 and x−24 = y−46 = z−78 is √2913 , then a value of λ is : (1) -1 (2) −1325 (3) 13 (4) 1 25

Q79.For λ > 0, let θ be the angle between the vectors →a = ^i + λ^j −3^k and →b = 3^i −^j + 2^k. If the vectors →a + →b and →a −→b are mutually perpendicular, then the value of (14 cos θ)2 is equal to (1) 50 (2) 40 (3) 25 (4) 20 JEE Main 2024 (04 Apr Shift 2) JEE Main Previous Year Paper

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.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.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.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.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.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.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.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.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.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.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.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 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

Q81.The number of real solutions of the equation x|x + 5| + 2|x + 7| −2 = 0 is_________

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

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 lines 𝐿1, 𝐿2, . .. , 𝐿20 are distinct. For 𝑛= 1, 2, 3, . .. , 10 all the lines 𝐿2𝑛−1 are parallel to each other and all the lines 𝐿2𝑛 pass through a given point 𝑃. The maximum number of points of intersection of pairs of lines from the set 𝐿1, 𝐿2, . .. , 𝐿20 is equal to: