Practice Questions

Q69.A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, – 2, 2 and 2, 3, –1 respectively. If, this plane also passes through the point (α, –3, 5), then α is equal to (1) 5 (2) −10 (3) 10 (4) −5

Q69.The mirror image of the point (1, 2, 3), in a plane is (−73 , −43 , −13 ). Which of the following points lies on this plane? (1) (1, 1, 1) (2) (1, −1, 1) (3) (−1, −1, 1) (4) (−1, −1, −1)

Q69.A plane P meets the coordinate axes at A, B and C respectively. The centroid of Δ ABC is given to be (1, 1, 2) . Then the equation of the line through this centroid and perpendicular to the plane P is : y−1 (1) x−1 2 = 1 = z−21 (2) x−11 = y−11 = z−22 y−1 (3) x−1 2 = 2 = z−21 (4) x−11 = y−12 = z−22

Q69.The plane which bisects the line joining the points (4, −2, 3) and (2, 4, −1) at right angles also passes through the point : (1) (0, −1, 1) (2) (4, 0, −1) (3) (4, 0, 1) (4) (0, 1, –1)

Q70.The probabilities of three events A, B and C are given P(A) = 0. 6, P(B) = 0. 4 and P(C) = 0. 5 . If P(A ∪B) = 0. 8, P(A ∩C) = 0. 3, P(A ∩B ∩C) = 0. 2, P(B ∩C) = β and P(A ∪B ∪C) = α , where 0. 85 ≤α ≤0. 95, then β lies in the interval : (1) [0. 35, 0. 36] (2) [0. 25, 0. 35] (3) [0. 20, 0. 25] (4) [0. 36, 0. 40]

Q70.Out of 11 consecutive natural number if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference is : (1) 15 (2) 5 101 101 (3) 5 (4) 10 33 99

Q70.If for some, α ∈R, the lines L1 : x+12 = y−2−1 = z−11 and L2 : x+2α = 5−αy+1 = z+11 are coplanar, then the line L2 passes through the point : (1) (10, 2, 2) (2) (2, –10, –2) (3) (10, –2, –2) (4) (–2, 10, 2)

Q70.If (a, b, c) is the image of the point (1, 2, −3) in the line, x+12 = y−3−2 = −1z , then a + b + c is equal to: (1) 2 (2) −1 (3) 3 (4) 1 JEE Main 2020 (05 Sep Shift 1) JEE Main Previous Year Paper

Q70.Box 1 contains 30 cards numbered 1 to 30 and Box 2 contains 20 cards numbered 31 to 50 . A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box 1 is (1) 2 (2) 8 3 17 (3) 4 (4) 2 17 5

Q70.Let E C denote the complement of an event E . Let E1, E2 and E3 be any pairwise independent events with P(E1) > 0 and P(E1 ∩E2 ∩E3) = 0 then P((E 2C ∩E 3C )/E1) is equal to (1) P(E 2C ) + P(E3) (2) P(E 3C ) −P(E 2C ) (3) P(E3) −P(E 2C ) (4) P(E 3C ) −P(E2) 1 n

Q70.A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared at least once is (1) 1 (2) 1 4 3 (3) 1 (4) 1 8 9 m n

Q70.An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5, otherwise X takes the value −1. Then the expected value of X, is (1) 3 (2) 1 16 8 (3) −316 (4) −18

Q70.Let A and B, be two events such that the probability that exactly one of them occurs is 2 , and the probability 5 that A or B, occurs is 1 , then the probability of both of them occur together is. 2 (1) 0.02 (2) 0.20 (3) 0.01 (4) 0.10

Q70.In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 4 1 . If the probability that at most two machines will be out of service on the same day is ( 43 ) 3k, then k is equal to (1) 17 (2) 17 8 4 (3) 17 (4) 4 2

Q70.In a box, there are 20 cards, out of which 10 are labelled as A and the remaining 10 are labelled as B . Cards are drawn at random, one after the other and with replacement, till a second A card is obtained. The probability that the second A card appears before the third B card is: (1) 9 (2) 11 16 16 (3) 13 (4) 15 16 16

Q71.The number of terms common to the two A.P.’s 3, 7, 11, … , 407 and 2, 9, 16, … , 709 is ____________.

Q71.Let (2x2 + 3x + 4) 10 = ∑20r=0 arxr. Then a13a7

Q71.If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x ⋅y is equal to

Q71.A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ___________

Q71.If ( 1−i1+i ) 2 = ( i−11+i ) 3 = 1, (m, n ∈N) then the greatest common divisor of the least values of m and n is 3 + 321 + 331 +….∞) is __________

Q71.The number of distinct solutions of the equation, log 1 |sin x| = 2 −log 1 |cos x| in the interval [0, 2π], is 2 2 ________

Q71.The least positive value of ‘ a ’ for which the equation, 2x2 + (a −10)x + 332 = 2a has real roots is ___________.

Q71.If the sum of the coefficients of all even powers of x in the product (1 + x + x2 + … + x2n)(1 −x + x2 −x3 + … + x2n) is 61, then n is equal to

Q71.For a positive integer n, (1 + x ) is expanded in increasing powers of x . If three consecutive coefficients in this expansion are in the ratio, 2 : 5 : 12, then n is equal to

Q71.The total number of 3−digit numbers whose sum of digits is 10, is ..........