Practice Questions

Q69.Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6) .Then the image of R in the plane P is (1) (6, 5, 2) (2) (6, 5, −2) (3) (4, 3, 2) (4) (3, 4, −2)

Q69.The shortest distance between the lines x−1 0 = y+1−1 = 1z and x + y + z + 1 = 0, 2 x −y + z + 3 = 0 is JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper (1) 1 (2) 1 √3 (3) 1 (4) 1 √2 2

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 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.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)

Q69.The distance of the point (1, −2, 3) from the plane x −y + z = 5 measured parallel to the line x2 = 3y = −6z is : (1) 7 (2) 1 5 (3) 1 (4) 7 7

Q69.The lines →r= (ˆi −ˆj) l(2ˆi ˆk) and →r= (2ˆi −ˆj) m(ˆi + ˆj −ˆk) (1) Do not intersect for any values of l and m (2) Intersect for all values of l and m (3) Intersect when l = 2 and m = 21 (4) Intersect when l = 1 and m = 2

Q69.Let →a, b and →c, be three unit vectors such that →a+ b +→c= 0. If λ =→a⋅ b + b ⋅→c+→c⋅→a and → → → → , is equal to. d =→a× b + b ×→c+→c×→a, then the order pair, (λ, d) 3 → , 3→a×→c) (1) ( 2 (2) (−3 2 , 3→c× b) 2 , 3b (3) ( 3 → (4) → ×→c) (−3 2 , 3→a× b)

Q69.Let D be the centroid of the triangle with vertices (3, −1) , (1, 3) and (2, 4) . Let P be the point of intersection of the lines x + 3y −1 = 10 and 3x −y + 1 = 0 . Then, the line passing through the points D and P also passes through the point: (1) (−9, −6) (2) (9,7) (3) (7,6) (4) (−9, −7)

Q69.The plane passing through the points (1, 2, 1), (2, 1, 2) and parallel to the line, 2x = 3y, z = 1 also passes through the point (1) (0, 6, −2) (2) (−2, 0, 1) (3) (0, −6, 2) (4) (2, 0, − 1)

Q69.If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is: (1) 965 (2) 965 211 210 (3) 945 (4) 945 210 211

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.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.A random variable X has the following probability distribution: X : 1 2 3 4 5 P(X) : k2 2k k 2k 5k2 Then, P(X > 2) is equal to: (1) 7 (2) 1 12 36 (3) 1 (4) 23 6 36

Q70.The probability that a randomly chosen 5- digit number is made from exactly two digits is : (1) 135 (2) 150 104 104 (3) 134 (4) 121 104 104

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

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.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.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.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.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.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.Let A and B be two independent events such that P(A) = 13 and P(B) = 16 . Then, which of the following is true? (1) P( BA ) = 32 (2) P( B'A ) = 13 = 14 (3) P( B'A' ) = 13 (4) P( (A∪B) A )

Q70.In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is : (1) 5 (2) 31 31 61 (3) 5 (4) 30 6 61