Practice Questions

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

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

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.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.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.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.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.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.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 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.Let x0 be the point of local maxima of f(x) =→a⋅(→ ×→c), →c= 7ˆi −2ˆj + xˆk. Then the value of →a⋅→b +→b ⋅→c+→c⋅→a at x = x0 is: (1) −4 (2) −30 (3) 14 (4) −22 is equal to ______

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 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.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.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

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

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

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

Q71.The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.

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

Q71.The coefficient of x4 in the expansion of (1 + x + x2 + x3)6 in powers of x, is … . .

Q71.If the letters of the word ′ MOTHER′ be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ′ MOTHER′ is.....

Q71.The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is