Practice Questions

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.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.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 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.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.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.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.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.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.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

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 least positive value of ‘ a ’ for which the equation, 2x2 + (a −10)x + 332 = 2a has real roots 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.Let (2x2 + 3x + 4) 10 = ∑20r=0 arxr. Then a13a7

Q71.The number of words (with or without meaning) that can be formed from all the letters of the word ′′LETTER′′ in which vowels never come together 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.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 number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

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