Practice Questions

Q80.Let A and B be independent events such that P(A) = p, P(B) = 2p. The largest value of p, for which P (exactly one of A, B occurs) = 59 , is: (1) 4 (2) 1 9 5 (3) 5 (4) 2 12 9

Q80.When a missile is fired from a ship, the probability that it is intercepted is 1 and the probability that the 3 missile hits the target, given that it is not intercepted, is 3 . If three missiles are fired independently from the 4 ship, then the probability that all three hit the target, is: (1) 3 (2) 1 8 27 (3) 1 (4) 3 8 4 JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper

Q80.Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M appears at the fourth position in any such word is: JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper (1) 1 (2) 1 66 11 (3) 1 (4) 2 9 11

Q80.Let A denote the event that a 6 -digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3 . Then probability of event A is equal to : (1) 9 (2) 4 56 9 (3) 3 (4) 11 7 27

Q81.If the digits are not allowed to repeat in any number formed by using the digits 0, 2, 4, 6, 8, then the number of all numbers greater than 10, 000 is equal to __________.

Q81.The number of solutions of the equation log(x+1)(2x2 + 7x + 5) + log(2x+5)(x 1)2

Q81.If the least and the largest real values of 𝛼, for which the equation 𝑧+ 𝛼𝑧- 1 + 2𝑖= 0 𝑧∈𝐶 and 𝑖= √-1 has a solution, are 𝑝 and 𝑞 respectively; then 4𝑝2 + 𝑞2 is equal to_______.

Q81.There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is

Q81.The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is

Q81.If log3 2, log3(2x −5), log3(2x −72 ) are in an arithmetic progression, then the value of x is equal to _____.

Q81.The total number of two digit numbers ′n′, such that 3n + 7n is a multiple of 10 , is ___ .

Q81.Let z1 and z2 be two complex numbers such that arg(z1 −z2) = π4 and z1, z2 satisfy the equation |z −3| =Re (z). Then the imaginary part z1 + z2 is equal to

Q81.If 𝛼, 𝛽 are roots of the equation 𝑥2 + 5√2𝑥+ 10 = 0, 𝛼> 𝛽 and 𝑃𝑛= 𝛼𝑛- 𝛽𝑛 for each positive integer 𝑛, then the value of 𝑃17𝑃20 + 5√2𝑃17𝑃192 is equal to 𝑃18𝑃19 + 5√2𝑃18

Q81.The number of the real roots of the equation (x + 1)2 + x −5 = 274 is ________.

Q81.The number of real roots of the equation e4x −e3x −4e2x −ex + 1 = 0 is equal to

Q81.If A = {x 1}, {x ∈R : √x2 −3 > 1}, {x ⩾2} and all integers, then the number of subsets of the set (A ∩B ∩C)c ∩Z is _________.

Q81.Let λ ≠0 be in R. If α and β are the roots of the equation x2 −x + 2λ = 0, and α and γ are the roots of the equation 3x2 −10x + 27λ = 0, then βγλ is equal to ________. (2i)n

Q81.If for the complex numbers 𝑧 satisfying |𝑧- 2 - 2𝑖| ≤1, the maximum value of |3𝑖𝑧+ 6| is attained at 𝑎+ 𝑖𝑏, then 𝑎+ 𝑏 is equal to _____ .

Q81.Let z and w be two complex numbers such that w = zz −2z + 2, z−3iz+i = 1 and Re (w) has minimum value. Then, the minimum value of n ∈N for which wn is real, is equal to _______.

Q81.Let 1 , a and b be in G.P. and a1 , 1b , 6 be in A.P., where a, b > 0 . Then 72(a + b) is equal to _______ . 16

Q81.A point z moves in the complex plane such that arg( z+2z−2 ) = π4 , then the minimum value of z −9√2 −2i 2 is equal to

Q81.The number of 4-digit numbers which are neither multiple of 7 nor multiple of 3 is . JEE Main 2021 (31 Aug Shift 2) JEE Main Previous Year Paper 7 9 13 19

Q81.Let α and β be two real numbers such that α + β = 1 and αβ = −1. Let pn = (α)n + (β)n , pn−1 = 11 and pn+1 = 29 for some integer n ⩾1 . Then, the value of p2n is______. ¯

Q81.If (2021)3762 is divided by 17, then the remainder is _______.

Q81.The sum of all integral values of k(k ≠0) for which the equation x−12 − x−21 = k2 in x has no real roots, is_____.