Practice Questions

Q90.The sum and product of the mean and variance of a binomial distribution are 82 . 5 and 1350 respectively. They the number of trials in the binomial distribution is JEE Main 2022 (29 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let the line x−3 7 = −1 = z−3−4 intersect the plane containing the lines x−41 = y+1−2 = 1z and 4ax −y + 5z −7a = 0 = 2x −5y −z −3, a ∈R at the point P(α, β, γ). Then the value of α + β + γ equals ______. JEE Main 2022 (27 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let 𝑃-2, - 1, 1 and 𝑄 17, 17, 17 be the vertices of the rhombus 𝑃𝑅𝑄𝑆. If the direction ratios of the diagonal 𝑅𝑆 are 𝛼, - 1, 𝛽, where both 𝛼 and $\beta$ are integers of minimum absolute values, then 𝛼2 + 𝛽2 is equal to JEE Main 2022 (28 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let y = y(x) be the solution of the differential equation dxdy = 4y3+2yx23xy2+x3 n ∈N, y(2) ∈[n −1, n), then n is equal to _______. JEE Main 2022 (25 Jul Shift 2) JEE Main Previous Year Paper

Q90.The line of shortest distance between the lines = = and = = makes an angle of 0 1 1 2 2 1 with the plane 𝑃: 𝑎𝑥- 𝑦- 𝑧= 0, 𝑎> 0. If the image of the point 1, 1, - 5 in the plane 𝑃 is 𝛼, 𝛽, 𝛾, sin-1√ 272 then 𝛼+ 𝛽- 𝛾 is equal to _____ . JEE Main 2022 (25 Jul Shift 1) JEE Main Previous Year Paper

Q90.Let the lines 𝐿1: →𝑟= 𝜆 ^𝑖+ 2 ^𝑗+ 3 ^𝑘, 𝜆∈𝑅 and 𝐿2: →𝑟= ^𝑖+ 3 ^𝑗+ ^𝑘+ 𝜇( ^𝑖+ ^𝑗+ 5 ^𝑘); 𝜇∈𝑅, intersect at the point 𝑆. If a plane 𝑎𝑥+ 𝑏𝑦- 𝑧+ 𝑑= 0 passes through 𝑆 and is parallel to the lines 𝐿1 and 𝐿2, then the value of JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper 𝑎+ 𝑏+ 𝑑 is equal to ______. JEE Main 2022 (25 Jun Shift 1) JEE Main Previous Year Paper

Q90.A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let X be the number of white balls, among the drawn balls. If σ2 is the variance of X , then 100σ2 is equal to JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper

Q90.Let S = {E, E2 … E8} be a sample space of raddom experiment such that P(En) = 36n for every n = 1, 2 … . 8. Then the number of elements in the set {A ⊂S : P(A) ≥45 } is _____. JEE Main 2022 (27 Jun Shift 2) JEE Main Previous Year Paper

Q90.The plane passing through the line 𝐿: 𝑙 𝑥- 𝑦+ 31 - 𝑙 𝑧= 1, 𝑥+ 2𝑦- 𝑧= 2 and perpendicular to the plane 3𝑥+ 2𝑦+ 𝑧= 6 is 3𝑥- 8𝑦+ 7𝑧= 4. If 𝜃 is the acute angle between the line 𝐿 and the 𝑦-axis, then 415 cos2𝜃 is equal to ______. JEE Main 2022 (26 Jul Shift 2) JEE Main Previous Year Paper

Q90.In an examination, there are 10 true-false type questions. Out of 10 , a student can guess the answer of 4 questions correctly with probability 3 4 and the remaining 6 questions correctly with probability 14 . If the JEE Main 2022 (24 Jun Shift 2) JEE Main Previous Year Paper probability that the student guesses the answers of exactly 8 questions correctly out of 10 is 27k , then k is 410 equal to JEE Main 2022 (24 Jun Shift 2) JEE Main Previous Year Paper

Q90.Let →a = ˆi −2ˆj + 3ˆk, b = ˆi + ˆj + ˆk and →cbe a vector such that →a× ( +→c) =→0 equal to _______. JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper

Q90.Let the mirror image of the point (a, b, c) with respect to the plane 3x −4y + 12z + 19 = 0 be (a −6, β, γ). If a + b + c = 5, then 7β −9γ is equal to ______. JEE Main 2022 (27 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let Q and R be two points on the line x+1 2 = 3 = z−12 at a distance √26 from the point P(4, 2, 7). Then the square of the area of the triangle PQR is ________. JEE Main 2022 (26 Jul Shift 1) JEE Main Previous Year Paper

Q61.The integer k, for which the inequality x2 −2(3k −1)x + 8k2 −7 > 0 is valid for every x in R is: (1) 4 (2) 2 (3) 3 (4) 0 JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper ¯¯

Q61.The number of pairs 𝑎, 𝑏 of real numbers, such that whenever 𝛼 is a root of the equation 𝑥2 + 𝑎𝑥+ 𝑏= 0, 𝛼2 - 2 is also a root of this equation, is : (1) 6 (2) 8 (3) 4 (4) 2

Q61.The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only is: (1) 77 (2) 82 (3) 42 (4) 35

Q61.Let n denote the number of solutions of the equation z2 + 3z = 0, where z is a complex number. Then the value of ∑∞k=0 nk1 is equal to (1) 1 (2) 34 (3) 32 (4) 2

Q61.Let 𝑆𝑛 be the sum of the first 𝑛 terms of an arithmetic progression. If 𝑆3𝑛= 3𝑆2𝑛, then the value of 𝑆4𝑛 is : 𝑆2𝑛 JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper (1) 6 (2) 4 (3) 2 (4) 8

Q61.The number of real solutions of the equation, x2 −|x| −12 = 0 is: (1) 2 (2) 3 (3) 1 (4) 4

Q61.The sum of 10 terms of the series 3 + 5 + 7 + … is : 12×22 22×32 32×42 (1) 143 (2) 99 144 100 (3) 1 (4) 120121

Q61.The equation arg( z+1z−1 ) = π4 represents a circle with: (1) centre at (0, 0) and radius √2 (2) centre at (0, 1) and radius 2 (3) centre at (0, −1) and radius √2 (4) centre at (0, 1) and radius √2 22

Q61.Let α = max{82 sin 3x ⋅44 cos 3x} and β = min sin 3x ⋅44 cos 3x}. If 8x2 + bx + c = 0 is a quadratic equation x∈R x∈R{82 whose roots are α1/5 and β1/5, then the value of c −b is equal to : (1) 42 (2) 47 (3) 43 (4) 50 JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper

Q61.If the real part of the complex number (1 −cos θ + 2i sin θ)−1 is 15 for θ ∈(0, π), then the value of the x dx is equal to: integral ∫θ0 sin JEE Main 2021 (20 Jul Shift 2) JEE Main Previous Year Paper (1) 1 (2) 2 (3) −1 (4) 0

Q61.Let α and β be the roots of x2 −6x −2 = 0. If an = αn −βn for n ⩾1, then the value of a10−2a83a9 is: (1) 1 (2) 3 (3) 2 (4) 4

Q61.If for x ∈(0, π2 ), log10 sin x + log10 cos x = −1 and log10(sin x + cos x) = 12 (log10 n −1), n > 0 , then the value of n is equal to : (1) 20 (2) 12 (3) 9 (4) 16