Practice Questions

Q89.Let S = {1, 2, 3, 4} . Then the number of elements in the set { f : S × S →S : f is onto and f(a, b) = f(b, a) ≥a∀(a, b) ∈S × S } is

Q89.Let →𝑎 and →𝑏 be two vectors such that →𝑎+ →𝑏 = →𝑎 + 2 →𝑏 , →𝑎· →𝑏= 3 and →𝑎× →𝑏 = 75. Then →𝑎 is equal to ______.

Q89.Let a line having direction ratios 1, −4, 2 intersect the lines x−73 = y−1−1 = z+21 and x2 = y−73 = 1z at the points A and B. Then (AB)2 is equal to + + = + + +

Q90.If →a = 2ˆi + ˆj + 3ˆk, b = 3ˆi + 3ˆj + ˆk and →c= c1ˆi + c2ˆj + c3ˆk are coplanar vectors and →a⋅→c= 5, b ⊥→c, then 122(c1 + c2 + c3) is equal to ______. JEE Main 2022 (28 Jun Shift 1) JEE Main Previous Year Paper

Q90.Let S = (0, 2π) −{ π2 , 3π4 , 3π2 , 7π4 }. Let y = y(x), x ∈S , be the solution curve of the differential equation dy dx = 1+sin1 2x , y( π4 ) = 21 . If the sum of abscissas of all the points of intersection of the curve y = y(x) with the curve y = √2 sin x is kπ12 , then k is equal to _____. JEE Main 2022 (26 Jun Shift 1) JEE Main Previous Year Paper

Q90.If the probability that a randomly chosen 6 -digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96p is equal to _____. JEE Main 2022 (26 Jun 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 →a, b,→cbe three non-coplanar vectors such that →a× b = 4→c, b ×→c= 9→a and →c×→a = αb, α > 0 → If →a + b + →c = 36, then α is equal to _______. JEE Main 2022 (27 Jul 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 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.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

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.If the shortest distance between the lines→r= (−ˆi 3ˆk) λ(ˆi −aˆj) and →r (−ˆj 2ˆk) μ(ˆi −ˆj ˆk) is , then the integral value of a is equal to _____ √23 JEE Main 2022 (24 Jun Shift 1) 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.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 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.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.Let 𝑙1 be the line in 𝑥𝑦-plane with 𝑥 and 𝑦 intercepts 8 and 4√2 respectively, and 𝑙2 be the line in 𝑧𝑥-plane with 𝑥 and 𝑧 intercepts -1 and - 1 respectively. If 𝑑 is the shortest distance between the line 𝑙1 and 𝑙2, then 𝑑-2 8 6√3 is equal to _____. JEE Main 2022 (25 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.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 P1 :→r⋅(2ˆi + ˆj −3ˆk) (2, − 3, 2)(2, −2, −3) and (1, −4, 2). If the direction ratios of the line of intersection of P1 and P2 be 16 , α, β, then the value of α + β is equal to ______. JEE Main 2022 (29 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 the image of the point P(1, 2, 3) in the line L : x−63 = y−12 = z−23 be Q. let R(α, β, γ) be a point that divides internally the line segment PQ in the ratio 1 : 3 . Then the value of 22(α + β + γ) is equal to JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper

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 a line with direction ratios a, −4 a, −7 be perpendicular to the lines with direction ratios 3, −1, 2b and b, a, −2. If the point of intersection of the line x+1 = y−2 = 1z and the plane x −y + z = 0 is (α, β, γ), a2+b2 a2−b2 then α + β + γ is equal to ________. JEE Main 2022 (29 Jul Shift 1) JEE Main Previous Year Paper