Practice Questions

Q88.Let S = {(−10 ab ); 100 elements in n=1Tn∩ is _____.

Q88.The number of matrices of order 3 × 3, whose entries are either 0 or 1 and the sum of all the entries is a prime number, is _______.

Q89.Let 𝜃 be the angle between the vectors →𝑎 and →𝑏, where →𝑎= 4, →𝑏= 3 and 𝜃∈𝜋 𝜋 Then 4, 3. 2 2 →𝑎- →𝑏× →𝑎+ →𝑏 + 4→𝑎· →𝑏 is equal to ______

Q89.Let an = ∫n−1(1 + x2 + x23 + … + xn−1n )dx for every {n ∈N : an ∈(2, 30)} is _________. , y(1) = 1. If for some

Q89.If 𝛼√2 + 𝛽√3, where 𝛼, 𝛽 are integers, then 𝛼+ 𝛽 is equal to ∫0 √1 + 𝑥2 + √1 + 𝑥23𝑑𝑥= 56 43 111

Q89.Let A1 = {(x, y) : |x| ≤y2, |x| + 2y ≤8} and A2 = {(x, y) : |x| + |y| ≤k}. If 27 (Area A1 ) = 5 (Area A2 ), then k is equal to

Q89.Let d be the distance between the foot of perpendiculars of the points P(1, 2 −1) and Q(2, −1, 3) on the plane −x + y + z = 1 . Then d2 is equal to ______. JEE Main 2022 (29 Jun Shift 1) JEE Main Previous Year Paper = 4 be a plane. Let P2 be another plane which passes through the points

Q89.Let y = y(x), x > 1 , be the solution of the differential equation (x −1) dxdy + 2xy = x−11 , with y(2) = 1+e42e4 . If y(3) = eα+1βeα . then the value of α + β is equal to ______. → → , then the value of is b 3(→c.→a)

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.The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is ______.

Q89.The integral 24 is equal to ______. π ∫ 0 (2+x2)√4+x4

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 + + = + + +

Q89.If 𝑙𝑖𝑚 lim ( 𝑛𝑘+ 1 ) + ( 𝑛𝑘+ 2 ) + … + 𝑛𝑘+ 𝑛= 33 . 1 1 · 1𝑘+ 2𝑘+ 3𝑘+ … + 𝑛𝑘, then the 𝑛𝑘+ 𝑛𝑘+ 𝑛→∞ 𝑛→∞ integral value of 𝑘 is equal to _____ . 𝑥- 2 𝑦- 1 𝑧 𝑥- 3 𝑦- 5 𝑧- 1

Q89.Let the solution curve y = y(x) of the differential equation (4 + x2)dy −2x(x2 + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to _____.

Q89.The value of the integral ∫ 0 2 60 sin(6x)sin x JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper

Q89.Let l be a line which is normal to the curve y = 2x2 + x + 2 at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to _____. → →

Q89.Let a curve y = y(x) pass through the point (3, 3) and the area of the region under this curve, above the x-axis y 3 and between the abscissae 3 and x(> 3) be ( x ) . If this curve also passes through the point (α, 6√10) in the first quadrant, then α is equal to _______. y+2

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 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.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.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 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 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.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