Practice Questions

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

Q88.Let the tangents at the points P and Q on the ellipse x2 S is 2 + 4 = 1 meet at the point R(√2, 2√2 −2). If the focus of the ellipse on its negative major axis, then SP 2 + SQ2 is equal to π dx is equal to

Q88.Let f(x) = min{[x −1], [x −2], … , [x −10]} where [t] denotes the greatest integer ≤t. Then ∫100 f(x)dx + ∫100 (f(x))2dx + ∫100 |f(x)|dx is equal _______. to x > 0 and f(1) = √3 . If y = f(x)

Q88.Let S be the region bounded by the curves y = x3 and y2 = x. The curve y = 2|x| divides S into two regions of areas R1 and R2 . If max|R1, R2| = R2 , then R1R2 is equal to ______

Q88.Let y = y(x) be the solution of the differential equation dx 2 2 cos4 x−cos 2x with y( π4 ) = π232 . If y( π3 ) = π218 e−tan−1(α) , then the value of 3α2 is equal to ______.

Q88.If the area of the region {(x,

Q88.Let A = {1, a1, a2 … … a18, 77} be a set of integers with 1 < a1 < a2 < … . . < a18 < 77. Let the set A + A = {x + y : x, y ∈A} contain exactly 39 elements. Then, the value of a1 + a2 + … . . +a18 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.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 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.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

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

Q89.Let f be a differentiable function satisfying f(x) = 2 ∫√30 f( λ2x3 )dλ, √3 passes through the point (α, 6), then α 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 p and p + 2 be prime numbers and let p! (p + 1)! (p + 2)! Δ = (p + 1)! (p + 2)! (p + 3)! (p + 2)! (p + 3)! (p + 4)! Then the sum of the maximum values of α and β , such that pα and (p + 2)β divide Δ , is _______.

Q89.Let y = y(x) be the solution curve of the differential equation = 0, 0 < x < √π2 sin(2x2) loge(tan x2)dy + (4xy −4√2x sin(x2 −π4 ))dx , which passes through the point (√π6 , 1). Then y(√π3 ) is equal to _______. y−2

Q89.Let →𝑏= ^𝑖+ ^𝑗+ 𝜆 ^𝑘, 𝜆∈ℝ. If →𝑎 is a vector such that →𝑎× →𝑏= 13 ^𝑖- ^𝑗- 4 ^𝑘 and →𝑎· →𝑏+ 21 = 0, then →𝑏- →𝑎· ^𝑘- ^𝑗+ →𝑏+ →𝑎· ^𝑖- ^𝑘 is equal to 1 1

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

Q89.The largest value of 𝑎, for which the perpendicular distance of the plane containing the lines →𝑟= ^𝑖+ ^𝑗+ 𝜆 ^𝑖+ 𝑎 ^𝑗- ^𝑘and →𝑟= ^𝑖+ ^𝑗+ 𝜇- ^𝑖+ ^𝑗- 𝑎𝑘 from the point 2, 1, 4 is √3, is ______.

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 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 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 ______