Practice Questions

Q72.If Cr ≡25Cr and C0 + 5 ∙C1 + 9 ∙C2 + … + (101) ∙C25 = 225 ∙k, then k is equal to ____________.

Q72.Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A →B ∣2 ∈f(A) and f is not one-one } is …

Q73.If the variance of the following frequency distribution: JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper Class: 10 −20 20 −30 30 −40 Frequency: 2 x 2 is 50, then x is equal to _______

Q73.Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy2 + x2y, for all real x and y. If lim f(x)x = 1, then f ′(3) is equal to : x→0

Q73.If y = ∑6k=1 k cos−1{ 53 cos kx −45 sin kx} then dxdy at x = 0 is

Q73. sin( x1 ) + 5x2 , x < 0 ⎧ x5 Let f : R →R be defined as f(x) = 0 , x = 0 . The value of λ for which f ′′(0) exists, ⎨ 1 ) + λx2 , x > 0 ⎩x5 cos( x is___.

Q74.Let [t] denote the greatest integer less than or equal to t. Then the value of ∫21 |2x −[3x]|dx is

Q74.If the vectors, p = (a + 1)ˆi + aˆj + aˆk,→q = aˆi + (a + 1)ˆj + aˆk and →r= aˆi + aˆj + (a + 1)ˆk(a ∈R) are 2 2 coplanar and q = 0 , then the value of λ is ________ 3(→p.→q) −λ→r×→

Q74.Let {x} and [x] denote the fractional part of x and the greatest integer ≤x respectively of a real number x. if n > 1) are three consecutive terms of a G.P. then n is equal ∫n0 {x}dx, ∫n0 [x]dx and 10(n2 −n), (n ∈N, to__ 2 2 2 , is equal to : + ˆj × × + ˆk × ×

Q74.Let f(x) = x ⋅[ x2 ], for −10 < x < 10, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f(x) is equal to

Q74.Let a line y = mx(m > 0), intersect the parabola, y2 = x, at a point P, other than the origin. Let the tangent to it a P , meet the x-axis at the point Q. If area (ΔOPQ) = 4 square unit, then m is equal to

Q74.The number of all 3 × 3 matrices A, with entries from the set {−1, 0, 1} such that the sum of the diagonal elements of AAT is 3, is ___________.

Q75.Let a plane P contain two lines →r= ˆi + λ(ˆi ˆj), λ ∈R and→r= −ˆj + μ(ˆj −ˆk), the foot of the perpendicular drawn from the point M(1, 0, 1) to P, then 3(α + β + γ) equals ....... JEE Main 2020 (03 Sep Shift 2) JEE Main Previous Year Paper

Q75.In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is . . . . . JEE Main 2020 (05 Sep Shift 2) JEE Main Previous Year Paper

Q75.If the distance between the plane, 23x −10y −2z + 48 = 0 and the plane containing the lines x+1 2 = y−34 = z+13 and x+32 = y+26 = z−1λ (λ ∈R) is equal to √633k , then k is equal to ____________. JEE Main 2020 (09 Jan Shift 2) JEE Main Previous Year Paper

Q75.Let S be the set of points where the function , f(x) = |2 −|x −3|, x ∈R, is not differentiable. Then ∑x∈S f(f(x)) is equal to JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper

Q75.Let f(x), be a polynomial of degree 3 , such that f(−1) = 10, f(1) = −6, f(x), has a critical point at x = −1 and f′(x), has a critical point at x = 1. Then f(x), has local minima at x = JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q61.If m is chosen in the quadratic equation (m2 + 1)x2 −3x + (m2 + 1)2 = 0 such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is: (1) 4√3 (2) 10√5 (3) 8√3 (4) 8√5

Q61.Consider the quadratic equation (c −5)x2 −2cx + (c −4) = 0, c ≠5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0, 2) and its other root lies in the interval (2, 3). Then the number of elements in S is (1) 11 (2) 12 (3) 18 (4) 10

Q61.The number of real roots of the equation 5 + 2𝑥- 1 = 2𝑥2𝑥- 2 is : (1) 2 (2) 3 (3) 1 (4) 4 π

Q61.If λ be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m −4)x + 2 = 0, then the least value of m for which λ + λ1 = 1, is : JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) 2 −√3 (2) −2 + √2 (3) 4 −2√3 (4) 4 −3√2 α −

Q61.If α and β are the roots of the quadratic equation x2 + xsinθ −2sinθ = 0, θ ∈(0, 2π ) , then α12+β12 is equal to : (α−12+β−12).(α−β)24 (1) 26 (2) 212 (sinθ+8)12 (sinθ−4)12 (3) 212 (4) 212 (sinθ+8)12 (sinθ−8)6 , has magnitude , then −z is equal to:

Q62.If 𝑧 and 𝜔 are two complex numbers such that 𝑧𝜔= 1 and 𝑎𝑟𝑔𝑧- 𝑎𝑟𝑔( 𝜔) = 2, then: (1) 𝑧¯ω = 1 - 𝑖 (2) ¯𝑧𝜔= 𝑖 √2 (3) 𝑧¯ω = -1 + 𝑖 (4) ¯𝑧ω = - 𝑖 √2

Q64.Let Sn = 1 + q + q2 + … . +qn and Tn = 1 + ( q+12 ) ( q+12 ) ( q+12 ) and q ≠1. If 101C1 + 101C2 ⋅S1 + … . +101C101 ⋅S100 = αT100, then α is equal to : (1) 299 (2) 202 (3) 200 (4) 2100

Q65.Let 𝑎1, 𝑎2, … , 𝑎30 be an A.P., 𝑆= ∑𝑖=30 1 𝑎𝑖 and 𝑇= ∑𝑖=15 1 𝑎( 2𝑖- 1 ) . If 𝑎5 = 27 and 𝑆- 2𝑇= 75, then 𝑎10 is equal to: (1) 52 (2) 47 (3) 42 (4) 57