Practice Questions

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×→

Q75.If →x and →y be two non-zero vectors such that →x+→y = x and 2→x+ λ→y is perpendicular to y, then the value of λ is ...... . JEE Main 2020 (06 Sep 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.If →a = 2ˆi + ˆj + 2ˆk, then, the value of ˆi × (→a׈i) (→a ˆj) (→a ˆk) JEE Main 2020 (04 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.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.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.Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is JEE Main 2020 (05 Sep Shift 1) JEE Main Previous Year Paper

Q75.Let the position vectors of points ' A' and ' B' be ˆi +ˆj + ˆk and 2ˆi +ˆj + 3ˆk, respectively. A point ′P′ divides the −−−−→ → → → 2 line segment AB internally in the ratio λ : 1(λ > 0). If O is the origin and OB ⋅OP −3 OA × OP = 6 then λ is equal to JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q75.The probability of a man hitting a target is 1 . The least number of shots required, so that the probability of his 10 hitting the target at least once is greater than 1 , is.... 4 JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper

Q75.Let A = [ x1 10 ], JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper

Q75.Let →a, →b and →cbe three unit vectors such that →a−→b 2 + →a−→c 2 = 8 . Then →a+ 2→b 2 + →a+ 2→c 2 is equal to JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper

Q75.If →a and b are unit vectors, then the greatest value of √3→a+ b + →a− b is JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper

Q75.The projection of the line segment joining the point (1, −1, 3) and (2, −4, 11) on the line joining the points (−1, 2, 3) and (3, −2,10) is _______ JEE Main 2020 (09 Jan Shift 1) JEE Main Previous Year Paper

Q75.If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through (α, 7,1) is ( 53 , 73 , 173 ), then α is equal to JEE Main 2020 (07 Jan Shift 2) 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

Q75.Let the normal at a point P on the curve y2 −3x2 + y + 10 = 0 intersect the y -axis at (0, 32 ). If m is the slope of the tangent at P to the curve, then |m| is equal to ___________. JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper

Q61.If α, β and γ are three consecutive terms of a non-constant G.P. Such that the equations αx2 + 2βx + γ = 0 and x2 + x −1 = 0 have a common root, then α(β + γ) is equal to: (1) βγ (2) αβ (3) αγ (4) 0

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 one real root of the quadratic equation 81x2 + kx + 256 = 0 is cube of the other root, then a value of k is : (1) -81 (2) 100 (3) 144 (4) -300 where x and y are real numbers then y −x equals

Q61.If 𝛼 and 𝛽 are the roots of the equation 375 𝑥2 - 25𝑥- 2 = 0, then 𝑛 𝛽𝑟 is equal to: ∑ 𝑟= 1 lim ∑ 𝑟=𝑛 1 𝛼𝑟+ 𝑛→∞lim 𝑛→∞ (1) 1 (2) 21 12 346 (3) 7 (4) 29 116 358

Q61.The value of λ such that sum of the squares of the roots of the quadratic equation, x2 + (3 −λ) x + 2 = λ has the least value is: (1) 2 (2) 49 (3) 15 (4) 1 8

Q61.Let α and β be the roots of the quadratic equation x2 sin θ −x(sin θ cos θ + 1) + cos θ = 0 (0 < θ < 45∘), and (−1)n is equal to : α < β. Then ∑∞n=0 (αn + βn ) 1 (1) 1−cos θ − 1+sin1 θ (2) 1+cos1 θ + 1−sin1 θ 1 (3) 1−cos θ + 1+sin1 θ (4) 1+cos1 θ − 1−sin1 θ JEE Main 2019 (11 Jan Shift 2) JEE Main Previous Year Paper

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 integral values of m for which the quadratic expression (1 + 2m) x2 −2(1 + 3m)x + 4(1 + m), x ∈R is always positive, is (1) 7 (2) 3 (3) 6 (4) 8