Practice Questions

Q74.Let →a, b and →cbe three vectors such that →a = √3, b = 5, b ∙→c= 10 and the angle between b and →cis 3 . → → is equal to ____________. b is perpendicular to the vector b ×→c, then →a× ( ×→c)

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.If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then the value of m + n is equal to

Q74.Let the vectors →a, b,→cbe such that →a = 2, b = 4 and →c = 4. If the projection of b on →a is equal to the → → projection of→con →a and b is perpendicular to→c, then the value of →a+ b −→c is …

Q74.Let AD and BC be two vertical poles at A and B respectively on a horizontal ground. If AD = 8m , BC = 11m , AB = 10m; then the distance (in meters) of a point M lying in between AB from the point A such that MD2 + MC2 is minimums, is__ → → →

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.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 →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 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.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.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.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 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.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.Let A = [ x1 10 ], JEE Main 2020 (03 Sep 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 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.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.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.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 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

Q1. A particle is moving with speed v = b√x along positive x− axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0 ) (1) b2τ (2) b2τ √2 (3) b2τ (4) b2τ 2 4

Q1. A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level, but he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is: (1) 2v (2) v √3 (3) v (4) √3 v 2 2

Q1. Let L, R, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of L in SI units will be: RCV (1) [LTA] (2) [A−1] (3) [LT 2] (4) [LA−2]

Q1. A particle moves from the point (2.0^i + 4.0^j)m, at t = 0 , with an initial velocity (5.0^i + 4.0^j)ms−1. It is acted upon by a constant force which produces a constant acceleration (4.0^i + 4.0^j)ms−2. What is the distance of the particle from the origin at time 2 s? (1) 15 m (2) 20√2 m (3) 5 m (4) 10√2 m