Practice Questions

Q73.Let S be the set of all integer solutions (x, y, z) of the system of equations x −2 y + 5 z = 0 −2 x + 4 y + z = 0 −7 x + 14 y + 9 z = 0 such that 15 ≤x2 + y2 + z2 ≤150. Then, the number of elements in the set S is equal to ..........

Q73.If lim x−1 = 820, (n ∈N) then the value of n is equal to.... x→1

Q73.If 1 , α, β ∈(0, π2 ), then tan(α + 2β), is equal to √1+cos2α = 17 and √1−cos2β2 = √10

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__ → → →

Q74.If the tangent to the curve y = ex at a point (c, ec) and the normal to the parabola y2 = 4x at the point (1, 2) intersect at the same point on the x−axis, then the value of c is ..... + μ ∈R. If Q(α, β, γ) is

Q74.Suppose that a function f : R →R satisfies f(x + y) = f(x) f(y) for all x, y ε R and f(1) = 3. If ∑ni=1 f(i) = 363 , then n is equal to ..... . JEE Main 2020 (06 Sep Shift 2) JEE Main Previous Year Paper → →

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.If the function f defined on (−13 , 1/3) { k , when x = 0 equal to.

Q74.If x→0{ x ε R and A4 = [aij]. If a11 = 109, then a22 is equal to_____________.

Q74.If the equation of a plane P , passing through the intersection of the planes, x + 4y −z + 7 = 0 and 3x + y + 5z = 8 is ax + by + 6z = 15 for some a, b ∈R, then the distance of the point (3, 2, −1) from the plane P is … …

Q74.The integral ∫20 ||x −1| −x|dx is equal to

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 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 …

Q75.Let A = [ x1 10 ], JEE Main 2020 (03 Sep 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.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 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.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.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

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 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.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.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.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

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