Practice Questions

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

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.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 →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.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.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 → →

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.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.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 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.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 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 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.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.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 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 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.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 →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

Q88. ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, μ) . If the median through A is equally inclined to the coordinate axes, then the value of (λ3 + μ3 + 5) is (1) 1130 (2) 1348 (3) 1077 (4) 676 → →a+→b+→c

Q61.The largest value of r, for which the region represented by the set {ω ∈C||ω −4 −i| ≤r} is contained in the region represented by the set {z ∈C||z −1| ≤|z + i|}, is equal to : (1) 2√2 (2) 32 √2 (3) √17 (4) 52 √2