Practice Questions

Q71.The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be 45°. After walking a distance of 80 meters towards the top, up a slope inclined at angle of 30° to the horizontal plane the angle of elevation of the top of the hill becomes 75°. Then the height of the hill (in meters) is _____.

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 …

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

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___.

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

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 ___________.

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

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

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.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.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

Q35.The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is: (Specific heat of water liquid and water vapour are 4.2 kJ K − and 2.0 kJ K −1kg−1 ; heat of liquid fusion and vaporization of water are 334 kJ kg−1 and 2491 kJ kg−1 , respectively). ( log 273 = 2.436, log 373 = 2.572, log 383 = 2.583 ) (1) 9.26 kJ kg−1K −1 (2) 2.64 kJ kg−1K −1 (3) 8.49 kJ kg−1K −1 (4) 7.90 kJ kg−1K −1

Q36.In order to oxidize a mixture of one mole of each of FeC2O4, Fe2 ( C2O4 ) 3, FeSO4 and Fe2 ( SO4 ) 3 in acidic medium, the number of moles of KMnO4 is: (1) 1 (2) 2 (3) 3 (4) 1.5

Q36.The molar solubility of Cd(OH)2 is 1.84 × 10−5M in water. The expectes solunility of Cd(OH)2 in a buffer solution of pH = 12 is: (1) 2.49 × 10−10M (2) 2.491.84 × 10−9M (3) 1.84 × 10−9M (4) 6.23 × 10−11M

Q45.Molecules of benzoic acid (C6H5 COOH) dimerise in 30 g of benzene. ' w ' g of benzoic acid shows a depression in freezing point equal to 2 K. If the percentage association of the acid to form dimer in the solution is 80, then w is: ( Given that Kf = 5 Kmol−1 , molar mass of benzoic acid = 122 gmol−1) (1) 1.0g (2) 2.4g (3) 1.8g (4) 1.5g Q46. ∧om for NaCl, HCl and NaA are 126.4, 425.9 and 100 .5 S cm2 mol−1 respectively. If the conductivity of 0 .001 M HA is 5 × 10−5S cm−1 , degree of dissociation of HA is (1) 0.125 (2) 0.75 (3) 0.25 (4) 0.50

Q53.The total number of isomers for a square planar complex: [MCl(F)(NO2)(SCN)] is: (1) 12 (2) 16 (3) 4 (4) 8

Q8. Take the mean distance of the moon and the sun from the earth to be 0.4 × 106 km and 150 × 106 km respectively. Their masses are 8 × 1022 kg and 2× 1030 kg respectively. The radius of the earth is 6400 km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1 is: ΔF2 (1) 2 (2) 6 (3) 10−2 (4) 0.6

Q49.How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27. 66 g of diborane? (Atomic weight of B = 10. 8 u) (1) 1. 6 hours (2) 6. 4 hours (3) 0. 8 hours (4) 3. 2 hours