Practice Questions

Q48.The elevation of boiling point of 0. 10m aqueous CrCl3. xNH3 solution is two times that of 0. 05 m aqueous CaCl2 solution. The value of x is … … … … . . [Assume 100% ionisation of the complex and CaCl2, coordination number of Cr as 6, and that all NH3 molecules are present inside the coordination sphere]

Q48.Consider the following reactions: NaCl + K2Cr2O7 + H2SO4 →(A)+ side products (Conc.) (A) + NaOH →(B)+ side products (B) + H2SO4 + H2O2 →(C)+ side products (dilute) The sum of the total number of atoms in one molecule each of (A), (B) and (C) is ________

Q48.The total number of monohalogenated organic products in the following (including stereoisomers) reaction is (i) H2/ Ni /Δ −A → (Simplest optically active alkene) (ii) X2/Δ

Q49.Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bond order between Cl and O atoms in (Y) is _______________.

Q50.The photoelectric current from Na (work function, w0 = 2. 3 eV ) is stopped by the output voltage of the cell Pt(s)∥H2(g, 1 bar)| HCl(aq⋅, pH = 1)| AgCl(s) ∣Ag(s) the pH of aq. HCl required to stop the photoelectric current from K(w0 = 2. 25 eV), all other conditions remaining the same, is … … … . ×10−2 (to the nearest integer). Given 2. 303 RTF = 0. 06V; E0AgCl / Ag /Cl = 0. 22V

Q50.Complexes (ML5) of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal geometries, respectively. The sum of the 90o, 120o and 180o L −M −L angles in the two complexes is_______

Q52.If z1, z2 are complex numbers such that Re (z1) = |z1 −1| and Re (z2) = |z2 −1| and arg(z1 −z2) = π6 , then Im(z1 + z2) is equal to : (1) 2√3 (2) √3 2 (3) 1 (4) 2 √3 √3

Q53.Let u = z−ki2z+i , z = x + iy and k > 0. If the curve represented by Re (u)+ Im (u) = 1 intersects the y-axis at points P and Q where PQ = 5 then the value of k is (1) 3 (2) 1 2 2 (3) 4 (4) 2

Q54.If α and β, be the coefficients of x4 and x2 , respectively in the expansion of 6 6 + √x2 + −√x2 (x −1) (x −1) , then (1) α + β = 60 (2) α + β = −30 (3) α −β = 60 (4) α −β = −132

Q54.The value of ( 2 ⋅1 P0 −3 ⋅2 P1 + 4 ⋅3 P2−. . . . . . . . up to 51th term) +( 1! −2! + 3!−. . . . . . . up to 51th term) is equal to (1) 1 −51(51)! (2) 1 + (51)! (3) 1 + (52)! (4) 1 1 1 n 2 + 5 8 is exactly 33, then the least value of n is

Q54.Let a, b, c, d and p be non-zero distinct real numbers such that (a2 + b2 + c2)p2 −2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then (1) a, b, c are in A.P. (2) a, c, p are in G.P. (3) a, b, c, d are in G.P. (4) a, b, c, d are in A.P. is equal to

Q55.Let α > 0, β > 0 be such that α3 + β2 = 4 . If the maximum value of the term independent of x in the 1 10 10k, then k is equal to binomial expansion of (αx 9 + βx−16 ) is (1) 336 (2) 352 (3) 84 (4) 176

Q55.Let S be the sum of the first 9 term of the series : {x + ka} + {x2 + (k + 2)a} + {x3 + (k + 4)a} + {x4 + (k + 6)a} + … where a ≠0 and x ≠ 1 . If x10−x+45a(x−1) S = x−1 , then k is equal to (1) −5 (2) 1 (3) −3 (4) 3

Q55.The value of cos3( π8 ). cos( 3π8 ) + sin3( π8 ). sin( 3π8 ) is: (1) 1 (2) 1 √2 2√2 (3) 1 (4) 1 2 4

Q56.A triangle ABC lying in the first quadrant has two vertices as A(1, 2) and B(3, 1). If ∠BAC = 90o,and ar (Δ ABC) = 5√5 sq. units, then the abscissa of the vertex C is : JEE Main 2020 (04 Sep Shift 1) JEE Main Previous Year Paper (1) 1 + √5 (2) 1 + 2√5 (3) 2 + √5 (4) 2√5 −1 y2

Q56.For a > 0, let the curves C1 : y2 = ax and C2 : x2 = ay intersect at origin O and a point P. Let the line x = b(0 < b < a) intersect the chord OP and the x -axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, C1 and C2, and the area of ΔOQR = 21 , then ‘ a ’ satisfies the equation: (1) x6 −6x3 + 4 = 0 (2) x6 −12x3 + 4 = 0 (3) x6 + 6x3 −4 = 0 (4) x6 −12x3 −4 = 0

Q56.The centre of the circle passing through the point (0, 1) and touching the parabola y = x2 at the point (2, 4) is : JEE Main 2020 (06 Sep Shift 2) JEE Main Previous Year Paper (1) ( −5310 , 165 ) (2) ( 65 , 5310 ) (3) ( 103 , 165 ) (4) ( −165 , 5310 )

Q56.Let P be a point on the parabola, y2 = 12x and N be the foot of the perpendicular drawn from P , on the axis of the parabola. A line is now drawn through the mid-point M of PN , parallel to its axis which meets the parabola at Q . If the y−intercept of the line NQ is 43 , then : JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper (1) PN = 4 (2) MQ = 13 (3) MQ = 14 (4) PN = 3

Q56.In the expansion of ( cosx θ + x sin1 θ )16, if l1 is the least value of the term independent of 8 ≤θ ≤π4 and l2 is the least value of the term independent of x when 16π ≤θ ≤π8 , then the ratio l2 : l1 is equal to: (1) 1 : 8 (2) 16 : 1 (3) 8 : 1 (4) 1 : 16

Q57.If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, −4), then PQ2 is equal to (1) 36 (2) 48 (3) 21 (4) 29

Q57.Let the line y = mx and the ellipse 2x2 + y2 = 1 intersect at a point P in the first quadrant. If the normal to , (0, β), then β is equal to 0) and this ellipse at P meets the co-ordinate axes at (− 3√21 (1) 2√2 (2) 2 3 √3 (3) 2 (4) √2 3 3 JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper Q58. 3x2+2 x21 lim is equal to x→0 ( 7x2+2 ) (1) 1 (2) 1 e e2 (3) e2 (4) e

Q58.The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola is (1) 64√3 (2) 256√3 (3) 192√3 (4) 128√3 JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q58.If the line y = m x + c is a common tangent to the hyperbola 100x2 −y264 = 1 and the circle x2 + y2 = 36, then which one of the following is true? (1) c2 = 369 (2) 5m = 4 (3) 4c2 = 369 (4) 8m + 5 = 0

Q58.Let P(3, 3) be a point on the hyperbola, x2 −y2 = 1. If the normal to it at P intersects the x-axis at (9, 0) a2 b2 and e is its eccentricity, then the ordered pair (a2, e2) is equal to: (1) ( 29 , 3) (2) ( 32 , 2) (3) ( 29 , 2) (4) (9, 3)

Q58.If α is the positive root of the equation, p(x) = x2 −x −2 = 0, then lim √1−cosx+α−4p(x) is equal to x→α+ (1) 23 (2) √23 (3) 1 (4) 12 √2