Practice Questions

Q61.A natural number has prime factorization given by n = 2x3y5z , where y and z are such that y + z = 5 and y−1 + z−1 = 56 , y > z. Then the number of odd divisors of n, including 1 , is: (1) 12 (2) 6 (3) 11 (4) 6x

Q61.Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be ( 103 , 73 ). If α, β are the roots of the equation ax2 + bx + 1 = 0, then the value of α2 + β2 −αβ is: (1) −71256 (2) 25669 (3) 256 71 (4) −69256

Q61.The set of all values of k > −1, for which the equation + + 4x + 3)(3x2 + 4x + 2)+ k(3x2 + 4x + 2) = 0 has real roots, is: (3x2 + 4x + 3) 2 −(k 2 1)(3x2 (1) [−12 , 1) (2) (1, 25 ] (3) ( 12 , 32 ] −{1} (4) [2, 3)

Q62.A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = √5 inches and ∠PCB = tan−1(2). The acute angle through which the pencil must be rotated about C so that the perpendicular distance between eraser and pencil becomes exactly 1 inch is : (1) tan−1( 43 ) (2) tan−1( 21 ) (3) tan−1( 43 ) (4) tan−1(1)

Q62.If S = {z ∈C : z+2iz−i ∈R}, then (1) S is a circle in the complex plane (2) S contains exactly two elements (3) S contains only one element (4) S is a straight line in the complex plane

Q62.The probability of selecting integers a ∈[−5, 30] such that x2 + 2 (a + 4) x −5a + 64 > 0 , for all x ∈R, is: (1) 7 (2) 2 36 9 (3) 1 (4) 1 6 4 JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper

Q62.If 0 < x < 1 and y = 21 x2 + 32 x3 + 43 x4 + … … , then the value of e1+y at x = 21 is: (1) 1 e2 (2) 2e 2 (3) 2e2 (4) 21 √e

Q27.The variation of equilibrium constant with temperature is given below : Temperature EquilibriumConstant T1 = 25°C K1 = 10 T2 = 100°C K2 = 100 JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper The values of ΔH°, ΔG° at T1 and ΔG° at T2 (in kJ mol−1 ) respectively, are close to [use R = 8. 314 JK−1 mol−1 ] (1) 28. 4, −7. 14 and −5. 71 (2) 0. 64, −7. 14 and −5. 71 (3) 28. 4, −5. 71 and −14. 29 (4) 0. 64, −5. 71 and −14. 29

Q34.A diatomic molecule X2 has a body-centred cubic (bcc) structure with a cell edge of 300 pm. The density of the molecule is 6. 17 gcm−3. The number of molecules present in 200 g of X2 is : (Avogadro constant (NA) = 6 × 1023 mol−1 ) (1) 40 NA (2) 8 NA (3) 4 NA (4) 2 NA

Q35.In Carius method of estimation of halogen, 0. 172 g of an organic compound showed presence of 0. 08 g of bromine. Which of these is the correct structure of the compound ? JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper (1) CH3 CHBr2 (2) (3) (4) H3C −CH2 −Br

Q35.A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A and B are 300 s and 180 s, respectively. If the concentrations of A and B are equal initially, the time required for the concentration of A to be four times that of B (in s) is : (Use ln 2 = 0. 693) (1) 180 (2) 900 (3) 300 (4) 120

Q36.The results given in the below table were obtained during kinetic studies of the following reaction: 2A + B →C + D Experiment [A]/ molL−1 [B]/ molL−1 Initial rate/ molL−1 min−1 I 0. 1 0. 1 6. 00 × 10−3 II 0. 1 0. 2 2. 40 × 10−2 III 0. 2 0. 1 1. 20 × 10−2 IV X 0. 2 7. 20 × 10−2 V 0. 3 Y 2. 88 × 10−1 X and Y in the given table are respectively : (1) 0. 4, 0. 4 (2) 0. 4, 0. 3 (3) 0. 3, 0. 4 (4) 0. 3, 0. 3

Q37.The rate of a certain biochemical reaction at physiological temperature (T) occurs 106 times faster with enzyme than without. The change in the activation energy upon adding enzyme is: (1) −6(2.303)RT (2) −6RT (3) +6(2.303)RT (4) +6RT

Q37.Given that the standard potentials (Eo) of Cu2+ / Cu and Cu+ / Cu are 0.34V and 0.522V respectively, the Eo of Cu2+ / Cu+ is: (1) 0.182V (2) +0.158V (3) −0.182V (4) −0.158V

Q40.The values of the crystal field stabilization energies for a high spin d6 metal ion in octahedral and tetrahedral fields, respectively, are: (1) −0 .4 Δo and −0. 6Δt (2) −2 .4 Δo and −0. 6 Δt (3) −1 .6 Δo and −0. 4Δt (4) −0 .4 Δo and −0 .27 Δt

Q41.The electronic spectrum of [Ti (H2O)6]3+ shows a single broad peak with a maximum at 20, 300 cm−1. The crystal field stabilization energy (CFSE) of the complex ion, in kJmol−1, is : (1 kJmol−1 = 83. 7 cm−1) (1) 145.5 (2) 242.5 (3) 83.7 (4) 97

Q46.For a dimerization reaction, JEE Main 2020 (05 Sep Shift 2) JEE Main Previous Year Paper 2A(g) →A2(g) at 298K, ΔU−= −20 kJmol−1, ΔS−= −30 JK−1 mol−1,then the ΔG− will be …..J.

Q46.The Gibbs energy change (in J) for the given reaction at [Cu2+] = [Sn2+] = 1 M and 298 K is : Cu(s) + Sn2+(aq. ) →Cu2+(aq. ) + Sn(s); = −0 .16 V, E0 = 0 .34 V,Take F = 96500 C mol−1) Cu2+ Cu (E0Sn2+|Sn

Q46. NaClO3 is used, even in spacecrafts, to produce O2. The daily consumption of pure O2 by a person in 492 L at 1 atm, 300K. How much amount of NaClO3, in grams, is required to produce O2 for the daily consumption of a person at 1 atm, 300K ? _____ NaClO3(s) + Fe(s) →O2(g) + NaCl(s) + FeO(s) R = 0 .082 L atm mol−1 K−1

Q46.For the reaction; A(l) →2B(g) ΔU = 2.1kcal, ΔS = 20calK−1 at 300K. Hence ΔG in kcal is _____________.

Q46.The atomic number of Unnilumium is ______.

Q46.The volume (in mL) of 0.125 M AgNO3 required to quantitatively precipitate chloride ions in 0.3g of [Co(NH3)6]Cl3 is __________. M[Co(NH3)6]Cl3 = 267.46g/mol MAgNO3 = 169.87g/mol Report the nearest integer as the answer.

Q46.The mass of ammonia in grams produced when 2. 8 kg of dinitrogen quantitatively reacts with 1 kg of dihydrogen is _____

Q46.The mole fraction of glucose (C6H12O6) in an aqueous binary solution is 0. 1. The mass percentage of water in it, to the nearest integer, is … … … JEE Main 2020 (03 Sep Shift 1) JEE Main Previous Year Paper

Q46.A spherical balloon of radius 3 cm containing helium gas has a pressure of 48 × 10−3 bar. At the same temperature, the pressure, of a spherical balloon of radius 12 cm containing the same amount of gas will be … … … … . ×10−6 bar.