Practice Questions

Q45.If 10−4dm3 of water is introduced into a 1.0dm3 flask to 300 K, how many moles of water are in the vapour phase when equilibrium is established? (Given : Vapour pressure of H2O at 300 K is 3170 Pa; R = 8.314 J K−1 mol−1 ) (1) 5.56 × 10−3 mol (2) 1.53 × 10−2 mol (3) 4.46 × 10−2 mol (4) 1.27 × 10−3 mol

Q47.On mixing, heptane and octane form an ideal solution. At 373 K, the vapour pressures of the two liquid components (heptane and octane) are 105kPa and 45kPa respectively. Vapour pressure of the solution obtained by mixing 25.0 g of heptane and 35 g of octane will be (molar mass of heptane = 100 g mol−1 an dof octane = 114 g mol−1 ). (1) 72.0kPa (2) 36.1kPa (3) 96.2kPa (4) 144.5kPa

Q48.The Gibbs energy for the decomposition of Al2O3 at 500∘C is as follows : 2 Al2O3 →4 Al + O2, ΔrG = +966 kJ mol−1 3 3 The potential difference needed for electrolytic reduction of Al2O3 at 500∘C is at least (1) 4.5 V (2) 3.0 V (3) 2.5 V (4) 5.0 V JEE Main 2010 JEE Main Previous Year Paper

Q49.The correct order of E0 values with negative sign for the four successive elements Cr, Mn, Fe and Co is SR2/M (1) Mn > Cr > Fe > Co (2) Cr > Fe > Mn > Co (3) Fe > Mn > Cr > Co (4) Cr > Mn > Fe > Co

Q50.The time for half life period of a certain reaction A → products is 1 hour. When the initial concentration of the reactant ' A ', is 2.0 mol L−1 , how much time does it take for its concentration to come from 0.50 to 0.25 mol L−1 if it is a zero order reaction? (1) 4 h (2) 0.5 h (3) 0.25 h (4) 1 h

Q53.A solution containing 2.675 g of CoCl3.6NH3 (molar mass = 267.5 g mol−1 ) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of AgNO3 to give 4.78 g of AgCl (molar mass = 143.5 g mol−1 ). The formula of the complex is (At. Mass of Ag = 108u ) (1) [Co(NH3)6]Cl3 (2) [CoCl2(NH3)4]Cl (3) [CoCl3(NH3)3] (4) [CoCl(NH3)5]Cl2

Q54.Which one of the following has an optical isomer ? (en = ethylenediamine) (1) [Zn(en)(NH3)2]2+ (2) [Co(en)3]3+ (3) [Co(H2O)4( en )]3+ (4) [Zn( en )2]2+

Q55. Consider the following bromides : The correct order of SN1 reactivity is JEE Main 2010 JEE Main Previous Year Paper (1) B > C > A (2) B > A > C (3) C > B > A (4) A > B > C

Q57.One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of 44u. The alkene is (1) propene (2) 1-butene (3) 2-butene (4) ethene

Q58. In the chemical reactions, the compounds ' A ' and ' B ' respectively are (1) nitrobenzene and fluorobenzene (2) phenol and benzene (3) benzene diazonium chloride and fluorobenzene (4) nitrobenzene and chlorobenzene

Q61.If α and β are the roots of the equation x2 −x + 1 = 0, then α2009 + β2009 = (1) −1 (2) 1 (3) 2 (4) −2

Q62.The number of complex numbers z such that |z −1| = |z + 1| = |z −i| equals (1) 1 (2) 2 (3) ∞ (4) 0

Q64.A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = … … = a10 = 150 and a10, a11, … … are in A.P. with common difference −2, then the time taken by him to count all notes is JEE Main 2010 JEE Main Previous Year Paper (1) 34 minutes (2) 125 minutes (3) 135 minutes (4) 24 minutes

Q65.Let S1 = ∑10j=1 j(j −1)10Cj, S2 = ∑10j=1 j10Cj and S3 = ∑10j=1 j210Cj . Statement-1: S3 = 55 × 29 Statement-2: S1 = 90 × 28 and S2 = 10 × 28 . (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Q66.Let cos(α + β) = 54 and let sin(α −β) = 135 , where 0 ≤α, β ≤π4 , then tan 2α = (1) 3356 (2) 1912 (3) 20 (4) 25 7 16 y

Q67.The line L given by x b = 1 passes through the point (13, 32). The line K is parallel to L and has the 5 + equation x c + 3y = 1. Then the distance between L and K is (1) √17 (2) 17 √15 (3) 23 (4) 23 √17 √15

Q68.The circle x2 + y2 = 4x + 8y + 5 intersects the line 3x −4y = m at two distinct points if (1) −35 < m < 15 (2) 15 < m < 65 (3) 35 < m < 85 (4) −85 < m < −35

Q71.For two data sets, each of size 5 , the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 , respectively. The variance of the combined data set is (1) 11 (2) 6 2 (3) 13 (4) 5 2 2

Q72.For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is (1) There is a regular polygon with 1 (2) There is a regular polygon with r = R R r = 32 √2 (3) There is a regular polygon with Rr = √32 (4) There is a regular polygon with Rr = 21

Q74.Consider the following relations: R = {(x, y) ∣x, y are real numbers and x = wy for some rational number w ∣m, n, p and q are integers such that n, q ≠0 and qm = pn} . Then } ; S = {( mn , pq ) (1) neither R nor S is an equivalence relation (2) S is an equivalence relation but R is not an equivalence relation (3) R and S both are equivalence relations (4) R is an equivalence relation but S is not an equivalence relation

Q76.Let A be a 2 × 2 matrix with non-zero entries and let A2 = 1 , where 1 is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A . Statement-1: Tr(A) = 0 Statement-2: |A| = 1 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1

Q77.Consider the system of linear equations: x1 + 2x2 + x3 = 3 2x1 + 3x2 + x3 = 3 3x1 + 5x2 + 2x3 = 1 The system has (1) exactly 3 solutions (2) a unique solution (3) no solution (4) infinite number of solutions

Q78.Let f : R →R be a continuous function defined by f(x) = ex+2e−x1 . Statement-1: f(c) = 31 , for some c ∈R. Statement-2: 0 < f(x) ≤ 1 , for all x ∈R 2√2 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the correct explanation for Statement-1 (3) Statement-1 is false, Statement-2 is true (4) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation for Statement-1 JEE Main 2010 JEE Main Previous Year Paper

Q79.Let f : (−1, 1) →R be a differentiable function with f(0) = −1 and f ′(0) = 1 . Let g(x) = [f(2f(x) + 2)]2 . Then g′(0) = (1) −4 (2) 0 (3) −2 (4) 4

Q81.Let f : R →R be defined by f(x) = {k2x−2x,+ 3, ifif xx ≤−1> −1 possible value of k is (1) 0 (2) −12 (3) −1 (4) 1