Practice Questions

Q58.Given E∘ = −0.72 V, E∘ = −0.42 V. The potential for the cell Cr3+/Cr Fe2+//Fe Cr Cr3+(0.1M) Fe2+(0.01M) Fe is (1) 0.26 V (2) 0.399 V (3) −0.339 V (4) −0.26 V

Q62.Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly? JEE Main 2008 JEE Main Previous Year Paper (1) Metal sulphides are thermodynamically more (2) CO2 is thermodynamically more stable than CS2 stable than CS2 (3) Metal sulphides are less stable than the (4) CO2 is more volatile than CS2 corresponding oxides

Q63.Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being (1) 4 f orbitals more diffused than the 5f orbitals (2) lesser energy difference between 5f and 6d than between 4f and 5d orbitals (3) more energy difference between 5f and 6d than (4) more reactive nature of the actinoids than the between 4f and 5d orbitals lanthanoids

Q64.Amount of oxalic acid present in a solution can be determined by its titration with KMnO4 solution in the presence of H2SO4 . The titration gives unsatisfactory result when carried out in the presence of HCl , because HCl (1) gets oxidised by oxalic acid to chlorine (2) furnishes H+ ions in addition to those from oxalic acid (3) reduces permanganate to Mn2+ (4) oxidises oxalic acid to carbon dioxide and water

Q65.The coordination number and the oxidation state of the element ' E ' in the complex [E(en)2 (C2O4)]NO2 (where (en) is ethylene diamine) are, respectively, (1) 6 and 2 (2) 4 and 2 (3) 4 and 3 (4) 6 and 3

Q66.In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of Δ∘ be the highest? (1) [Co(CN)6]3− (2) [Co(C2O4)3]3− (3) [Co(H2O)6]3+ (4) [Co(NH3)6]3+

Q67.The organic chloro compound, which shows complete stereochemical inversion during a SN2 reaction, is (1) (C2H5)2CHCl (2) (CH3)3CCl (3) (CH3)2CHCl (4) CH3Cl

Q68.Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives (1) 2,4,6-trinitrobenzene (2) o-nitrophenol (3) p-nitrophenol (4) nitrobenzene

Q72.The quadratic equations x2 −6x + a = 0 and x2 −cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (1) 1 (2) 4 (3) 3 (4) 2

Q74.In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement -1: The number of different ways the child can buy the six ice-creams is 10C5 . Statement −2 : The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row. (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.

Q76.The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is (1) −4 (2) −12 (3) 12 (4) 4

Q77.Statement-1: ∑nr=0(r + 1)nCr = (n + 2)2n−1 Statement -2: ∑nr=0(r + 1)nCrxr = (1 + x)n + nx(1 + x)n−1 . JEE Main 2008 JEE Main Previous Year Paper (1) Statement −1 is false, Statement −2 is true (2) Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1 (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1.

Q78.The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept - 4. Then a possible value of k is (1) 1 (2) 2 (3) −2 (4) −4

Q81.A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is (1) 8 (2) 2 3 3 (3) 4 (4) 5 3 3

Q83.The statement p →(q →p) is equivalent to (1) p →(p →q) (2) p →(p ∨q) (3) p →(p ∧q) (4) p →(p ↔q)

Q84.The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b ? (1) a = 0, b = 7 (2) a = 5, b = 2 (3) a = 1, b = 6 (4) a = 3, b = 4 JEE Main 2008 JEE Main Previous Year Paper

Q85. AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60∘ . He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45∘ . Then the height of the pole is (1) 7√3 + 1)m 2 ⋅ √3−11 m (2) 7√32 ⋅(√3 (3) 7√3 2 ⋅(√3 −1)m (4) 7√32 ⋅ √3+11

Q86.Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x −y is an integer }. Which one of the following is true? (1) neither S nor T is an equivalence relation on R (2) both S and T are equivalence relations on R (3) S is an equivalence relation on R but T is not (4) T is an equivalence relation on R but S is not

Q88.Let A be a square matrix all of whose entries are integers. Then which one of the following is true? (1) If det A = ±1, then A−1 exists but all its entries (2) If det A ≠±1, then A−1 exists and all its entries are not necessarily integers are non-integers (3) If det A = ±1, then A−1 exists and all its entries (4) If det A = ±1, then A−1 need not exist are integers

Q89.Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x = cy + bz, y = az + cx and z = bx + ay. Then a2 + b2 + c2 + 2abc is equal to (1) 2 (2) −1 (3) 0 (4) 1

Q90.The value of cot (cosec−1 53 + tan−1 23 ) is (1) 6 (2) 3 17 17 (3) 4 (4) 5 17 17

Q92.Let f(x) = −1) sin ( {(x0, if x = 1 JEE Main 2008 JEE Main Previous Year Paper (1) f is neither differentiable at x = 0 nor at x = 1 (2) f is differentiable at x = 0 and at x = 1 (3) f is differentiable at x = 0 but not at x = 1 (4) f is differentiable at x = 1 but not at x = 0

Q94.How many real solutions does the equation x7 + 14x5 + 16x3 + 30x −560 = 0 have? (1) 7 (2) 1 (3) 3 (4) 5

Q95.The value of √2 ∫ sin xdx is sin(x−π4 ) (1) x + log cos (x −π4 ) + c (2) x −log sin (x −π4 ) + c (3) x + log sin (x −π4 ) + c (4) x −log cos (x −π4 ) + c dx. Then which one of the following is true?

Q97.The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to (1) 5 (2) 1 3 3 (3) 2 (4) 4 3 3