Practice Questions

Q57.In the given transformation, which of the following is the most appropriate reagent? (1) (−) (2) Zn −Hg/HCl NH2NH2, OH (3) Na , Liq. NH3 (4) NaBH4

Q57.The product of the reaction between ethyl benzene and N-bromosuccinamide is (1) (2) (3) (4)

Q58.The species which can best serve as an initiator for the cationic polymerization is : (1) LiAlH4 (2) HNO3 (3) AlCl3 (4) BuLi

Q58.Which one of the following is a chain growth polymerisation? (1) Nucleic acid (2) Polystyrene (3) Protein (4) Starch

Q59.Aspirin can be prepared by the reaction of (1) Salicyldehyde with acetic anhydride in presence (2) Salicylic acid with methanol in presence of of H2SO4 H2SO4 (3) Salicylic acid with acetic anhydride in presence (4) Cinnamic acid with acetic anhydride in presence of H2SO4 of H2SO4

Q60.Which of the following statements is correct? (1) RNA controls the synthesis of proteins. (2) The sugar present in DNA is D-(-)-ribose. (3) RNA has double stranded α-helix structure. (4) DNA mainly occurs in the cytoplasm of the cell.

Q61.The value of k for which the equation (K −2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is (1) 6 (2) 3 (3) 4 (4) 1

Q61.If a, b, c ∈R and 1 is a root of equation ax2 + bx +c = 0, then the curve y = 4ax2 + 3bx + 2c, a ≠0 intersect x-axis at JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) two distinct points whose coordinates are always (2) no point rational numbers (3) exactly two distinct points (4) exactly one point Q62. |z1 + z2|2 + |z1 −z2|2 is equal to + (1) 2 (|z1| + |z2| (2) 2 (|z1|2 |z2|2) (3) |z1| |z2| (4) |z1|2 + |z2|2

Q61.Let p, q, r ∈R and r > p > 0. If the quadratic equation px2 + qx + r = 0 has two complex roots α and β, then |α| + |β| is (1) equal to 1 (2) less than 2 but not equal to 1 (3) greater than 2 (4) equal to 2 x2 b

Q61.If z ≠1 and z−1z2 is real, then the point represented by the complex number (1) either on the real axis or on a circle passing (2) on a circle with centre at the origin through the origin (3) either on the real axis or on a circle not passing (4) on the imaginary axis through the origin

Q62.If the sum of the square of the roots of the equation x2 −(sin α −2)x −(1 + sin α) = 0 is least, then α is equal to (1) π (2) π 6 4 (3) π (4) π 3 2

Q62.Consider a quadratic equation ax2 + bx + c = 0, where 2a + 3b + 6c = 0 and let g(x) = a x33 + 2 + cx. Statement 1: The quadratic equation has at least one root in the interval (0, 1). Statement 2: The Rolle's theorem is applicable to function g(x) on the interval [0, 1]. (1) Statement 1 is false, Statement 2 is true. (2) Statement 1 is true, Statement 2 is false. (3) Statement 1 is true, Statement 2 is true, (4) Statement 1 is true, Statement 2 is true, , Statement 2 is not a correct explanation for Statement 2 is a correct explanation for Statement 1. Statement 1.

Q62.Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is (1) 880 (2) 629 (3) 630 (4) 879

Q63.Let Z and W be complex numbers such that |Z| = |W|, and arg Z denotes the principal argument of Z . Statement 1:If arg Z + arg W = π, then Z = −¯W . Statement 2: |Z| = |W|, implies arg Z −arg ¯W = π. (1) Statement 1 is true, Statement 2 is false. (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 false, Statement 2 is true. Statement 2 is not a correct explanation for Statement 1.

Q63.Let X = {1, 2, 3, 4, 5} . The number of different ordered pairs (Y , Z) that can be formed such that Y ⊆X, Z ⊆X and Y ∩Z is empty, is (1) 52 (2) 35 (3) 25 (4) 53

Q63.The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is (1) 2|z|2 (2) 1/2|z|2 (3) 4|z|2 (4) |z|2 JEE Main 2012 (12 May Online) JEE Main Previous Year Paper

Q63.If seven women and seven men are to be seated around a circular table such that there is a man on either side of every woman, then the number of seating arrangements is (1) 6!7! (2) (6!)2 (3) (7!)2 (4) 7 !

Q64.The sum of the series 1 1 1 + + + … 1 + √2 √2 + √3 √3 + √4 upto 15 terms is (1) 1 (2) 2 (3) 3 (4) 4

Q64.The number of arrangements that can be formed from the letters a, b, c, d, e, f taken 3 at a time without repetition and each arrangement containing at least one vowel, is (1) 96 (2) 128 (3) 24 (4) 72

Q64.The difference between the fourth term and the first term of a Geometrical Progresssion is 52. If the sum of its first three terms is 26 , then the sum of the first six terms of the progression is JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 63 (2) 189 (3) 728 (4) 364

Q65.If the sum of the series 12 + 2 ⋅22 + 32 + 2 ⋅42 + 52+ ... 2.62 + … upto n terms, when n is even, is n(n+1)22 then the sum of the series, when n is odd, is (1) n2(n + 1) (2) n2(n−1) 2 (3) n2(n+1) (4) n2(n −1) 2

Q65.If 100 times the 100th term of an AP with non zero common difference equals the 50 times its 50th term, then the 150th term of this AP is (1) −150 (2) 150 times its 50th term (3) 150 (4) zero

Q65.The sum of the series 12 + 2.22 + 32 + 2.42 + 52 + 2.62 + … . . +2(2m)2 is (1) m(2m + 1)2 (2) m2(m + 2) (3) m2(2m + 1) (4) m(m + 2)2

Q65.The number of terms in the expansion of (y1/5 + x1/10) 55 , in which powers of x and y are free from radical signs are (1) six (2) twelve (3) seven (4) five

Q66.If n is a positive integer, then (√3 + 1)2n −(√3 −1)2n is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a rational number other than positive integers