Practice Questions

Q60.Which one of the following bases is not present in DNA ? (1) Quinoline (2) Adenine (3) Cytosine (4) Thymine

Q60.Which of the following will not show mutarotation? (1) Maltose (2) Lactose (3) Glucose (4) Sucrose

Q60.Which one of the following class of compounds is obtained by polymerization of acetylene ? (1) Poly-ene (2) Poly-amide (3) Poly-yne (4) Poly-ester

Q61.The sum of the roots of the equation, x2 + |2x −3| −4 = 0, is: (1) 2 (2) −2 (3) √2 (4) −√2

Q61.If 1 , 1 are the roots of the equation ax2 + bx + 1 = 0, (a ≠0, a, b ∈R), then the equation √α √β x(x + b3) + (a3 −3abx) = 0 has roots: 2 and β−32 (1) √αβ and αβ (2) α−3 (3) αβ 21 and α 21 β (4) α 23 and β 23

Q61.If α and β are roots of the equation, x2 −4√2kx + 2e4 ln k −1 = 0 for some k, and α2 + β2 = 66, then α3 + β3 is equal to: (1) 248√2 (2) 280√2 (3) −32√2 (4) −280√2 + arg

Q61.The equation √3x2 + x + 5 = x −3, where x is real, has (1) no solution (2) exactly four solutions (3) exactly one solution (4) exactly two solutions JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper

Q61.If a ∈ R and the equation −3(x − [x])2 + 2(x − [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval (1) (−2, −1) (2) ( −∞, −2) ∪(2,∞) (3) (−1, 0) ∪(0, 1) (4) (1, 2)

Q62.Let z ≠−i be any complex number such that z+iz−i is a purely imaginary number. Then z + 1z is: (1) 0 (2) any non-zero real number other than 1 . (3) any non-zero real number. (4) a purely imaginary number. Q63.8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places, is: (1) 160 (2) 120 (3) 60 (4) 48

Q62.Let α and β be the roots of equation px2 + qx + r = 0, p ≠0. If p, q, r are in A.P. and α1 + β1 = 4, then the value of |α −β| is (1) √34 (2) 2√13 9 9 (3) √61 (4) 2√17 9 9

Q62.If equations ax2 + bx + c = 0, (a, b, c ∈R, a ≠0) and 2x2 + 3x + 4 = 0 have a common root, then a : b : c equals : (1) 2 : 3 : 4 (2) 4 : 3 : 2 (3) 1 : 2 : 3 (4) 3 : 2 : 1

Q62.If z1, z2 and z3, z4 are 2 pairs of complex conjugate numbers, then arg ( z1z4 ) ( z2z3 ) equals: (1) 0 (2) π 2 (3) 3π (4) π 2 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q62.For all complex numbers z of the form 1 + iα, α ∈R, if z2 = x + iy, then (1) y2 −4x + 4 = 0 (2) y2 + 4x −4 = 0 (3) y2 −4x + 2 = 0 (4) y2 + 4x + 2 = 0

Q63.Let w(Im w≠0) be a complex number. Then, the set of all complex numbers z satisfying the equation ¯w −wz = k(1 −z), for some real number k, is (1) {z : z ≠1} (2) {z : |z| = 1, z ≠1} ¯(3) {z : z = z} (4) {z : |z| = 1}

Q63.Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between them-selves exceeds the number of games that the men played with the women by 66 , then the number of men who participated in the tournament lies in the interval (1) (11, 13] (2) (14, 17) (3) [10, 12) (4) [8, 9]

Q63.If z is a complex number such that |z| ≥2, then the minimum value of z + 12 : (1) Is strictly greater than 5 (2) Is strictly greater than 3 but less than 5 2 2 2 (3) Is equal to 5 (4) Lies in the interval (1, 2) 2

Q63.An eight digit number divisible by 9 is to be formed using digits from 0 to 9 without repeating the digits. The number of ways in which this can be done is: (1) 72(7!) (2) 18(7!) (3) 40(7!) (4) 36(7!)

Q64.Let G be the geometric mean of two positive numbers a and b, and M be the arithmetic mean of 1a and 1b . If 1 : G is 4 : 5, then a : b can be: M JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper (1) 1 : 4 (2) 1 : 2 (3) 2 : 3 (4) 3 : 4

Q64.In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49 , and the sum of the first and the third term is 35. Then the first term of this geometric progression is: (1) 7 (2) 21 (3) 28 (4) 42

Q64.The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6 , without repetition is : (1) 18 (2) 36 (3) 108 (4) 432

Q64.If (10)9 + 2(11)1(10)8 + 3(11)2(10)7 + ...... + 10(11)9 = k(10)9, then k is equal to : JEE Main 2014 (06 Apr) JEE Main Previous Year Paper (1) 100 (2) 110 (3) 121 (4) 441 10 100

Q64.Let f(n) = [ 13 + 1003n ]n, where [n] denotes the greatest integer less than or equal to n. Then ∑56n=1 f(n) is equal to (1) 56 (2) 1287 (3) 1399 (4) 689

Q65.The sum of the first 20 terms common between the series 3 + 7 + 11 + 15+ and 1 + 6 + 11+ 16 + … .. is (1) 4000 (2) 4020 (3) 4200 (4) 4220

Q65.Three positive numbers form an increasing G. P. If the middle term in this G. P. is doubled, the new numbers are in A. P. Then the common ratio of the G. P. is : (1) 2 −√3 (2) 2 + √3 (3) √2 + √3 (4) 3 + √2

Q65.The number of terms in an A. P. is even, the sum of the odd terms in it is 24 and that the even terms is 30. If the last term exceeds the first term by 10 12 , then the number of terms in the A. P. is (1) 4 (2) 8 (3) 16 (4) 12