Practice Questions

Q62.If α, β ∈C are the distinct roots of the equation x2 −x + 1 = 0, then α101 + β107 is equal to (1) 2 (2) −1 (3) 0 (4) 1

Q63.The least positive integer n for which ( 1−i√31+i√3 ) (1) 2 (2) 5 (3) 6 (4) 3

Q63.The set of all α ∈R, for which w = 1+(1−8α)z1−z is a purely imaginary number, for all and Re(z) ≠1 , is : (1) {0} (2) {0, 14 , −14 } (3) equal to R (4) an empty set

Q63.Let An = ( 34 ) −( 43 ) 2 + ( 43 ) 3 −… + (−1)n−1( 43 ) n , so that Bn > An , for all n ≥p is (1) 5 (2) 7 (3) 11 (4) 9

Q63. n - digit numbers are formed using only three digits 2,5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed, is (1) 6 (2) 8 (3) 9 (4) 7

Q63.From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is: (1) At least 750 but less than 1000 (2) At least 1000 (3) Less than 500 (4) At least 500 but less than 750

Q64. n-digit numbers are formed using only three digits 2, 5 and 7 . The smallest value of n for which 900 such distinct numbers can be formed is : (1) 9 (2) 7 (3) 8 (4) 6

Q64.Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series 12 + 2 ⋅22 + 32 + 2 ⋅42 + 52 + 2 ⋅62 + … If B −2A = 100λ, then λ is equal to : (1) 496 (2) 232 (3) 248 (4) 464

Q64.If b is the first term of an infinite G. P whose sum is five, then b lies in the interval. (1) (−∞, −10) (2) (10, ∞) (3) (0, 10) (4) (−10, 0)

Q64.The number of numbers between 2, 000 and 5, 000 that can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is not allowed) and are multiple of 3 is (1) 36 (2) 30 (3) 24 (4) 48

Q64.If a, b, c are in A.P. and a2, b2, c2 are in G.P. such that a < b < c and a + b + c = 34 , then the value of a is JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper (1) 1 4 − 3√21 (2) 14 − 4√21 (3) 1 (4) 1 1 − 4 √2 4 − 2√21

Q65.Let a1, a2, a3, … … , a49 be in A. P. such that Σ12 = 416 and a9 + a43 = 66. If k=0a4k+1 a21 + a22 + … + a217 = 140m, then m is equal to: (1) 33 (2) 66 (3) 68 (4) 34

Q65.Let 1 , 1 , … , 1 ≠0 for i = 1, 2, … . , n) be in A.P. such that x1 = 4 and x21 = 20. If n is the least x1 x2 xn (xi is equal to positive integer for which xn > 50, then ∑ni=1( xi1 ) (1) 3 (2) 18 (3) 13 (4) 13 4 8

Q65.The coefficient of x10 in the expansion of (1 + x)2 (1 + x2)3(1 + x3)4 is equal to (1) 52 (2) 44 (3) 50 (4) 56

Q65.If b is the first term of an infinite geometric progression whose sum is five, then b lies in the interval (1) [10, ∞) (2) (−∞, −10] (3) (−10, 0) (4) (0, 10)

Q65.If x1, x2, … . , xn and h11 , h21 , … . . hn1 are two A.P's such that x3 = h2 = 8 and x8 = h7 = 20 , then x5. h10 equals. (1) 2560 (2) 2650 (3) 3200 (4) 1600

Q66.If n is the degree of the polynomial, 1 8 1 8 + [ √5x3 + 1 −√5x3 −1 ] [ √5x3 + 1 + √5x3 −1 ] and m is the coefficient of xn in it, then the ordered pair (n, m) is equal to (1) (12, (20)4) (2) (8, 5(10)4) (3) (24, (10)8) (4) (12, 8(10)4) JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q66.The sum of the co-efficient of all odd degree terms in the expansion of 5 5 + , (x > 1) is (x + √x3 −1) (x −√x3 −1) (1) 2 (2) −1 (3) 0 (4) 1

Q66.The sum of the first 20 terms of the series 1 + 23 + 47 + 158 + 1631 + … is (1) 39 + 1 (2) 38 + 1 219 220 (3) 38 + 1 (4) 39 + 1 219 220 is

Q66.If x1, x2, … . . , xn and h11 , h21 , … . . , hn1 are two A.P.s such that x3 = h2 = 8 & x8 = h7 = 20 , then x5 ⋅h10 is equal to (1) 3200 (2) 1600 (3) 2650 (4) 2560

Q66.The number of solutions of sin 3x = cos 2x, in the interval ( π2 , π) is (1) 3 (2) 4 (3) 2 (4) 1

Q67.If tan A and tan B are the roots of the quadratic equation, 3x2 −10x −25 = 0 then the value of 3 sin2(A + B) −10 sin(A + B) ⋅cos(A + B) −25 cos2 (A + B) is (1) 25 (2) −25 (3) −10 (4) 10

Q67.If sum of all the solutions of the equation 8 cos x ⋅(cos( π6 + x) ⋅cos( π6 −x) −12 ) = 1 in [0, π] is kπ, then k is equal to: JEE Main 2018 (08 Apr) JEE Main Previous Year Paper (1) 20 (2) 2 9 3 (3) 13 (4) 8 9 9

Q67.The coefficient of x2 in the expansion of the product (2 −x2){(1 + 2x + 3x2) 6 + (1 −4x2) 6} (1) 107 (2) 108 (3) 155 (4) 106

Q67.Consider the following two statements. Statement p : The value of sin 120∘ can be divided by taking θ = 240∘ in the equation θ 2 sin = √1 + sin θ −√1 −sin θ. 2 Statement q : The angles A, B, C and D of any quadrilateral ABCD satisfy the equation 1 1 cos (A + + cos (B + = 0 ( 2 C)) ( 2 D)) Then the truth values of p and q are respectively. (1) F, T (2) T, T (3) F, F (4) T, F