Practice Questions

Q62.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) 10 (3) −10 (4) 25 z ∈C satisfying |z| = 1

Q62.If an angle A of a ΔABC satisfies 5 cos A + 3 = 0, then the roots of the quadratic equation 9x2 + 27x + 20 = 0 are (1) sec A, cot A (2) sec A, tan A (3) tan A, cos A (4) sin A, sec A n = 1 is

Q62.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) an empty set (3) {0, 14 , −14 } (4) equal to R

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

Q62.The number of four letter words that can be formed using the letters of the word BARRACK is (1) 144 (2) 120 (3) 264 (4) 270 and Bn = 1 −An . Then, the least odd natural number p

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

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.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.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.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

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.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

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

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.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 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

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.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.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

Q68.A circle passes through the points (2, 3) and (4, 5). If its centre lies on the line y −4x + 3 = 0, then its radius is equal to : (1) √5 (2) √2 (3) 2 (4) 1