Practice Questions

Q62.If for z = α + iβ, |z + 2| = z + 4(1 + i), then α + β and αβ are the roots of the equation (1) x2 + 3x −4 = 0 (2) x2 + 7x + 12 = 0 (3) x2 + x −12 = 0 (4) x2 + 2x −3 = 0

Q62.The number of ways of selecting two numbers a and b, a ∈{2, 4, 6, … … , 100} and b ∈{1, 3, 5, … … , 99} such that 2 is the remainder when a + b is divided by 23 is (1) 186 (2) 54 (3) 108 (4) 268 JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q62.Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is (1) 1120 (2) 3360 (3) 1680 (4) 560 1

Q63.The sum to 10 terms of the series 1 2 3 + + + … is :- 1 + 12 + 14 1 + 22 + 24 1 + 32 + 34 59 55 (1) (2) 111 111 (3) 56 (4) 58 111 111

Q63.The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is (1) 6 (2) 12 (3) 120 (4) 72

Q63.Let a1, a2, a3, … …. be an A.P. If a7 = 3, the product (a1a4) is minimum and the sum of its first n terms is zero then n! −4an(n+2) is equal to (1) 381 (2) 9 4 (3) 33 (4) 24 4

Q63.If the number of words, with or without meaning. which can be made using all the letters of the word MATHEMATICS in which C and S do not come together, is (6!)k then k is equal to (1) 2835 (2) 5670 (3) 1890 (4) 945

Q63.If the coefficient of 𝑥7 in 𝑎𝑥- and the coefficient of 𝑥-5 in 𝑎𝑥+ are equal, then 𝑎4𝑏4 is equal to: 𝑏𝑥2 𝑏𝑥2 (1) 11 (2) 44 (3) 22 (4) 33. 𝜋 2𝜋 4𝜋 8𝜋 16𝜋 Q64.96 cos cos cos cos cos is equal to 33 33 33 33 33 (1) 3 (2) 1 (3) 4 (4) 2

Q63.The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is (1) 16800 (2) 33600 (3) 18000 (4) 14800

Q63.Let x and y be distinct integers where 1 ≤x ≤25 and 1 ≤y ≤25. Then, the number of ways of choosing x and y, such that x + y is divisible by 5 , is _____ .

Q63.The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is

Q63.The number of five-digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits 0, 1, 3, 5, 7 and 9 without repetition, is equal to (1) 132 (2) 120 (3) 72 (4) 96

Q63.The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is (1) 120 (2) 168 (3) 220 (4) 48 13+23+33......upto n terms

Q63.All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is (1) 576 (2) 578 (3) 580 (4) 582

Q63.If all the six digit numbers x1x2x3x4x5x6 with 0 < x1 < x2 < x3 < x4 < x5 < x6 are arranged in the increasing order, then the sum of the digits in the 72th number is _______.

Q63.The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8, if repetition of digits is allowed, is (1) 21 (2) 20 (3) 22 (4) 18

Q63.Let 𝑎1, 𝑎2, 𝑎3, . . . . , 𝑎𝑛 be n positive consecutive terms of an arithmetic progression. If 𝑑> 0 is its common difference, then lim 𝑑 1 + 1 + … + 1 is 𝑛→∞√ 𝑛 √𝑎1 + √𝑎2 √𝑎2 + √𝑎3 √𝑎𝑛- 1 + √𝑎𝑛 (1) 1 (2) √𝑑 √𝑑 (3) 1 (4) 2 𝑛

Q63.The number of triplets 𝑥, 𝑦, 𝑧 where 𝑥, 𝑦, 𝑧 are distinct non negative integers satisfying 𝑥+ 𝑦+ 𝑧= 15, is (1) 80 (2) 136 (3) 114 (4) 92

Q63.If the coefficient of 𝑥15 in the expansion of 𝑎𝑥3 + 1 is equal to the coefficient of 𝑥-15 in the expansion of 𝑏𝑥 3 1 15 1 𝑎𝑥 3 - , where 𝑎 and 𝑏 are positive real numbers, then for each such ordered pair 𝑎, 𝑏: 𝑏𝑥3 (1) 𝑎= 𝑏 (2) 𝑎𝑏= 1 (3) 𝑎= 3𝑏 (4) 𝑎𝑏= 3

Q63.Number of integral solutions to the equation x + y + z = 21 , where x ≥1, y ≥3, z ≥4 , is equal to _____ .

Q63.Let S = {z ∈C −{i, 2i} z2−3iz−2 ∈R}. JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q63.Let s1, s2, s3. . . . , s10 respectively be the sum of 12 terms of 10 A. Ps whose first terms are 1, 2, 3, . . . . , 10 and the common differences are 1, 3, 5, . . . , 19 respectively. Then ∑10i=1 si is equal to (1) 7220 (2) 7360 (3) 7260 (4) 7380

Q63.The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is : (1) 89 (2) 84 (3) 86 (4) 79

Q63.The value of ∑𝑟=22 0 22𝐶𝑟· 23𝐶𝑟 is (1) 45𝐶23 (2) 44𝐶23 (3) 45𝐶24 (4) 44𝐶22

Q63.If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296, respectively, then the sum of common ratios of all such GPs is 9 (1) 7 (2) 2 (3) 3 (4) 14