Practice Questions

Q62.The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to : (1) 179 (2) 177 (3) 181 (4) 175

Q62.The number of common terms in the progressions 4, 9, 14, 19, … …, up to 25th term and 3, 6, 9, 12,.... up to 37th term is : (1) 9 (2) 5 (3) 7 (4) 8 n

Q62.The value of 1×22+2×32+…+100×(101)2 is 12×2+22×3+….+1002×101 (1) 32 (2) 31 31 30 (3) 306 (4) 305 305 301 JEE Main 2024 (04 Apr Shift 2) JEE Main Previous Year Paper

Q62.Let z be a complex number such that the real part of z−2i is zero. Then, the maximum value of |z −(6 + 8i)| z+2i is equal to (1) 12 (2) 10 (3) 8 (4) ∞

Q62.If 𝑧 is a complex number such that 𝑧≤1, then the minimum value of 𝑧+ 1 + 4𝑖 is: 23 5 (1) 2 (2) 2 3 (3) (4) 3 2

Q62.Let z be a complex number such that |z + 2| = 1 and Im ( z+2 ) = 5 . Then the value of |Re(z + 2)| is (1) 2√6 (2) 24 5 5 (3) 1+√6 (4) √6 5 5

Q63.If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then the word at 315th position in this arrangement is : (1) NRAGUP (2) NRAPUG (3) NRAPGU (4) NRAGPU

Q63.There are 5 points P1, P2, P3, P4, P5 on the side AB, excluding A and B, of a triangle ABC . Similarly there are 6 points P6, P7, … , P11 on the side BC and 7 points P12, P13, … , P18 on the side CA of the triangle. The number of triangles, that can be formed using the points P1, P2, … , P18 as vertices, is : (1) 776 (2) 796 (3) 751 (4) 771

Q63.In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70 and the 3 product of the third and fifth terms is 49 . Then the sum of the 4th , 6th and 8th terms is equal to : (1) 96 (2) 91 (3) 84 (4) 78

Q63.The sum of the series + + + . ... up to 10 terms is 1 −3 ⋅12 + 14 1 −3 ⋅22 + 24 1 −3 ⋅32 + 34 (1) 45 (2) - 45 109 109 55 55 (3) (4) - 109 109

Q63.Let A = {n ∈[100, 700] ∩N : n is neither a multiple of 3 nor a multiple of 4 }. Then the number of elements in A is (1) 290 (2) 280 (3) 300 (4) 310

Q63.Suppose θϵ [0, π4 ] is a solution of 4 cos θ −3 sin θ = 1. Then cos θ is equal to : (1) 4 (2) 6+√6 (3√6+2) (3√6+2) (3) 4 (4) 6−√6 (3√6−2) (3√6−2)

Q63.Let three real numbers a, b, c be in arithmetic progression and a + 1, b, c + 3 be in geometric progression. If a > 10 and the arithmetic mean of a, b and c is 8, then the cube of the geometric mean of a, b and c is (1) 128 (2) 316 (3) 120 (4) 312

Q63.Suppose 28 - 𝑝, 𝑝, 70 - 𝛼, 𝛼 are the coefficient of four consecutive terms in the expansion of ( 1 + 𝑥) 𝑛. Then the value of 2𝛼- 3𝑝 equals (1) 7 (2) 10 (3) 4 (4) 6 𝜋

Q63.For x ⩾0, the least value of K, for which 41+x + 41−x, K2 , 16x + 16−x are three consecutive terms of an A.P., is equal to : (1) 8 (2) 4 (3) 10 (4) 16

Q63.Let a, ar, ar2 , be an infinite G.P. If ∑∞n=0 arn = 57 and ∑∞n=0 a3r3n = 9747, then a + 18r is equal to (1) 46 (2) 38 (3) 31 (4) 27 is

Q63.If loge a, loge b, loge c are in an A. P. and loge a −loge 2b, loge 2b −loge 3c, loge 3c −loge a are also in an A. P., then a : b : c is equal to (1) 9 : 6 : 4 (2) 16 : 4 : 1 (3) 25 : 10 : 4 (4) 6 : 3 : 2

Q63.Let 𝑆𝑛 denote the sum of the first n terms of an arithmetic progression. If 𝑆10 = 390 and the ratio of the tenth and the fifth terms is 15 : 7, then 𝑆15 −𝑆5 is equal to: (1) 800 (2) 890 (3) 790 (4) 690 1 18 1 1

Q63.If the set R = {(a, b) : a + 5b = 42, a, b ∈N} has m elements and ∑mn=1 (1 −in!) = x + iy, where i = √−1 , then the value of m + x + y is (1) 12 (2) 4 (3) 8 (4) 5

Q63.If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to (1) 7 (2) 4 (3) 5 (4) 6

Q63.If 2 sin3 x + sin 2x cos x + 4 sin x −4 = 0 has exactly 3 solutions in the interval [0, nπ2 ⌉, n ∈N , then the roots of the equation x2 + nx + (n −3) = 0 belong to : (1) (0, ∞) (2) (−∞, 0) (3) (−√172 , √172 ) (4) Z

Q63.If 𝑛 is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then 𝑛 is equal to: (1) 47 (2) 53 (3) 51 (4) 43

Q64.The sum of the coefficient of x2/3 and x−2/5 in the binomial expansion of (x2/3 + 12 x−2/5) 9 (1) 21/4 (2) 63/16 (3) 19/4 (4) 69/16

Q64.If each term of a geometric progression a1, a2, a3, … with a1 = 18 and a2 ≠a1 , is the arithmetic mean of the next two terms and Sn = a1 + a2 + … + an , then S20 −S18 is equal to (1) 215 (2) −218 (3) 218 (4) −215

Q64.Let 𝛼, 𝛽, 𝛾, 𝛿∈𝑍 and let 𝐴𝛼, 𝛽, 𝐵1, 0, 𝐶𝛾, 𝛿 and 𝐷1, 2 be the vertices of a parallelogram 𝐴𝐵𝐶𝐷. If 𝐴𝐵= √10 and the points 𝐴 and 𝐶 lie on the line 3𝑦= 2𝑥+ 1, then 2𝛼+ 𝛽+ 𝛾+ 𝛿 is equal to (1) 10 (2) 5 (3) 12 (4) 8