Practice Questions

Q62.If 1 + 1 + … + 1 = m and 1⋅21 + 2⋅31 + … + 99⋅1001 = n , then the point (m, n) lies on the √1+√2 √2+√3 √99+√100 line (1) 11(x −1) −100(y −2) = 0 (2) 11x −100y = 0 (3) 11(x −2) −100(y −1) = 0 (4) 11(x −1) −100y = 0

Q62.Let 𝑆= 𝑧∈𝐶: 𝑧−1 = 1 and √2 −1𝑧+ ¯𝑧- 𝑖𝑧- ¯𝑧= 2√2. Let 𝑧1, 𝑧2 ∈𝑆 be such that 𝑧1 = max𝑧∈𝑠𝑧 and 2 𝑧2 = min𝑧∈𝑠𝑧. Then √2𝑧1 −𝑧2 equals: (1) 1 (2) 4 (3) 3 (4) 2

Q62.Let 0 ≤r ≤n. If n+1Cr+1 : nCr : n−1Cr−1 = 55 : 35 : 21, then 2n + 5r is equal to: JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper (1) 50 (2) 62 (3) 55 (4) 60

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.The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is (1) 406 (2) 130 (3) 142 (4) 136

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.The 20th term from the end of the progression 20, 191 181 173 … , - 1291 is :- 4, 2, 4, 4 (1) -118 (2) -110 (3) -115 (4) -100

Q63.If A denotes the sum of all the coefficients in the expansion of (1 −3x + 10x2) and B denotes the sum of all the coefficients in the expansion of (1 + x2)n , then : (1) A = B3 (2) 3 A = B (3) B = A3 (4) A = 3 B

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.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.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.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.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.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.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 coefficient of x70 in x2(1 + x)98 + x3(1 + x)97 + x4(1 + x)96 + … + x54(1 + x)46 is 99Cp −46Cq . Then a possible value of p + q is : (1) 55 (2) 83 (3) 61 (4) 68

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.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

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.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 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 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.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)

Q64.If sin x = −35 , where π < x < 3π2 , then 80 (tan2 x −cos x) is equal to (1) 108 (2) 109 (3) 18 (4) 19 JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper

Q64.Let two straight lines drawn from the origin O intersect the line 3x + 4y = 12 at the points P and Q such that △OPQ is an isosceles triangle and ∠POQ = 90∘ . If l = OP2 + PQ2 + QO2 , then the greatest integer less than or equal to l is : (1) 42 (2) 46 (3) 44 (4) 48