Practice Questions

Q63.A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is 1750, then n is equal to (1) 24 (2) 27 (3) 25 (4) 28

Q63.If ∑25r=0{(50Cr)(50−rC25−r)} = K(50C25) , then K is equal to (1) 225 (2) 225 −1 (3) 224 (4) (25)2 is 720, is

Q63.Let S = {1, 2, 3, … . , 100}, then number of non-empty subsets A of S such that the product of elements in A is even is : (1) 2100 −1 (2) 250 + 1 (3) 250(250 −1) (4) 250 −1

Q63.All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is (1) 175 (2) 162 (3) 180 (4) 160

Q63.If 𝑧= √3 + 𝑖= √-1, then 1 + 𝑖𝑧+ 𝑧5 + 𝑖𝑧89 is equal to: 2 2 (1) -1 (2) 1 (3) 0 (4) -1 + 2𝑖9

Q63.There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds the number of games played between the men and the women by 84, then the value of m is : (1) 11 (2) 12 (3) 7 (4) 9 is equal to 225K,

Q63.The number of 6 digit number that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digit is repeated is: (1) 36 (2) 60 (3) 72 (4) 48

Q64.Consider three boxes, each containing 10 balls labelled 1, 2, … . , 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni , the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1 < n2 < n3 is : (1) 240 (2) 82 (3) 120 (4) 164

Q64.The sum 1 + 13 + 23 + 13 + 23 + 33 + . . . + 13 + 23 + 33 + . . . + 153 - 1 + 2 + 3 + . . . + 15 is equal to 1 + 2 1 + 2 + 3 1 + 2 + 3 + . . . + 15 21 (1) 620 (2) 1240 (3) 1860 (4) 660

Q64.The positive value of λ for which the co-efficient of x2 in the expansion x2(√x + x2λ ) 10 (1) √5 (2) 3 (3) 4 (4) 2√2

Q64.The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is 27 . 19 Then the common ratio of this series is: JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper (1) 1 (2) 2 3 3 (3) 2 (4) 4 9 9

Q64.Let Sn = 1 + q + q2 + … . +qn and Tn = 1 + ( q+12 ) ( q+12 ) ( q+12 ) and q ≠1. If 101C1 + 101C2 ⋅S1 + … . +101C101 ⋅S100 = αT100, then α is equal to : (1) 299 (2) 202 (3) 200 (4) 2100

Q64.Let the sum of the first n terms of a non-constant A. P. , a1, a2, a3, . . . . , an be 50n + n(n−7)2 A, where a constant. If d is the common difference of this A. P., then the ordered pair (d, a50) is equal to (1) (50, 50 + 46A) (2) (A, 50 + 45A) (3) (50, 50 + 45A) (4) (A, 50 + 46A) x is

Q64.The number of natural numbers less than 7000 which can be formed by using the digits 0, 1, 3, 7, 9 (repetition of digits allowed) is equal to: (1) 375 (2) 250 (3) 374 (4) 372 up to 15 terms,

Q64.If a1, a2, a3. . . . . . . . . , an are in A. P. and a1 + a4 + a7. . . . . . . . . +a16 = 114 , then a1 + a6 + a11 + a16 is equal to : (1) 64 (2) 98 (3) 38 (4) 76 JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper

Q64.If 𝑎, 𝑏 and 𝑐 be three distinct real numbers in G.P. and 𝑎+ 𝑏+ 𝑐= 𝑥𝑏, then 𝑥 cannot be: (1) -3 (2) 2 (3) 4 (4) -2

Q64.If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is: 1 3 (1) (2) 10 10 (3) 1 (4) 3 5 20

Q64.The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is (1) 1356 (2) 1365 (3) 1256 (4) 1465 = 21k , then k equals

Q64.If the sum of the first 15 terms of the series ( 43 ) 3 + (1 12 ) 3 + (2 14 ) 3 + 33 + (3 34 ) 3 + … then K is equal to : (1) 9 (2) 27 (3) 54 (4) 108

Q64.The sum of all natural numbers 𝑛 such that 100 < 𝑛< 200 and 𝐻. 𝐶. 𝐹. 91, 𝑛> 1 is (1) 3203 (2) 3221 (3) 3121 (4) 3303

Q64.The number of four-digit numbers strictly greater than 4321 that can be formed using the digit 0,1, 2,3, 4,5 (repetition of digits is allowed) is: (1) 360 (2) 288 (3) 306 (4) 310 JEE Main 2019 (08 Apr Shift 2) JEE Main Previous Year Paper 20 1

Q64.If a1, a2, a3, . . . . are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P is: (1) 280 (2) 120 (3) 150 (4) 200

Q64.Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square, whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is (1) 262 (2) 190 (3) 225 (4) 157

Q65.The sum of the co-efficient of all even degree terms in 𝑥 in the expansion of 6 6 𝑥+ √𝑥3 - 1 +𝑥- √𝑥3 - 1 , 𝑥> 1 is equal to (1) 26 (2) 32 (3) 24 (4) 29

Q65.Let 𝑎1, 𝑎2, … , 𝑎30 be an A.P., 𝑆= ∑𝑖=30 1 𝑎𝑖 and 𝑇= ∑𝑖=15 1 𝑎( 2𝑖- 1 ) . If 𝑎5 = 27 and 𝑆- 2𝑇= 75, then 𝑎10 is equal to: (1) 52 (2) 47 (3) 42 (4) 57