Permutations & Combinations · JEE Main previous year questions

2019 7 questions

1. Q72019 · 12 Apr 2019 · Shift 1

   The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :

   1. A.$2^{20}-1$
   2. B.$2^{20}$
   3. C.$2^{20}+1$
   4. D.$2^{21}$
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   Answer: B

2. Q82019 · 12 Apr 2019 · Shift 2

   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. A.24
   2. B.25
   3. C.27
   4. D.28
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   Answer: B

3. Q182019 · 10 Apr 2019 · Shift 1

   The number of 6 digit numbers 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. A.36
   2. B.60
   3. C.72
   4. D.48
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   Answer: B

4. Q92019 · 9 Apr 2019 · Shift 1

   A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then :

   1. A.n = m – 8
   2. B.m = n = 78
   3. C.m + n = 68
   4. D.m = n = 68
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   Answer: B

5. Q232019 · 9 Apr 2019 · Shift 2

   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 addded to the total number of balls used in forming the equilaterial 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. A.262
   2. B.190
   3. C.157
   4. D.225
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   Answer: B

6. Q202019 · 8 Apr 2019 · Shift 2

   The number of four-digit numbers strictly greater than 4321 that can be formed using the digits 0,1,2,3,4,5 (repetition of digits is allowed) is :

   1. A.306
   2. B.288
   3. C.310
   4. D.360
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   Answer: C

7. Q232019 · 12 Jan 2019 · Shift 1

   Consider three boxes, each containing, 10 balls labelled 1, 2, ..., 10. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$, the label of the ball drawn from the $i^{\text{th}}$ box, $(i=1,2,3)$. Then, the number of ways in which the balls can be chosen such that $n_1<n_2<n_3$ is :

   1. A.164
   2. B.240
   3. C.82
   4. D.120
   Show answer

   Answer: D