Permutations & Combinations · JEE Main previous year questions

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2026 14 questions

Q92026 · 8 Apr 2026 · Shift 2
A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is :
1. A. $18$
2. B. $36$
3. C. $39$
4. D. $72$
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Answer: B
Q72026 · 6 Apr 2026 · Shift 1
The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:
1. A.2670
2. B.2840
3. C.2920
4. D.3600
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Answer: D
Q72026 · 6 Apr 2026 · Shift 2
A building has ground floor and 10 more floors. Nine persons enter in a lift at the ground floor. The lift goes up to the $1 0^{th}$ floor. The number of ways, in which any 4 persons exit at a floor and the remaining 5 persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to :
1. A.2184
2. B.3064
3. C.7056
4. D.11340
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Answer: C
Q222026 · 5 Apr 2026 · Shift 1· Numerical answer
Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is ____.
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Answer: 126
Q92026 · 5 Apr 2026 · Shift 2
A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :
1. A. $4100$
2. B. $4140$
3. C. $4230$
4. D. $4290$
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Answer: A
Q82026 · 4 Apr 2026 · Shift 1
The number of ways, of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:
1. A.5040
2. B.3050
3. C.3410
4. D.4320
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Answer: D
Q62026 · 2 Apr 2026 · Shift 1
The number of seven-digit numbers, that can be formed by using the digits $1, 2, 3, 5$ and $7$ such that each digit is used at least once, is :
1. A.15400
2. B.17800
3. C.16800
4. D.29400
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Answer: C
Q72026 · 2 Apr 2026 · Shift 2
Let $p_{n}$ denote the total number of triangles formed by joining the vertices of an n-side regular polygon. If $P_{n + 1} - P_{n} = 66$ , then the sum of all distinct prime divisors of n is :
1. A.7
2. B.8
3. C.5
4. D.6
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Answer: C
Q162026 · 28 Jan 2026 · Shift 1
Let $S = {1, 2, 3, 4, 5, 6, 7, 8, 9}$ . Let $x$ be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let $y$ be the number of 9 - digit numbers formed using the digits of the set S such that only two digits are repeated and each of these is repeated exactly twice. Then,
1. A. $56 x = 9 y$
2. B. $21 x = 4 y$
3. C. $45 x = 7 y$
4. D. $29 x = 5 y$
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Answer: B
Q222026 · 28 Jan 2026 · Shift 2· Numerical answer
Three persons enter in a lift at the ground floor. The lift will go up to $1 0^{th}$ floor. The number of ways, in which the three persons can exit the lift at three different floors, if the lift does not stop at first, second and third floors, is equal to ________.
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Answer: 210
Q252026 · 24 Jan 2026 · Shift 1· Numerical answer
The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits $0, 1, 2, 5, 9$ , if the repetition of the digits is allowed, is ____
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Answer: 42
Q12026 · 23 Jan 2026 · Shift 2
The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is
1. A.384
2. B.403
3. C.429
4. D.455
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Answer: D
Q242026 · 23 Jan 2026 · Shift 2· Numerical answer
Let $S$ denote the set of 4-digit numbers $ab c d$ such that $a > b > c > d$ and $P$ denote the set of 5-digit numbers having product of its digits equal to 20. Then $n (S) + n (P)$ is equal to _____.
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Answer: 260
Q102026 · 21 Jan 2026 · Shift 1
Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive terms such that $a_{2} \cdot a_{3} \cdot a_{4} = 64$ and $a_{1} + a_{3} + a_{5} = \frac{813}{7}$ . Then $a_{3} + a_{5} + a_{7}$ is equal to :
1. A.3256
2. B.3252
3. C.3248
4. D.3244
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Answer: B