Permutations & Combinations · JEE Main previous year questions

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2023 35 questions

Q22023 · 10 Apr 2023 · Shift 2
Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is :
1. A.560
2. B.1680
3. C.3360
4. D.1120
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Answer: B
Q232023 · 10 Apr 2023 · Shift 2· Numerical answer
The sum of all the four-digit numbers that can be formed using all the digits 2, 1, 2, 3 is equal to __________.
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Answer: 26664
Q12023 · 8 Apr 2023 · Shift 1
The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is :
1. A.16800
2. B.14800
3. C.18000
4. D.33600
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Answer: A
Q62023 · 8 Apr 2023 · Shift 1
The number of ways, in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together, is :
1. A. $720$
2. B. $7 (360)^{2}$
3. C. $7 (720)^{2}$
4. D. $126 (5!)^{2}$
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Answer: D
Q92023 · 8 Apr 2023 · Shift 2
If the number of words, with or without meaning, which can be made using all the letters of the word $MATHEMATICS$ in which $C$ and $S$ do not come together, is $(6!) k$ , then $k$ is equal to :
1. A. $5670$
2. B. $1890$
3. C. $2835$
4. D. $945$
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Answer: A
Q272023 · 6 Apr 2023 · Shift 1· Numerical answer
The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ___________.
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Answer: 3483638676
Q32023 · 6 Apr 2023 · Shift 2
All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is :
1. A.578
2. B.576
3. C.580
4. D.582
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Answer: D
Q232023 · 6 Apr 2023 · Shift 2· Numerical answer
The number of 4-letter words, with or without meaning, each consisting of 2 vowels and 2 consonants, which can be formed from the letters of the word UNIVERSE without repetition is __________.
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Answer: 432
Q252023 · 1 Feb 2023 · Shift 1· Numerical answer
The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7, is ____________.
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Answer: 514
Q262023 · 1 Feb 2023 · Shift 1· Numerical answer
The number of words, with or without meaning, that can be formed using all the letters of the word ASSASSINATION so that the vowels occur together, is ___________.
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Answer: 50400
Q222023 · 31 Jan 2023 · Shift 1· Numerical answer
Let 5 digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is ___________.
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Answer: 2997
Q242023 · 31 Jan 2023 · Shift 1· Numerical answer
Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to ____________.
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Answer: 710
Q222023 · 30 Jan 2023 · Shift 1· Numerical answer
Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to ___________.
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Answer: 21
Q202023 · 29 Jan 2023 · Shift 1
If $p, q$ and $r$ are three propositions, then which of the following combination of truth values of $p, q$ and $r$ makes the logical expression ${(p \lor q) \land ((\sim p) \lor r)} \to ((\sim q) \lor r)$ false?
1. A. $p = F, q = T, r = F$
2. B. $p = T, q = T, r = F$
3. C. $p = T, q = F, r = T$
4. D. $p = T, q = F, r = F$
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Answer: A
Q252023 · 29 Jan 2023 · Shift 1· Numerical answer
If all the six digit numbers $x_{1} x_{2} x_{3} x_{4} x_{5} x_{6}$ with $0 < x_{1} < x_{2} < x_{3} < x_{4} < x_{5} < x_{6}$ are arranged in the increasing order, then the sum of the digits in the $7 2^{nd}$ number is ____.
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Answer: 32
Q272023 · 29 Jan 2023 · Shift 1· Numerical answer
Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is ____________.
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Answer: 1436
Q32023 · 29 Jan 2023 · Shift 2
The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a series. Then the serial number of the word TOUGH is :
1. A.79
2. B.84
3. C.89
4. D.86
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Answer: C
Q52023 · 29 Jan 2023 · Shift 2
The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :
1. A.400
2. B.472
3. C.507
4. D.432
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Answer: D
Q212023 · 29 Jan 2023 · Shift 2· Numerical answer
The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.
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Answer: 3000
Q232023 · 25 Jan 2023 · Shift 1· Numerical answer
Let $x$ and $y$ be distinct integers where $1 \leq x \leq 25$ and $1 \leq y \leq 25$ . Then, the number of ways of choosing $x$ and $y$ , such that $x + y$ is divisible by 5, is ____.
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Answer: 120
Q132023 · 25 Jan 2023 · Shift 2
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is :
1. A.120
2. B.6
3. C.72
4. D.12
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Answer: C
Q252023 · 25 Jan 2023 · Shift 2· Numerical answer
Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is ____________
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Answer: 6860 or 3
Q252023 · 24 Jan 2023 · Shift 1· Numerical answer
A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is __________
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Answer: 546
Q282023 · 24 Jan 2023 · Shift 1· Numerical answer
The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is ______________.
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Answer: 60
Q32023 · 24 Jan 2023 · Shift 2
The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition is :
1. A.48
2. B.120
3. C.168
4. D.220
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Answer: C