Permutations & Combinations · JEE Main previous year questions

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2023 35 questions

Q232023 · 13 Apr 2023 · Shift 1· Numerical answer
The number of seven digit positive integers formed using the digits 1, 2, 3 and 4 only and sum of the digits equal to 12 is __________.
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Answer: 413
Q12023 · 13 Apr 2023 · Shift 2
Let $a_{1}, a_{2}, a_{3}, \dots$ be a G.P. of increasing positive numbers. Let the sum of its $6^{th}$ and $8^{th}$ terms be $2$ and the product of its $3^{rd}$ and $5^{th}$ terms be $\frac{1}{9}$ . Then $6 (a_{2} + a_{4}) (a_{4} + a_{6})$ is equal to
1. A. $22$
2. B. $2$
3. C. $33$
4. D. $3$
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Answer: D
Q32023 · 13 Apr 2023 · Shift 2
All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is :
1. A.324
2. B.328
3. C.326
4. D.327
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Answer: D
Q292023 · 13 Apr 2023 · Shift 2· Numerical answer
Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ___________.
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Answer: 16
Q52023 · 12 Apr 2023 · Shift 1
The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $0, 1, 3, 5, 7$ and $9$ without repetition, is equal to :
1. A. $132$
2. B. $72$
3. C. $120$
4. D. $96$
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Answer: C
Q222023 · 12 Apr 2023 · Shift 1· Numerical answer
Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that three consecutive digits are in A.P. at least once. How many such numbers can be formed?
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Answer: 1260
Q242023 · 12 Apr 2023 · Shift 1· Numerical answer
A fair $n (n > 1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$ , then $n$ is equal to _________.
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Answer: 10
Q242023 · 11 Apr 2023 · Shift 1· Numerical answer
In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is _________.
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Answer: 44
Q52023 · 11 Apr 2023 · Shift 2
If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is :
1. A.103
2. B.104
3. C.102
4. D.101
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Answer: A
Q252023 · 10 Apr 2023 · Shift 1· Numerical answer
The number of permutations, of the digits 1, 2, 3, ..., 7 without repetition, which neither contain the string 153 nor the string 2467, is ___________.
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Answer: 4898
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