Skip to main content
Back to PERMUTATION AND COMBINATION

Your Progress

0 / 250 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • PERMUTATION AND COMBINATION

Permutation and combination practice · Medium

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 1-30 of 250 questions
1 Medium
1 of 250
Application +4 | -1
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?
View answer and explanation
Correct option: C
60
Option C (60) is correct because it represents the number of ways to arrange the digits such that the odd digits occupy the even positions, calculated using permutations.
2 Medium
2 of 250
Application +4 | -1
The number of four-digit numbers that can be made with the digits 1,2,3,41,2,3,4 and 5 in which atleast two digits are identical, is
View answer and explanation
Correct option: B
505
Option B (505) is correct because it calculates the number of four-digit numbers with at least two identical digits by subtracting the number of numbers with distinct digits from the total number of possible numbers.
3 Medium
3 of 250
Application +4 | -1
Five digited numbers with distinct digits are formed by using the digits, 5, 4, 3, 2, 1, 0. The number of those numbers which are multiples of 3, is
View answer and explanation
Correct option: C
216
Option C (216) is correct because the numbers formed must have a digit sum divisible by 3, considering both cases: including and excluding 0.
4 Medium
4 of 250
Application +4 | -1
The number of four letter words that can be formed using the letters of the word BARRACK is
View answer and explanation
Correct option: D
270
Option D (270) is correct because it accounts for all possible four-letter words formed using the letters of BARRACK, considering cases with different letters, two R's, and two A's.
5 Medium
5 of 250
Application +4 | -1
Number of ways in which four prize can be given away to 8 students when a students can get any number of prize is
View answer and explanation
Correct option: B
848^4
Option D (None of these) is correct. There appears to be an error in the provided solution. The correct approach involves derangements, and the number of functions f: A -> B such that f(i) != a_i is given by the number of derangements of 5 elements, which is 44. Therefore, none of the given options are correct.
6 Medium
6 of 250
Application +4 | -1
The total number of numbers that are less than 3⋅1083 \cdot 10^8 and can be formed using the digits 1,2,31,2,3, is equal to
View answer and explanation
Correct option: C
12(7⋅38−3)\frac{1}{2}\left(7 \cdot 3^8-3\right)
Option C (12(7⋅38−3)\frac{1}{2}\left(7 \cdot 3^8-3\right)) is correct because it represents the total numbers that can be formed using the digits 1, 2, and 3, and are less than 3⋅1083 \cdot 10^8.
7 Medium
7 of 250
Application +4 | -1
No. of ways in which nn different prizes can be distributed among mm - persons (m<n)(m<n) if each is entitled to receive at most (n−1)(n-1) prizes is
View answer and explanation
Correct option: D
mn−mm^n-m
Option D (mn−mm^n-m) is correct because it subtracts the cases where one person receives all prizes from the total possible distributions.
8 Medium
8 of 250
Application +4 | -1
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. It internal arrangement inside the car does not matter then the number of ways in which they can travel, is
View answer and explanation
Correct option: C
126
Option C (126) is correct because it calculates the number of ways to divide 8 students into two cars, one seating 5 and the other seating 4 (but only needing 3), or one seating 4 and the other seating 5 (but only needing 4).
9 Medium
9 of 250
Application +4 | -1
Total number of positive integral solutions of 15<x1+x2+x3≤2015 < x_1+x_2+x_3 \leq 20 is equal to
View answer and explanation
Correct option: D
685
Option D (685) is correct because it calculates the total number of positive integral solutions for the given inequality by summing the solutions for each possible sum value.
10 Medium
10 of 250
Analyzing +4 | -1
Five digit numbers divisible by 9 are to be formed by using the digits 0,1,2,3,4,5,70,1,2,3,4,5,7 without repetition. The total numbers of such numbers is λ3\lambda^3, then λ\lambda is
View answer and explanation
Correct option: B
6
Option B (6) is correct because the total number of such numbers is 216, which is equal to 636^3, thus λ=6\lambda = 6.
11 Medium
11 of 250
Application +4 | -1
Let A={x∣xA=\{x \mid x is a prime number and x<30}x < 30\}. The number of dif- ferent rational numbers whose numerator and denominator belong to AA is
View answer and explanation
Correct option: C
91
Option C (91) is correct because it counts the number of distinct rational numbers formed from the given set of prime numbers.
12 Medium
12 of 250
Analyzing +4 | -1
Number of ordered triplets (x,y,z)(x, y, z) such that x,y,zx, y, z are primes and xy+1=zx^y+1=z, is
View answer and explanation
Correct option: B
1
Option B (1) is the correct answer because only one ordered triplet (2,2,5) satisfies the given conditions.
13 Medium
13 of 250
Application +4 | -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
View answer and explanation
Correct option: B
126(5!)2126(5 !)^{2}
The correct answer is 126(5!)2126(5 !)^{2} because it represents the number of ways to arrange the boys around the table and then arrange the girls in the spaces between them.
14 Medium
14 of 250
Analyzing +4 | -1
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two SS are adjacent?
View answer and explanation
Correct option: A
7.  6C4.  8C47.{\;^6}{C_4}.{\;^8}{C_4}
Option A (7.  6C4.  8C47.{\;^6}{C_4}.{\;^8}{C_4}) is correct because it represents the number of ways to arrange the letters of MISSISSIPPI such that no two S's are adjacent.
15 Medium
15 of 250
Application +4 | -1
The total number of seven-digit numbers the sum of whose digits is even is
View answer and explanation
Correct option: B
4500000
Option B (4500000) is correct because half of all possible seven-digit numbers will have an even sum of digits.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
16 Medium
16 of 250
Application +4 | -1
The number less than 1000 that can be formed using the digits 0,1,2,3,4,50,1,2,3,4,5 when repetition is not allowed is equal to
View answer and explanation
Correct option: B
131
Option B (131) is correct because it correctly calculates the total number of possible numbers less than 1000 using the given digits without repetition.
17 Medium
17 of 250
Application +4 | -1
If the letters of the word 'NAAGI' are arranged as in a dictionary then the rank of the given word is
View answer and explanation
Correct option: C
49
Option C (49) is correct because it calculates the rank of the word NAAGI based on dictionary order, accounting for repeated letters.
18 Medium
18 of 250
Application +4 | -1
The letters of the word 'HEXAGON' are arranged in all possible ways. If the order of the vowels is not to be considered then the number of possible arrangements is
View answer and explanation
Correct option: B
840
Option B (840) is correct because it calculates the arrangements of the consonants and then divides by the number of ways to arrange the vowels to remove the order restriction.
19 Medium
19 of 250
Application +4 | -1
In a 12 - storey house ten people enter a lift cabin. It is known that they will left in groups of 2,3 and 5 people at different storeys. The number of ways they can do so if the lift does not stop to the second storey is
View answer and explanation
Correct option: C
720
Option C (720) is correct because there are 10 possible floors for the groups to leave, and we need to find the number of permutations of choosing 3 of those floors.
20 Medium
20 of 250
Analyzing +4 | -1
1P1+2.2P2+3.3P3+⋯+n.nPn{ }^1 \mathrm{P}_1+2 .{ }^2 \mathrm{P}_2+3 .{ }^3 \mathrm{P}_3+\cdots+n .{ }^n \mathrm{P}_n is equal to
View answer and explanation
Correct option: B
n+1Pn+1−1{ }^{n+1} \mathrm{P}_{n+1}-1
The correct answer is B (n+1Pn+1−1{ }^{n+1} \mathrm{P}_{n+1}-1) because the given sum can be simplified to a telescoping series of factorials.
21 Medium
21 of 250
Application +4 | -1
The pages of a book are numbered 1 to n\mathrm{n}. When page numbers of the book were added, one of the page number was mistakenly added twice \& hence resulting is a incorrect sum 1986 . What was the number of page that was added twice :
View answer and explanation
Correct option: C
33
Option C (33) is correct because it is the page number that, when added twice, results in the incorrect sum of 1986.
22 Medium
22 of 250
Application +4 | -1
Determine nn, if 2nC2:nC2=9:2{ }^{\text {2n}} C_2:{ }^n C_2=9: 2.
View answer and explanation
Correct option: A
5
Option A (5) is correct because solving the ratio 2nC2:nC2=9:2{ }^{2n} C_2:{ }^n C_2=9: 2 leads to n=5n=5.
23 Medium
23 of 250
Application +4 | -1
The total number of ways of selecting two numbers from the set {1,2,3,4,…,3n}\{1,2,3,4, \ldots, 3 n\}, so that their sum of divisible by 3, is
View answer and explanation
Correct option: B
3n2−n2\frac{3 n^2-n}{2}
Option B (3n2−n2\frac{{3 n^2-n}}{{2}}) is correct because it accounts for selecting two numbers from the same remainder group modulo 3 or one number from each of the two different remainder groups.
24 Medium
24 of 250
Application +4 | -1
Total number of ways in which 15 identical blankets can be distributed among 4 persons, so that each of them gets atleast two blankets, is
View answer and explanation
Correct option: A
10C3{ }^{10} {C}_3
Option A (10C3{ }^{10} {C}_3) is correct because it represents the number of ways to distribute the blankets after giving each person the minimum required number of blankets.
25 Medium
25 of 250
Application +4 | -1
In a class tournament, all participants were to play different games with one another. Two players fell ill after having played three games each. If the total number of games played in the tournament is equal to 84 , the total number of participants in the beginning was equal to
View answer and explanation
Correct option: B
15
Option B (15) is correct because solving the combination equation with the given conditions yields 15 as the total number of participants.
26 Medium
26 of 250
Application +4 | -1
The number of ways in which nn things of which rr are alike, can be arranged in a circular order, is
View answer and explanation
Correct option: A
(n−1)!r!\frac{(n-1) !}{r !}
Option A ((n−1)!r!\frac{{(n-1) !}}{{r !}}) is correct because it accounts for the circular arrangement and the identical objects.
27 Medium
27 of 250
Application +4 | -1
A student is allowed to select atmost nn books from a collection of (2n+1)(2n + 1) books. If the number of ways in which he can do this, is 64, then the value of nn is
View answer and explanation
Correct option: C
3
Option C (3) is correct because the sum of binomial coefficients from 0 to n equals half of the total sum, which is used to solve for n.
28 Medium
28 of 250
Analyzing +4 | -1
The number of triangles whose vertices are at the vertices of an octagon but none of whose sides happen to come from the octagon, is
View answer and explanation
Correct option: A
16
Option A (16) is correct because it represents the number of triangles that can be formed from the vertices of an octagon without sharing any sides with the octagon itself.
29 Medium
29 of 250
Application +4 | -1
The sum of 4 digited numbers formed by using the digits 0,2,4,7,80,2,4,7,8 without repetition is
View answer and explanation
Correct option: A
545958
Option A (545958) is correct because it uses the formula for the sum of 4-digit numbers formed by the given digits, considering the zero.
30 Medium
30 of 250
Application +4 | -1
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
View answer and explanation
Correct option: A
327
Option A (327) is correct because calculating the rank of the word MONDAY involves finding the number of words that come before it in lexicographical order, which results in 327.
Revision notes and key takeaways

Review PERMUTATION AND COMBINATION in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

  • ✓ This set contains 250 single-correct-answer MCQs on PERMUTATION AND COMBINATION.
  • ✓ Try each question before opening its answer. Read the explanation where one is available.
  • ✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.
Showing 1-30 of 250 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - PERMUTATION AND COMBINATION MCQs (All) 742 MCQs → ENGINEERING MATHEMATICS - PERMUTATION AND COMBINATION MCQs (Easy) 485 MCQs → ENGINEERING MATHEMATICS - PERMUTATION AND COMBINATION MCQs (Hard) 7 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs
📚 Switch Set (MEDIUM)
Chapter Sets
ALL 742 MCQs EASY 485 MCQs HARD 7 MCQs MEDIUM 250 MCQs
0 /250
0✓ 0✗
0% Accuracy
Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →