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JEE • MATHEMATICS • COMBINATIONS

Combinations practice · Medium

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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.

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Showing 1-30 of 83 questions
1 Medium
1 of 83
Application +4 | -1
The number of ways selecting three numbers from 1 to 30, so as to exclude every selection of three consecutive number is:
View answer and explanation
Correct option: C
4032
Option C (4032) is correct because it calculates the total number of ways to select three numbers from 1 to 30 and subtracts the number of ways to select three consecutive numbers.
2 Medium
2 of 83
Application +4 | -1
There are nn different books and m copies of each in a college library. The number of ways in which a student can make a selection of one or more books is
View answer and explanation
Correct option: D
(m+1)n−1{\left( {m + 1} \right)^n} - 1
Option D ((m+1)n−1{\left( {m + 1} \right)^n} - 1) is correct because it represents the total number of ways to select one or more books, excluding the case where no book is selected.
3 Medium
3 of 83
Application +4 | -1
The number of ways of selecting 4 letters out of the letters of the word MINIMAL is
View answer and explanation
Correct option: B
17
Option B (17) is correct because it accounts for all possible combinations of selecting 4 letters from the word MINIMAL, considering repetitions.
4 Medium
4 of 83
Application +4 | -1
Number of divisors of the form (4n+2),  n≥0\left( {4n + 2} \right),\;n \ge 0 of the integer 240 is
View answer and explanation
Correct option: A
4
Option A (4) is correct because there are four divisors of 240 that are of the form 4n+2, specifically 2, 6, 10, and 30.
5 Medium
5 of 83
Application +4 | -1
AA is a set containing n1n_{1} elements and BB is another set containing n2n_{2} elements. The number of non-decreasing functions from A→BA \rightarrow B is
View answer and explanation
Correct option: A
n1+n2−1Cn1{ }^{n_{1}+n_{2}-1} C_{n_{1}}
Option A (n1+n2−1Cn1{}^{n_{1}+n_{2}-1} C_{n_{1}}) is correct because it represents the number of non-decreasing functions from A to B using stars and bars.
6 Medium
6 of 83
Application +4 | -1
The number of ordered triplets of positive integer which satisfy the inequality 20≤x+y+w≤50−20 \leq x+y+w \leq 50- is
View answer and explanation
Correct option: A
20C3−19C3{ }^{20} {C}_3-{ }^{19} {C}_3
The provided answer 20C3−19C3{ }^{20} {C}_3-{ }^{19} {C}_3 is incorrect. The correct approach involves stars and bars. The correct answer should be the sum of solutions to x+y+z = k, where k ranges from 20 to 50. This requires a different calculation than the options provided.
7 Medium
7 of 83
Understanding +4 | -1
There are nn seats around a table numbered 1,2,3,⋯ ,n1,2,3, \cdots, n. The number of ways in which m(n)m(n) persons can take seats, is
View answer and explanation
Correct option: A
nPm{ }^n P_m
Option A (nPm{ }^n P_m) is correct because it represents the number of ways to arrange m persons in n numbered seats, which is a permutation.
8 Medium
8 of 83
Application +4 | -1
S={1,2,3,…,20}S=\{1,2,3, \ldots, 20\} is to be partitioned into four sets AA, B,CB, C and DD of equal size. The number of ways it can be done, is
View answer and explanation
Correct option: C
20!(5!)4\frac{20 !}{(5 !)^4}
Option C (20!(5!)4\frac{{20 !}}{{(5 !)^4}}) is correct because it represents the number of ways to partition a set of 20 elements into four equal-sized subsets.
9 Medium
9 of 83
Analyzing +4 | -1
The number of positive divisors of (2008)8(2008)^8 that are less than (2008)4(2008)^4 are
View answer and explanation
Correct option: B
112
Option A (0) is correct because using the property of definite integrals and simplifying the expression leads to the integral evaluating to zero.
10 Medium
10 of 83
Analyzing +4 | -1
If 29!+23!7!+15!5!=2ab!,\frac{2}{{9!}} + \frac{2}{{3!7!}} + \frac{1}{{5!5!}} = \frac{{{2^a}}}{{b!}}, where a,b,∈Na,b, \in N, then the ordered pair (a,b)\left( {a,b} \right) is
View answer and explanation
Correct option: A
(9,10)\left( {9,10} \right)
Option A ((9,10)) is correct because simplifying the given expression results in 2910!\frac{{{2^9}}}{{10!}}.
11 Medium
11 of 83
Understanding +4 | -1
The number of ways in which 52 cards be formed into 4 groups of 13 cards each is
View answer and explanation
Correct option: A
52!(13!)44!\frac{52 !}{(13 !)^4 4 !}
Option A (52!(13!)44!\frac{{52 !}}{{(13 !)^4 4 !}}) is correct because it represents dividing 52 cards into 4 unordered groups of 13 cards each.
12 Medium
12 of 83
Application +4 | -1
There are three men and seven women taking a dance class. Number of different ways in which each man is paired with a woman partner, and the four remaining women are paired into two pairs each of two is
View answer and explanation
Correct option: C
630
Option C (630) is correct because it correctly accounts for the selection of 3 women out of 7, pairing them with the 3 men, and then pairing the remaining 4 women into two pairs.
13 Medium
13 of 83
Application +4 | -1
The number of ways in which 9 persons can be divided into three equal groups is
View answer and explanation
Correct option: A
1680
Option A (1680) is correct because it represents the number of ways to divide 9 people into three equal groups, accounting for the fact that the order of the groups doesn't matter.
14 Medium
14 of 83
Application +4 | -1
A crocodile is known to have not more than 68 teeth the total number of crocodiles with different set of teeth is
View answer and explanation
Correct option: C
161716^{17}
Option C (161716^{17}) is correct because each tooth can either be present or absent, leading to 268 possible combinations, which simplifies to 1617.
15 Medium
15 of 83
Analyzing +4 | -1
A committee of 12 is to be formed from 9 women and 8 men in which at least 5 women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively
View answer and explanation
Correct option: D
2702, 1008
Option D (2702, 1008) is correct because it accurately calculates the number of committees with women in the majority and men in the majority, respectively, given the constraints.

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16 Medium
16 of 83
Application +4 | -1
For a game in which two partner oppose to other partner 8 men are available. If every possible pair must play with every other pair the number of games played is
View answer and explanation
Correct option: C
8C2⋅3{ }^8 {C}_2 \cdot 3
Option B (4) is correct because solving the given equation for n yields n=4.
17 Medium
17 of 83
Application +4 | -1
The number of ways in which an examiner can assign 30 marks to 8 questions, giving not less than 2 marks to any question, is :
]
View answer and explanation
Correct option: C
21C7{ }^{21} C_{7}
Option C (21C7{}^{21}C_7) is correct because after giving each question a minimum of 2 marks, the remaining marks are distributed among the questions, which can be calculated using combinations.
18 Medium
18 of 83
Application +4 | -1
A box contains 5 pairs of shoes. If 4 shoes are selected, then the number of ways in which exactly one pair of shoes obtained is
View answer and explanation
Correct option: A
120
Option A (120) is correct because we choose one pair and then choose two other shoes from the remaining shoes, making sure not to pick another pair.
19 Medium
19 of 83
Application +4 | -1
The number of integral solution of the inequality 4<x1+x2+x3+x4<94 < x_1+x_2+x_3+x_4 < 9 where x1,x2,x3,x4≥0x_1, x_2, x_3, x_4 \geq 0
View answer and explanation
Correct option: C
425
The correct answer is C (425) because it is the number of integral solutions to the inequality, calculated by subtracting the number of solutions less than or equal to 4 from the number of solutions less than 9.
20 Medium
20 of 83
Application +4 | -1
7 relatives of a man comprise 4 ladies and 3 gentlemen his wife has also 7 relatives, 3 of them are ladies and 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the wife’s relative?
View answer and explanation
Correct option: A
485
Option A (485) is correct because it sums the number of ways to invite relatives based on different combinations of ladies and gentlemen from both families.
21 Medium
21 of 83
Application +4 | -1
From a company of 20 soldiers any 5 are placed on guard, each batch to watch 5 hours. The total number of hours watched by different batches selected is
View answer and explanation
Correct option: C
20C5×5{ }^{20} C_5 \times 5
Option C (20C5×5{}^{20} C_5 \times 5) is correct because it represents the total number of hours watched by different batches, where each batch consists of 5 soldiers and watches for 5 hours.
22 Medium
22 of 83
Application +4 | -1
If r>p>q,r > p > q, the number of different selections of p+qp + q thing taking r at a time, where p things are identical and qq other things are identical, is
View answer and explanation
Correct option: B
p+q−r+1p + q - r + 1
Option B (p+q−r+1p + q - r + 1) is correct because it represents the number of ways to select the items given the constraints.
23 Medium
23 of 83
Analyzing +4 | -1
If a, ba,\,b and cc are the greatest values of 19Cp 20Cq^{19}{C_p}{\,^{20}}{C_q} and 21Cr^{21}{C_r} respectively, then
View answer and explanation
Correct option: D
a11=b22=c42\frac{a}{{11}} = \frac{b}{{22}} = \frac{c}{{42}}
Option D (a11=b22=c42\frac{a}{{11}} = \frac{b}{{22}} = \frac{c}{{42}}) is correct because by finding the greatest values of the binomial coefficients, we can establish the ratios between aa, bb, and cc.
24 Medium
24 of 83
Application +4 | -1
The number of ways choosing 10 balls from infinite white, red blue and green balls is
View answer and explanation
Correct option: C
286
Option C (286) is correct because it represents the number of non-negative integer solutions to the equation x1 + x2 + x3 + x4 = 10, which can be found using stars and bars method.
25 Medium
25 of 83
Application +4 | -1
A student is allowed to select atmost nn books from a collection of (2n+1)(2 n+1) books. If the total number of ways in which he can select atleast one book is 225, then the value of nn is
View answer and explanation
Correct option: C
4
Option C (4) is correct because the given condition leads to the equation 2n+1C1+2n+1C2+…+2n+1Cn=255{ }^{2 n+1} C_1+{ }^{2 n+1} C_2+\ldots+{ }^{2 n+1} C_n=255, which simplifies to 22n=2562^{2n} = 256, giving n=4n=4.
26 Medium
26 of 83
Application +4 | -1
A student is to answer 10out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
View answer and explanation
Correct option: C
196
Option C (196) is correct because it calculates the sum of combinations where at least 4 questions are chosen from the first five.
27 Medium
27 of 83
Application +4 | -1
In an steamer there are stalls for 12 animals and there are hours, cows and calves (not less then 12 each) ready to be shipped in how many ways can the ship load be made?
View answer and explanation
Correct option: B
312{3^{12}}
Option B (312{3^{12}}) is correct because each stall can be filled with any of the 3 types of animals, leading to 3 options for each of the 12 stalls.
28 Medium
28 of 83
Analyzing +4 | -1
Let N\mathbf{N} be the total number of six digits number formed which consists the digit {0,1,2,3}\{0,1,2,3\} at least once and whose sum of digits is 10 , then the sum of even divisors of N\mathrm{N} is
View answer and explanation
Correct option: A
640
Option A (640) is correct because it represents the total number of six-digit numbers formed with the given conditions, calculated using combinations and permutations.
29 Medium
29 of 83
Application +4 | -1
The number of square matrices of order 5 with
entries from the set {0, 1}, such that the sum of all
the elements in each row is 1 and the sum of all the
elements in each column is also 1, is
View answer and explanation
Correct option: A
120
Option D (120) is correct because it represents the number of permutations of placing 5 ones in a 5x5 matrix such that each row and column has exactly one 1.
30 Medium
30 of 83
Application +4 | -1
A committee of 11 members is to be formed from 8 males and 5 females. If mm is the number of ways the committee is formed with at least 6 males and nn is the number of ways the committee is formed with atleast 3 females, then
View answer and explanation
Correct option: C
m=n=78m = n = 78
Option C (m=n=78m = n = 78) is correct because both the number of ways with at least 6 males and at least 3 females are equal to 78.
Revision notes and key takeaways

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

Key Takeaways

  • ✓ This set contains 83 single-correct-answer MCQs on COMBINATIONS.
  • ✓ 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.
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