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JEE • MATHEMATICS • COMBINATIONS

Combinations practice · Mixed difficulty

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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 324 questions
1 Hard
1 of 324
Application +4 | -1
A rectangle of dimension m×nm \times n ( mm and nn being odd) is divided into square of unit length by drawing horizontal and vertical lines. The number of rectangles having side of odd unit length is
View answer and explanation
Correct option: B
((m+1)(n+1)4)2\left(\frac{(m+1)(n+1)}{4}\right)^{2}
Option B (((m+1)(n+1)4)2\left(\frac{(m+1)(n+1)}{4}\right)^{2}) is correct because it represents the number of rectangles with odd side lengths within the given rectangle.
2 Medium
2 of 324
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.
3 Easy
3 of 324
Application +4 | -1
Team A consists of 7 boys and n girls and Team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams, when a boy plays against a boy and a girl plays against a girl, then n is equal to
View answer and explanation
Correct option: C
4
Option C (4) is correct because it satisfies the equation formed by the total number of matches between boys and girls of the two teams.
4 Easy
4 of 324
Application +4 | -1
The number of ways choosing a committee of 4 woman and 5 men from 10 women and 9 men, if Mr. AA refuses to serve on the committee when Ms. BB is a member of the committee, is
View answer and explanation
Correct option: A
20580
Option A (20580) is correct because it is calculated by subtracting the number of committees with both Mr. A and Ms. B from the total number of possible committees.
5 Easy
5 of 324
Application +4 | -1
A man has 7 friends. In how many ways he can invite one or more of them for a tea party?
View answer and explanation
Correct option: C
127
Option C (127) is correct because each friend can either be invited or not, leading to 27 possibilities, but we subtract 1 for the case where no one is invited.
6 Easy
6 of 324
Application +4 | -1
If   n+2C8:  n−2P4=5716{\;^{n + 2}}{C_8}:{\;^{n - 2}}{P_4} = \frac{{57}}{{16}}, then nn is equal to
View answer and explanation
Correct option: A
19
Option A (19) is correct because solving the given equation involving combinations and permutations leads to n = 19.
7 Easy
7 of 324
Application +4 | -1
If the ratio 2nC3:nC3{ }^{2 n} {C}_3:{ }^n {C}_3 is equal to 11:1,n11: 1, n equals
View answer and explanation
Correct option: A
6
Option A (6) is correct because simplifying the ratio 2nC3:nC3=11:1{ }^{2 n} {C}_3:{ }^n {C}_3 = 11: 1 leads to the equation 8n−4=11n−228n - 4 = 11n - 22, which gives n=6n=6.
8 Medium
8 of 324
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.
9 Easy
9 of 324
Application +4 | -1
25 lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of points in which these lines intersect, is
View answer and explanation
Correct option: A
300
Option A (300) is correct because it represents the number of ways to choose 2 lines out of 25, which corresponds to the number of intersection points.
10 Easy
10 of 324
Application +4 | -1
The number of four letter words can be formed from the letters of the word INFINITY so that 3 are alike, one is different is
View answer and explanation
Correct option: C
16
Option C (16) is correct because it represents the number of four-letter words that can be formed from the letters of the word INFINITY such that 3 are alike and one is different.
11 Easy
11 of 324
Application +4 | -1
A father with 8 children takes 3 at a time to the Zoological Gardens, as often as he can without taking the same 3 children together more than once. The number of times each child will go to the garden is
View answer and explanation
Correct option: B
21
Option B (21) is correct because each child goes to the garden with every possible pair of the other 7 children, which is   7C2{{\;^7}{C_2}}.
12 Easy
12 of 324
Application +4 | -1
A lady gives a dinner party to 5 guests to be selected from nine friends. The number of ways of forming the party of 5, given that two of the friends will not attend the party together is
View answer and explanation
Correct option: C
91
Option C (91) is correct because it calculates the total number of ways to choose 5 guests from 9, then subtracts the number of ways where the two friends are both included.
13 Easy
13 of 324
Analyzing +4 | -1
If   nCr−1=36,  nCr=84{\;^n}{C_{r - 1}} = 36,{\;^n}{C_r} = 84 and   nCr+1=126,{\;^n}{C_{r + 1}} = 126, then
View answer and explanation
Correct option: B
n=9,r=3n = 9,r = 3
Option B (n=9,r=3n = 9, r = 3) is correct because it satisfies the given combinatorial equations when the ratios of consecutive binomial coefficients are calculated.
14 Easy
14 of 324
Application +4 | -1
If 2nC4,2nC5{ }^{2 {n}} C_4,{ }^{2 {n}} C_5 and 2nC6{ }^{2 {n}} C_6 are in A.P, then nn is equal to
View answer and explanation
Correct option: C
7
Option C (7) is correct because solving the given equation involving combinations leads to a quadratic equation with n=7 as a valid solution.
15 Easy
15 of 324
Application +4 | -1
A polygon has 65 diagonals. The number of its sides is
View answer and explanation
Correct option: D
13
Option D (13) is correct because the number of sides of a polygon can be found using the formula for the number of diagonals.

Explore Other Chapters in MATHEMATICS

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SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
16 Easy
16 of 324
Application +4 | -1
If n≥2n \ge 2 is a positive integer, then the sum of the series
n+1C2+2(2C2+3C2+4C2+...+nC2)^{n + 1}{C_2} + 2{(^2}{C_2}{ + ^3}{C_2}{ + ^4}{C_2} + ...{ + ^n}{C_2}) is
View answer and explanation
Correct option: B
n (n+1)  (2n+1)6\frac{{n\,(n + 1)\,\,(2n + 1)}}{6}
Option B (n (n+1) (2n+1)6\frac{{n\,(n + 1)\,(2n + 1)}}{6}) is the correct sum of the series, derived using combinatorial identities and simplification.
17 Easy
17 of 324
Application +4 | -1
The value of the expression 47C4+∑j=15(52−j)C3{ }^{47} C_4+\sum\limits_{{j=1}}^5 {}^{(52-j)} C_3 is equal to
View answer and explanation
Correct option: C
52C4{ }^{52} C_4
Option C (52C4{ }^{52} C_4) is correct because the expression simplifies to 52C4{ }^{52} C_4 using the identity n+1Cr=nCr+nCr−1{ }^{n+1} C_r={ }^n C_r+{ }^n C_{r-1} repeatedly.
18 Easy
18 of 324
Application +4 | -1
∑r=0n(−1)r  nCr\sum \limits_{r = 0}^n \frac{{{{\left( { - 1} \right)}^r}}}{{{\;^n}{C_r}}} equals
View answer and explanation
Correct option: A
(n+1)(n+2)[1+(−1)n]\frac{{\left( {n + 1} \right)}}{{\left( {n + 2} \right)}}\left[ {1 + {{\left( { - 1} \right)}^n}} \right]
Option A is correct because the given summation can be simplified using properties of binomial coefficients and telescoping series.
19 Medium
19 of 324
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.
20 Easy
20 of 324
Application +4 | -1
Kunal Gaba has nn objects, each of weight ww. He weighs them in pairs and finds the sum of the weights of all possible pairs is 120 g120 \mathrm{~g}. When his friend Rakshit weighs them in triplets, the sum of all possible weights is 240 g240 \mathrm{~g}. The value of nn is
View answer and explanation
Correct option: B
6
Option C (4032) is correct because it is calculated by subtracting the number of selections with three consecutive numbers from the total number of selections.
21 Medium
21 of 324
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.
22 Medium
22 of 324
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.
23 Medium
23 of 324
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.
24 Easy
24 of 324
Application +4 | -1
If a,b,c,d,ea,b,c,d,e are prime integers, then the number of divisors of ab2c2dea{b^2}{c^2}de excluding 1 as a factor is
View answer and explanation
Correct option: D
71
Option D (71) is correct because the number of divisors is calculated by adding 1 to each exponent in the prime factorization, multiplying the results, and then subtracting 1 to exclude 1 as a factor.
25 Medium
25 of 324
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.
26 Easy
26 of 324
Application +4 | -1
Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?
View answer and explanation
Correct option: A
26
Option A (26) is correct because it calculates the number of lines formed by 8 points, accounting for the collinearity of 3 points.
27 Easy
27 of 324
Application +4 | -1
A polygon has 54 diagonals. Number of sides of this polygon is
View answer and explanation
Correct option: A
12
Option A (12) is correct because the number of sides of the polygon is found by solving the quadratic equation derived from the formula for the number of diagonals.
28 Medium
28 of 324
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.
29 Medium
29 of 324
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.
30 Easy
30 of 324
Understanding +4 | -1
If nn is even and nC0<nC1<nC2<⋯<nCr>nCr+1>⋯>nCn{ }^n C_0 < { }^n C_1 < { }^n C_2 < \cdots < n C_r>{ }^n C_{r+1}>\cdots > { }^n C_n then r=r=
View answer and explanation
Correct option: A
n2\frac{n}{2}
Option A (n2\frac{{n}}{{2}}) is correct because for even n, the binomial coefficient nCr{ }^n C_r is maximum when r = n/2.
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Key Takeaways

  • ✓ This set contains 324 single-correct-answer MCQs on COMBINATIONS.
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