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JEE • MATHEMATICS • PERMUTATION AND COMBINATION

Permutation and combination practice · Easy

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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 485 questions

1 Easy

1 of 485

Application +4 | -1

The number of ways in which

r

letters can be posted in

n

letterboxes in a town is

View answer and explanation

Correct option: A

n^{r}

Option A (

n^{r}

) is correct because each of the

r

letters can be posted in any of the

n

letterboxes, giving

n

choices for each letter.

2 Easy

2 of 485

Application +4 | -1

The number of ways in which a pack of 52 cards can be divided equally into four groups, is

View answer and explanation

Correct option: B

\frac{{52!}}{{{{\left( {13!} \right)}^4} \times 4!}}

Option B (

\frac{{52!}}{{{{\left( {13!} \right)}^4} \times 4!}}

) is correct because it represents the number of ways to divide 52 cards into four equal groups without considering the order of the groups.

3 Easy

3 of 485

Application +4 | -1

A man invites a party to

\left( {m + n} \right)

friends to dinner and places m at one round table and

n

at another. The number of ways of arranging the guests is

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because the given options do not match the correct formula for arranging guests at two round tables.

4 Easy

4 of 485

Application +4 | -1

There are 5 gentlemen and 4 ladies to dine at a round table. The number of ways in which they can seat themselves so that no two ladies are together is

View answer and explanation

Correct option: B

2880

Option B (2880) is correct because it calculates the number of arrangements where men are seated first, then ladies are arranged in the gaps.

5 Easy

5 of 485

Analyzing +4 | -1

n>1

, then

View answer and explanation

Correct option: C

\frac{(2 n) !}{(n !)^2}>\frac{4 n}{2 n+1}

Option C (

\frac{{(2n)!}}{{(n!)^2}} > \frac{{4n}}{{2n+1}}

) is correct because substituting n=2 into the expression confirms the inequality.

6 Easy

6 of 485

Application +4 | -1

Let

A

and

B

be finite sets containing respectively 3 and 2 elements. Find the number of functions that can be defined from A to B

View answer and explanation

Correct option: A

Option A (8) is correct because the number of functions from A to B is 2³ = 8.

7 Easy

7 of 485

Application +4 | -1

{ }^{{n}} P_{{r}}=2520

and

{ }^{{n}} C_{{r}}=21

then

n

is equal to:

View answer and explanation

Correct option: B

Option B (7) is correct because by using the given values of

{}^{{n}} P_{{r}}

and

{}^{{n}} C_{{r}}

, we can find r=5 and then solve for n, which results in n=7.

8 Easy

8 of 485

Application +4 | -1

The number of ways in which ten candidates

A_1, A_2, A_3, A_4, \cdots, A_{10}

can be arranged in a row "If

A_1

is always above

A_2

and

A_2

is above

A_3

View answer and explanation

Correct option: A

\frac{10 !}{3 !}

Option A (

\frac{10 !}{3 !}

) is correct because it represents the total arrangements divided by the arrangements of the three specific candidates.

9 Easy

9 of 485

Application +4 | -1

A boy has 3 library tickets and 9 books of his interest in the library. Out of these 8, he does not want to borrow Chemistry part II, unless Chemistry part I is also borrowed. The number of ways in which he can choose the three books to be borrowed, is

View answer and explanation

Correct option: A

Option A (41) is correct because it considers both cases: including and excluding Chemistry part II.

10 Easy

10 of 485

Application +4 | -1

The number of wards can be formed with the letters of the word PATALIPUTRA without changing the relative positions of vowels and consonants is

400 \mathrm{n}

then

\mathrm{n}=

View answer and explanation

Correct option: A

Option A (9) is correct because the number of arrangements of the letters in PATALIPUTRA, keeping the relative positions of vowels and consonants unchanged, is 3600, and 3600/400 = 9.

11 Easy

11 of 485

Application +4 | -1

The number of ways in which a committee of 3 women and 4 men be chosen from 8 women and 7 men if Ms Bryn refuses to serve on the committee if Mr. Arnav is a member of the committee (Ms. Bryn and Mr. Arnav are among 8 women & 7 men respectively) is :

View answer and explanation

Correct option: C

1540

Option C (

5050 \pi

) is correct because it is the sum of the total area of the green regions, calculated by summing the areas of alternating annuli.

12 Easy

12 of 485

Understanding +4 | -1

Let

S

be the set of all functions from the set

A

to the set

A

. If

n(A)=k

, then

n(S)

View answer and explanation

Correct option: B

k^k

Option B (

k^k

) is correct because each of the k elements in set A can be mapped to any of the k elements in set A, resulting in

k^k

possible functions.

13 Easy

13 of 485

Application +4 | -1

Let

x_1, x_2, x_3

______

x_n

n

observation such that

\Sigma\left(x_i\right)^2=400

and

\Sigma x_i=40

then a possible value of

n

among the following is

View answer and explanation

Correct option: B

Option B (4) is correct because the condition derived from AM-GM inequality requires n > 4, making 4 the smallest possible integer value for n.

14 Easy

14 of 485

Application +4 | -1

Anil have tiled his square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue. If he used 121 blue tiles, then the number of red tiles used are

View answer and explanation

Correct option: C

3600

Option C (3600) is correct because with 121 blue tiles, the square is 61x61, and subtracting the blue tiles leaves 3600 red tiles.

15 Easy

15 of 485

Application +4 | -1

The total number of arrangements of the letters in the expression

{a^3}{b^2}{c^4}

when written at full length, is

View answer and explanation

Correct option: A

1260

Option A (1260) is correct because the total number of arrangements is calculated by dividing the total factorial by the factorials of the repeated letters.

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16 Easy

16 of 485

Application +4 | -1

Let

f(n)

denotes the number of different ways the positive integer

n

can be expressed as the sum of 1's and 2's. For example

f(4)=5

, since

4=1+1+1+1,1+1+2,1+2+1,2+1+1,2+2

(Note Order of 1's and 2's is important). Then,

f\{f(6)\}

View answer and explanation

Correct option: C

f(13)

Option C (

f(13)

) is correct because

f(6)

is calculated to be 13, and therefore

f(f(6)) = f(13)

17 Easy

17 of 485

Application +4 | -1

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from each group. The number of ways in which he can choose the 7 questions is

View answer and explanation

Correct option: A

780

Option A (780) is correct because it sums the number of ways to choose questions from each group under the given constraints.

18 Easy

18 of 485

Application +4 | -1

The number of proper divisors of

2^p \cdot 6^q \cdot 15^r

View answer and explanation

Correct option: B

(p+q+1)(q+r+1)(r+1)-2

Option B (

(p+q+1)(q+r+1)(r+1)-2

) is correct because it calculates the total number of divisors and then subtracts 2 to exclude 1 and the number itself, giving the number of proper divisors.

19 Easy

19 of 485

Application +4 | -1

The number of ways in which 10 identical balls can be distributed in 4 distinct boxes, so that none of the boxes remain empty, is

View answer and explanation

Correct option: D

None of these

None of these is correct because the correct answer is 84, calculated using stars and bars with the condition that no box is empty.

20 Easy

20 of 485

Understanding +4 | -1

Which of the following statement is false?

View answer and explanation

Correct option: D

None of these

Option D (None of these) is correct because all the statements A, B, and C are true; it is possible to find consecutive natural numbers that are not prime.

21 Easy

21 of 485

Application +4 | -1

The maximum possible number of points of intersection of 7 straight lines and 5 circles is:

View answer and explanation

Correct option: A

111

Option A (111) is correct because it represents the sum of the maximum number of intersection points between lines, circles, and lines and circles.

22 Easy

22 of 485

Understanding +4 | -1

\sum\limits_{0 \leqslant i} {\sum\limits_{ < j < } {\sum\limits_{k < l} {\sum\limits_{ \leqslant n} {} } } }

is equal to

View answer and explanation

Correct option: B

n^{n+1} C_4

Option A is correct because the given expression represents the number of ways to choose 4 distinct elements from the set {0, 1, 2, ..., n}.

23 Easy

23 of 485

Application +4 | -1

How many ways are three to arrange the letters in the word ‘GARDEN’ with the vowels in alphabetical order?

View answer and explanation

Correct option: C

360

Option C (360) is correct because it divides the total arrangements by the number of ways to arrange the vowels.

24 Easy

24 of 485

Application +4 | -1

If the letters of the word SACHIN arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at series number

View answer and explanation

Correct option: C

601

Option C (601) is correct because it is the number of words that come before SACHIN in the dictionary order, plus 1.

25 Easy

25 of 485

Analyzing +4 | -1

How many different non-digit numbers can be formed from the digits of the number 223355888 by rearrangement of the digits so that the odd digits occupy even places?

View answer and explanation

Correct option: C

Option C (60) is correct because it is the product of arranging odd digits in even places and arranging even digits in odd places.

26 Easy

26 of 485

Application +4 | -1

The units digit of

{17^{2009}} + {11^{2009}} - {7^{2009}}

View answer and explanation

Correct option: A

Option A (1) is correct because the units digit of 17²⁰⁰⁹ is the same as 7²⁰⁰⁹, and the units digit of 11²⁰⁰⁹ is 1, so the expression simplifies to 1.

27 Easy

27 of 485

Analyzing +4 | -1

The value of

\sum\limits_{{r=0}}^{n-1}{ }^n C_r /\left({ }^n C_r+{ }^n C_{r+1}\right)

equals

View answer and explanation

Correct option: B

n / 2

Option B (

n / 2

) is correct because the summation simplifies to

n/2

after applying properties of binomial coefficients.

28 Easy

28 of 485

Application +4 | -1

Let

S=\left\{\left[\begin{array}{cc}18 & a \\ b & 25\end{array}\right]: a, b \in {N}\right\}

The number of singular matrices in

S

View answer and explanation

Correct option: A

Option A (18) is correct because it represents the number of divisors of the determinant that make the matrix singular.

29 Easy

29 of 485

Application +4 | -1

The total number of

n

-digit numbers

(n > 1)

having the property that no two consecutive digits are same, is

View answer and explanation

Correct option: A

9^n

Option A (

9^n

) is correct because the first digit has 9 choices (1-9) and each subsequent digit also has 9 choices (0-9, excluding the previous digit).

30 Easy

30 of 485

Application +4 | -1

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

View answer and explanation

Correct option: D

582

Option B (2) is correct. The sum of the values of

\alpha

for which the points are coplanar is equal to 2, which is the sum of the roots of the quadratic equation.

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 485 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.

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