These Permutation And Combination Class 11 NCERT Solutions are most important for your upcoming examinations including JEE Main & JEE Advanced. These Permutation And Combination Class 11 NCERT Solutions will help you to score good marks in your exams by helping you to prepare the concepts better and hence, help you to understand the concepts more clearly.

## Permutation And Combination Class 11 NCERT Solutions

1. Out of 5 apples, 10 mangoes, and 13 oranges, any 15 fruits are to be distributed among 2 persons. Then the total number of ways of distribution is

(A) 1800

(B) 1080

(C) 1008

(D) 8001

**Answer:** 1008

2. 6 men and 4 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is

(A) 604800

(B) 17280

(C) 120960

(D) 518400

**Answer:** 604800

3. Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon on n sides. If Tn+1 – Tn = 21, then n equals

(A) 5

(B) 7

(C) 6

(D) 4

**Answer:** 7

4. How many factors are 25 × 36 × 52 are perfect squares

(A) 24

(B) 12

(C) 16

(D) 22

**Answer:** 24

5. In a room there are 2 green chairs, 3 yellow chairs, and 4 blue chairs. In how many ways can Raj choose 3 chairs so that at least one yellow chair is included?

(A) 3

(B) 30

(C) 64

(D) 84

**Answer:** 64

6. The number of words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants that occur together are

(A) 144

(B) 1044

(C) 1404

(D) 1440

**Answer:** 1440

7. A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of at least 3 girls

(A) 588

(B) 885

(C) 858

(D) None of these

**Answer:** 588

8. Six boys and six girls sit along a line alternately in x ways and along a circle (again alternatively in y ways), then

(A) x = y

(B) y = 12x

(C) x = 10y

(D) x = 12y

**Answer:** x = 12y

9. 4 boys and 4 girls sit alternately in a row and then alternately along a circle. The ratio of the number of ways of sitting in a row to the number of ways of sitting along a circle is

(A) 8 : 1

(B) 4 : 1

(C) 2 : 1

(D) none of these

**Answer:** 8 : 1

10. In an examination, a question paper consists of 12 questions divided into two parts i.e. Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. The number of ways a student can select the questions is

(A) 120

(B) 240

(C) 340

(D) 420

**Answer:** 420

11. There are 10 points in a plane in which 4 points are collinear. The number of distinct straight lines can be formed by using these points

(A) 40

(B) 39

(C) 41

(D) none of these

**Answer:** 40

12. Four dice are rolled. The number of possible outcomes in which at least one dice show 2 is

(A) 1296

(B) 671

(C) 625

(D) 585

**Answer:** 671

13. A student is to answer 10 out 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

(A) 40

(B) 196

(C) 280

(D) 346

**Answer:** 196

14. A five-digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4, and 5 without repetition. The total number of ways in which this can be done is

(A) 216

(B) 600

(C) 240

(D) 3125

**Answer:** 216

15. The English alphabet has 5 vowels and 21 consonants. The number of words with two different vowels and 2 different consonants that can be formed from the alphabet is

(A) 504

(B) 5040

(C) 50400

(D) None of these

**Answer:** 50400

16. 4 members form a group out of a total of 8 members.

(i) In how many ways it is possible to make the group if two particular members must be included.

(ii) In how many ways it is possible to make the group if two particular members must not be included?

(A) 15 and 360

(B) 15 and 15

(C) 30 and 360

(D) 360 and 360

**Answer:** 15 and 15

17. Without repetition, using digits 2, 3, 4, 5, 6, 8, and 0, how many numbers can be made that lie between 500 and 1000?

(A) 70

(B) 147

(C) 60

(D) 90

**Answer:** 90

18. A box contains 4 black, 3 red, and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?

(A) 12/74

(B) 24/78

(C) 13/78

(D) None of these

**Answer:** 24/78

19. There are 8 routes from London to Delhi. And there are 6 routes from Delhi to Tokyo. In how many different ways can Raj travel from London to Tokyo via Delhi?

(A) 100

(B) 48

(C) 24

(D) 14

**Answer:** 48

20. If Suraj doesn’t want three vowels together, then in how many, can he arrange letters of the word ‘MARKER’?

(A) 500

(B) 720

(C) 240

(D) 360

**Answer:** 240