These Class 11 Permutation And Combination Questions and Answers are most important for your upcoming examinations including JEE Main & JEE Advanced. These Class 11 Permutation And Combination Questions and Answers 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.

## Class 11 Permutation And Combination Questions

1. There are 30 people at a party. If everyone is to shake hands with one another, how many handshakes are possible?

(A) 180

(B) 256

(C) 386

(D) 435

**Answer:** 435

2. Mayur travels from Mumbai to Jammu in 7 different ways. But he is allowed to return to Mumbai by any way except the one he used earlier. In how many ways can he complete his journey?

(A) 49

(B) 42

(C) 48

(D) 6

**Answer:** 42

3. A locker in the bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed for Mahesh to try all the combinations?

(A) 90 minutes

(B) 120 minutes

(C) 60 minutes

(D) 100 minutes

**Answer:** 100 minutes

4. On a railway line there are 20 stops. A ticket is needed to travel between any 2 stops. How many different tickets would the government need to prepare to cater to all possibilities?

(A) 760

(B) 190

(C) 380

(D) 72

**Answer:** 380

5. 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

6. How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order?

(A) 120

(B) 240

(C) 360

(D) 480

**Answer:** 360

7. The number of ways can the letters of the word ASSASSINATION be arranged so that all the S are together is

(A) 152100

(B) 1512

(C) 15120

(D) 151200

**Answer:** 151200

8. A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is

(A) 216

(B) 600

(C) 240

(D) 3125

**Answer:** 216

9. Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to

(A) 60

(B) 120

(C) 7200

(D) 720

**Answer:** 7200

10. The sum of the digits in unit place of all the numbers formed with the help of 3, 4, 5 and 6 taken all at a time is

(A) 432

(B) 108

(C) 36

(D) 18

**Answer:** 108

11. The number of different four-digit numbers that can be formed with the digits 2, 3, 4, 7 and using each digit only once is

(A) 120

(B) 96

(C) 24

(D) 100

**Answer:** 24

12. The number of possible outcomes when a coin is tossed 6 times is

(A) 36

(B) 64

(C) 12

(D) 32

**Answer:** 64

13. ^{n}C_{12} = ^{n}C_{8}, then n is equal to

(A) 20

(B) 12

(C) 6

(D) 30

**Answer:** 20

14. On a shelf, 2 books of Geology, 2 books of Sociology and 5 of Economics are to be arranged in such a way that the books of any subject are to be together. Find in how many ways can this be done?

(A) 3846

(B) 2880

(C) 900

(D) 90

**Answer:** 2880

15. A person can go from place “P” to “Q” by 7 different modes of transport, but is allowed to return back to “P” by any mode other than the one used earlier. In how many different ways can he complete the entire journey?

(A) 42

(B) 30

(C) 56

(D) 65

**Answer:** 42

16. A briefcase has a number-lock system containing a combination of 3 digits (Each digit can be of numbers 0 to 8). If the correct combination is unknown, how much maximum time would be required to open the bag if each “trial” of the combination takes 3 seconds?

(A) 45.23 minutes

(B) 36.45 minutes

(C) 60.34 minutes

(D) 90.15 minutes

**Answer:** 36.45 minutes

17. A box contains 2 white, 3 black, and 5 red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

(A) 29

(B) 36

(C) 48

(D) 85

**Answer:** 85

18. In how many different ways can the letters of the word ‘GEOMETRY’ be arranged so that the vowels always come together?

(A) 720

(B) 4320

(C) 2160

(D) 40320

**Answer:** 4320

19. How many words can be formed by using all letters of word ALIVE.

(A) 86

(B) 95

(C) 105

(D) 120

**Answer:** 120

20. How many 3-letter words can be formed out of the letters of the word ‘CORPORATION’, if repetition of letters is not allowed?

(A) 990

(B) 336

(C) 720

(D) 504

**Answer:** 336