#### Combinations and Mathematical Induction Sample Questions

11th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is

(a)

432

(b)

108

(c)

36

(d)

18

2. The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

3. If a2-a C2=a2-a C4 then the value of 'a' is

(a)

2

(b)

3

(c)

4

(d)

5

4. The number of ways to average the letters of the word CHEESE are

(a)

120

(b)

240

(c)

720

(d)

6

5. Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is

(a)

24

(b)

30

(c)

125

(d)

100

6. 6 x 2 = 12
7. In how many ways 5 persons can be seated in a row?

8. A mobile phone has a pass code of 6 distinct digits. What is the maximum number of attempts one makes to retrieve the pass code?

9. In how many ways can the letters of the word PENCIL be arranged so that N is always next to E.

10. How many words can be formed using the letter A thrice, the letter B twice and the letter C thrice?

11. There are six periods in each working day of a school. In how many ways can one arrange 5 subjects such that each subject is allowed atleast one period?

12. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has at least three girls

13. 6 x 3 = 18
14. If 10Pr-1 = 2 X 6Pr, find r.

15. If (n + 1)C8 : (n - 3) P4 = 57:16, find n.

16. Evaluate $\frac { (2n)! }{ n! }$

17. Prove that n!(n+2)=n!+(n+1)!

18. If (n+2)!=60(n-1)! find n.

19. 32n - 1 is divisible by 8

20. 3 x 5 = 15
21. How many numbers are there between 100 and 500 with the digits 0, 1, 2, 3, 4, 5 ? if
(i) repetition of digits allowed
(ii) the repetition of digits is not allowed.

22. If nPr = nPr+1 and nCr = nCr-1 find the values of n and r.

23. Find r if 5pr= 26pr-1