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#### Combinations and Mathematical Induction Two Marks Question

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. count the total number of ways of answering 6 objective type questions,each question having 4 choices

2. Find the value of $\frac { 12! }{ 9!\times 3! }$

3. Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?

4. Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?

5. Prove that 15C3+2 x 15C4+ 15C4+ 15C5= 17C5.

6. 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?

7. If the ratio 2nC3:nC3 = 11:1, find n.

8. Find the number of strings of 4 letters that can be formed with the letters of the word EXAMINATION?

9. How many triangles can be formed by joining 15 points on the plane, in which no line joining any three points?

10. If nC12=nC9 find 21Cn.

11. If 9Pr = 3024 find r.

12. If nPr = nPr+1 and nCr = nCr-1 find n and r.

13. 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 no girls

14. 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 atleast one boy and one girl

15. 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