#### Combinations and Mathematical Induction - Important Question Paper

11th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50

Part A

10 x 1 = 10
1. In 3 fingers, the number of ways four rings can be worn is ways.

(a)

43-1

(b)

34

(c)

68

(d)

64

2. If (n+5)P(n+1)=$\frac { 11(n-1) }{ 2 }$.(n+3)Pn, then the value of n are

(a)

7 and 11

(b)

6 and 7

(c)

2 and 11

(d)

2 and 6

3. The product of r consecutive positive integers is divisible by

(a)

r!

(b)

(r-1)!

(c)

(r+1)!

(d)

rr

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

(a)

90000

(b)

10000

(c)

30240

(d)

69760

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

(a)

2

(b)

3

(c)

4

(d)

5

6. There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

(a)

45

(b)

40

(c)

39

(d)

38

7. Number of sides of a polygon having 44 diagonals is

(a)

4

(b)

4!

(c)

11

(d)

22

8. If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

(a)

45

(b)

40

(c)

10!

(d)

210

9. In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

(a)

110

(b)

10C3

(c)

120

(d)

116

10. In 2nC3 : nC3 = 11 : 1 then n is

(a)

5

(b)

6

(c)

11

(d)

7

11. Part B

6 x 2 = 12
12. There are 3 types of toy car and 2 types of toy train are available in a shop. Find the number of ways a baby can buy a toy car and a toy train?

13. How many two-digit numbers can be formed using 1, 2, 3, 4, 5 without repetition of digits?

14. Three persons enter into a conference hall in which there are 10 seats. In how many ways they can take their seats?

15. How many three-digit numbers, which are divisible by 5, can be formed using the digits 0, 1, 2, 3, 4, 5 if
(i) repetition of digits are not allowed?
(ii) repetition of digits are allowed?

16. Part C

6 x 3 = 18
17. Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?

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

19. Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?

20. If 9P5+5.9P4=10Pr , find r.

21. Part D

2 x 5 = 10
22. In how many ways can the following prizes be given away to a class of 30 students, first and second in mathematics, first and second in physics, first in chemistry and first in English?

23. By the principle of mathematical induction, prove that, for n$\in$N, cosα+cos(α+β)+cos(α+2β)+...+ cos(α+(n-1)β) = $\left( \alpha +\frac { (n-1)\beta }{ 2 } \right) \times \frac { sin\left( \frac { n\beta }{ 2 } \right) }{ sin\left( \frac { \beta }{ 2 } \right) }$.