#### Algebra Important Questions

11th Standard

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Business Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. If nC3 = nC2, then the value of nC4 is

(a)

2

(b)

3

(c)

4

(d)

5

2. The value of n, when nP2 = 20 is

(a)

3

(b)

6

(c)

5

(d)

4

3. The number of ways selecting 4 players out of 5 is

(a)

4!

(b)

20

(c)

25

(d)

5

4. If nPr = 720 (nCr), then r is equal to

(a)

4

(b)

5

(c)

6

(d)

7

5. The possible out comes when a coin is tossed five times

(a)

25

(b)

52

(c)

10

(d)

$\frac { 5 }{ 2 }$

6. 6 x 2 = 12
7. Expand the following by using binomial theorem.$\left( x+\frac { 1 }{ y } \right) ^{ 7 }$

8. Expand the following by using binomial theorem.${ \left( x+\frac { 1 }{ { x }^{ 2 } } \right) }^{ 6 }$

9. Evaluate the following using binomial theorem:(101)4

10. ResoIve into partial fractions :$\frac { 12x-17 }{ (x-2)(x-1) }$

11. In a railway compartment, 6 seats are vacant on a bench. In how many ways can 3 passengers sit on them?

12. Evaluate$\frac { 1 }{ 5! } +\frac { 1 }{ 6! } +\frac { 1 }{ 7! }$

13. 6 x 3 = 18
14. Find the 5th term in the expansion of (x - 2y)13.

15. Resolve into partial fractions for the following:
$\frac { 2x^{ 2 }-5x-7 }{ (x-2)^3 }$

16. Resolve into partial fractions for the following:
$\frac { { x }^{ 2 }-3 }{ (x+2)({ x }^{ 2 }+1) }$

17. There are 6 gentlemen and 4 ladies to line at a round table. In how many ways can they seat themselves so that no two ladies together?

18. In how many ways can n prizes be given to n boys, when a boy may receive any number of prizes?

19. In how many ways can 12 things be equally divided among 4 persons?

20. 3 x 5 = 15
21. Prove that the term independent of x in the expansion of ${ \left( x+\frac { 1 }{ x } \right) }^{ 2n }is\quad \frac { 1.3.5.....,(2n-1){ 2 }^{ n } }{ n! }$

22. If nP4=12(nP2) find n.

23. If m parallel lines in a plane are intersected by a family of n parallel lines. Find the number of parallelogram formed?