#### Algebra Book Back Questions

11th Standard

Reg.No. :
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Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. The value of n, when nP2 = 20 is

(a)

3

(b)

6

(c)

5

(d)

4

2. The number of diagonals in a polygon of n seates is equal to

(a)

nC2

(b)

nC2 - 2

(c)

nC2 - n

(d)

nC2 - 1

3. The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for n $\in$ N is

(a)

2

(b)

6

(c)

20

(d)

24

4. For all n > 0, nC1 + nC2 + nC3 + ... +nCn is equal to

(a)

2n

(b)

2n- 1

(c)

n2

(d)

n2 - 1

5. The middle term in the expansion of ${ \left( x+\frac { 1 }{ x } \right) }^{ 10 }$

(a)

10C4$\left( \frac { 1 }{ x } \right)$

(b)

10C5

(c)

10C6

(d)

10C7x4

6. 3 x 2 = 6
7. Evaluate the following using binomial theorem:(999)5

8. How many triangles can be formed by joining the vertices of a hexagon?

9. How many distinct words can be formed using all the letters of the following words.
MISSISSIPPI

10. 3 x 3 = 9
11. Find the middle terms in the expansion of ${ \left( x+\frac { 1 }{ x } \right) }^{ 11 }$

12. Find x if $\frac { 1 }{ 6! } +\frac { 1 }{ 7! } =\frac { x }{ 8! }$.

13. Find the number of arrangements that can be made out of the letters of the word "ASSASSINATION".

14. 2 x 5 = 10
15. Prove that the term independent of x in the expansion of ${ \left( x+\frac { 1 }{ x } \right) }^{ 2n }is\quad \frac { 1.3.5.....,(2n-1){ 2 }^{ n } }{ n! }$

16. By the principle of mathematical induction, prove the following.
13+23+33+.......+n3=$\frac { { n }^{ 2 }(n+1)^{ 2 } }{ 4 }$ for all $n\in N$.