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#### Binomial Theorem, Sequences and Series Model Question Paper

11th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The sequence$\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } } \frac { 1 }{ \sqrt { 3 } +2\sqrt { 2 } }$...form an

(a)

AP

(b)

GP

(c)

HP

(d)

AGP

2. The sum up to n terms of the series $\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +$....is

(a)

$\sqrt { 2n+1 }$

(b)

$\frac { \sqrt { 2n+1 } }{ 2 }$

(c)

$\sqrt { 2n+1 } -1$

(d)

$\frac { \sqrt { 2n+1 } -1 }{ 2 }$

3. The coefficient of x5 in the series e-2x is

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 2 }{ 3 }$

(c)

$\frac { -4 }{ 15 }$

(d)

$\frac { 4 }{ 15 }$

4. The term without x in ${ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }$ is

(a)

495

(b)

-495

(c)

-7920

(d)

7920

5. The value of ${ 9 }^{ \frac { 1 }{ 3 } }$ ,${ 9 }^{ \frac { 1 }{ 9 } }$${ 9 }^{ \frac { 1 }{ 27 } }$ ,$\infty$is

(a)

1

(b)

3

(c)

9

(d)

none of these

6. 5 x 2 = 10
7. Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of 'them $\frac { 2n+3 }{ 3n+4 }$

8. Write the first 6 terms of the sequences whose nth terms are given below and classify them as arithmetic progression, geometric progression, arithmetic -geometric progression, harmonic progression and none of 'them 2018

9. If $x=a+\frac { a }{ r } +\frac { a }{ { r }^{ 2 } } +...+\infty ,y=b-\frac { b }{ r } +\frac { b }{ { r }^{ 2 } } +.....+\infty \quad z=c+\frac { c }{ { r }^{ 2 } } +\frac { c }{ { r }^{ 4 } } +...+\infty$ then show that $\frac{xy}{z}=\frac{ab}{c}$

10. If H be the H. M. between a and b, then show that (H - 2a) (H - 2b) = H2

11. Find a positive value of m for which the coefficient of x2 in the expansion of (1+x)m is 6.

12. 5 x 3 = 15
13. Compute 97

14. Write the first 4 terms of the logarithmic series of log (1 - 2x)

15. The sum of two members is$\frac { 13 }{ 6 }$ .An even number A.M.S are being inserted between them and their sum exceeds their number by 1.Find the number of A.M.S inserted.

16. Find $\sum_{1}^{\infty}{\frac{1}{(k+1)(k+2)}}$.

17. Sum the series: (1 + x) + (1 + x + x2) + (1 + x + x2 +x3) + ... up to n terms

18. 4 x 5 = 20
19. Compute the sum of first n terms of 1 + (1 + 4) + (1 + 4 + 42) + (1 + 4 + 42 + 43) + ...

20. Find the value of n if the sum to n terms of the series $\sqrt { 3 } +\sqrt { 75 } +\sqrt { 243 } +....is\quad 435\sqrt { 3 } .$

21. Find the sum of the series $1+\frac { 2 }{ 5 } +\frac { 3 }{ { 5 }^{ 2 } } +\frac { 5 }{ { 5 }^{ 3 } } +$

22. Find the fourth root of 623 correct to seven places of decimal.