#### Binomial Theorem : Sequences and Series - 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. The HM of two positive numbers whose AM and GM are 16,8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

2. If Sn denotes the sum of n terms of an AP whose common difference is d, the value of Sn-2Sn-1+Sn-2 is

(a)

0

(b)

2d

(c)

4d

(d)

d2

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

(a)

$\sqrt { 2n+1 }$

(b)

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

(c)

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

(d)

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

4. The nth term of the sequence $\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 }$.+.....is

(a)

2n-n-1

(b)

1-2n

(c)

2-n+n-1

(d)

2n-1

5. The sum up to n terms of the series $\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +$.....is

(a)

$\frac { n(n+1) }{ 2 }$

(b)

2n(n+)

(c)

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

(d)

1

6. The value of the series$\quad \frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 6 } +$.....is

(a)

14

(b)

7

(c)

4

(d)

6

7. The sum of an infinite GP is 18. If the first term is 6, the common ratio is

(a)

$\frac { 1 }{ 3 }$

(b)

$\frac { 2 }{ 3 }$

(c)

$\frac { 1 }{ 6 }$

(d)

$\frac { 3 }{ 4 }$

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

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 2 }{ 3 }$

(c)

$\frac { -4 }{ 15 }$

(d)

$\frac { 4 }{ 15 }$

9. If $\frac { { T }_{ 2 } }{ { T }_{ 3 } }$is the expansion of (a+b)n and $\frac { { T }_{ 3 } }{ { T }_{ 4 } }$ is the expansion of (a+b)n+3 are equal, then n=

(a)

3

(b)

4

(c)

5

(d)

6

10. The Co-efficient of x-17 in ${ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \right) }^{ 15 }$is

(a)

1365

(b)

-1365

(c)

3003

(d)

-3003

11. Part B

6 x 2 = 12
12. Find the sum of first n terms of the series 12+32+52+...

13. Find a negative value of m if the Co-efficient of x2 in the expansion of (1+x)m ,|x|<1 is 6

14. Find the general term in the expansion of ${ \left( \frac { 4x }{ 5 } -\frac { 5 }{ 2x } \right) }^{ 9 }$

15. Find the middle term in ${ \left( x-\frac { 1 }{ 2y } \right) }^{ 10 }$

16. Find the greatest term in (1 + 2x)8 when x = 2.

17. Find the $\sqrt [ 3 ]{ 126 }$ approximately to two decimal places.

18. Part C

6 x 3 = 18
19. If the roots of the equation (q - r) x2 + (r - p)x + p - q = 0 are equal, then show that p, q and r are in A.P.

20. 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 $\frac { (-1)^{ n } }{ n }$

21. 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 $\frac { 2n+3 }{ 3n+4 }$

22. 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

23. Write the nth term of the following sequences
$\frac { 1 }{ 2 } ,\frac { 2 }{ 3 } ,\frac { 3 }{ 4 } ,\frac { 4 }{ 5 } ,\frac { 5 }{ 6 }$

24. Expand ${\left( 2x-{1\over 2x} \right)}^{4}.$

25. Part D

2 x 5 = 10
26. In a race, 20 balls are placed in a line at intervals of 4 meters, with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?

27. Prove that $\sqrt [ 3 ]{ x^3+7 } -\sqrt [ 3 ]{ x^3+4 }$ is approximately equal to ${1\over x^2}$ when x is large.