#### Binomial Theorem, Sequences and Series Book Back Questions

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

(a)

2

(b)

1

(c)

4

(d)

16

2. The HM of two positive numbers whose AM and GM are 16,8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

3. 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

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

(a)

$\frac { 2 }{ 3 }$

(b)

$\frac { 2 }{ 3 }$

(c)

$\frac { -4 }{ 15 }$

(d)

$\frac { 4 }{ 15 }$

5. The value of 2 + 4 + 6 + + 2n is

(a)

$\frac { n\left( n-1 \right) }{ 2 }$

(b)

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

(c)

$\frac { 2n\left( 2n-1 \right) }{ 2 }$

(d)

n(n + 1)

6. 3 x 2 = 6
7. Compute 97

8. Write the first 6 terms of the sequences whose nth term an given below
${ a }_{ n }=\begin{cases} n+1\quad if\quad n\quad is\quad odd \\ n\quad \quad if\quad n\quad is\quad even \end{cases}$

9. Find the middle terms in the expansion of (x +y)7.

10. 3 x 3 = 9
11. Expand the following in ascending powers of x and find the condition on x for which the binomial expansion is valid.
$\frac { 1 }{ 5+x }$

12. 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 $\frac { \left( n+1 \right) \left( n+2 \right) }{ \left( n+3 \right) (n+4) }$

13. Expand ${1\over(1+3x)^2}$ in powers of x. Find a condition on x for which the expansion is valid.

14. 2 x 5 = 10
15. Find the value of n if the sum to n terms of the series $\sqrt { 3 } +\sqrt { 75 } +\sqrt { 243 } +....is\quad 435\sqrt { 3 } .$

16. Find the sum of the first 20-terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77.