Integration to solve modified sum of binomial coefficients

Q.

The value of $\frac{C_1}{2}$ + $\frac{C_3}{4}$ + $\frac{C_5}{6}$ + ...... is equal to

1. $\frac{2^n-1}{n+1}$

2. $\frac{2^n}{n+1}$

3. $n\cdot 2^n$

4. $2^{n-1}$

Q.

If the sum of the n terms of G.P. is S product is P and sum of their inverse is R, than $P^2$ is equal to

1. 

2. 

3. 

4. 

Q.

If the third term in the binomial expansion of $(1+x{)}^{m}is-x^2$, then the rational value of m is

1. 

2. 

3. 

4. 

Q.

The sum to (n+1) terms of the following series

$\frac{C_0}{2}-\frac{C_1}{3}+\frac{C_2}{4}-\frac{C_3}{5}$ + ......... is

1. 

2. 

3. 

4. None of these

Q. $C_0+\frac{C_{1}x}{2}+\frac{C_2{X}^2}{3}+\dots \frac{C_n{X}^n}{n+1}$ =

1. 
2. 
3. 
4. 

Q.

If $C_r$ means ${}^n{C}_r$ then $\frac{C_0}{1}+\frac{C_2}{3}+\frac{C_4}{5}+\cdots =$

1. \frac{2^(n+2)}{n+1}\)

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

3. $\frac{2^n}{n}$

4. $\frac{2^n}{n+1}$

Q. The sum to (n+1) terms of the following series $\frac{C_0}{2}-\frac{C_1}{3}+\frac{C_2}{4}-\frac{C_3}{5}+\cdots$ is

1. $\frac{1}{n+1}$
2. $\frac{1}{n+2}$
3. $\frac{1}{n(n+1)}$
4. None of these

Q. The value of $\frac{C_1}{2}+\frac{C_3}{4}+\frac{C_5}{6}+\cdots$ equals to

1. $\frac{2^n-1}{n+1}$
2. $n{2}^n$
3. $\frac{2^n}{n}$
4. $\frac{2^n+1}{n+1}$

Q. Find the middle terms in the expansion of ${(3-\frac{x^3}{6})}^7$

Q. In the expansion of $(2x^2-8){(x-4)}^2$; find coefficient of $x^2$ .

1. $24$
2. $22$
3. $16$
4. $20$

Q. The value of $2c_0+\frac{2^2}{2}{C}_1+\frac{2^3}{3}{C}_2+\frac{2^4}{4}{C}_3+....+\frac{2^{11}}{11}{C}_{10}is$

1. 
2. 
3. 
4.