Sum of coefficients of all terms

Q.

The value of ${2000}_{C_2}+{2000}_{C_5}+{2000}_{C_8}+...+{2000}_{C_{2000}}=?$

A. $\frac{2^{1999}+1}{3}$

B. $\frac{2^{1999}-1}{3}$

C. $\frac{2^{2000}+1}{3}$

D. $\frac{2^{2000}-1}{3}$

Q.

If ${}^{56}p_{r+6}:{}^{54}p_r+3=30800:1$, then the value of $r$ is:

1. $40$

2. $51$

3. $41$

4. 510

5. 101

Q.

The coefficient of the middle term in the binomial expansion of $(1+ax{)}^4$ and of $(1-ax{)}^6$ is the same, if a equals:

1. 

2. 

3. 

4. 

Q.

Find the value of $a_1$ for which the coefficient of the middle term in the expansions of $(1+ax{)}^4$and $(1-ax{)}^6$ are equal.

Q. ${\sum }_{m=1}^n\left({\sum }_{k=1}^m\left({\sum }_{p=k}^m{}^n{C}_m{.}^m{C}_p{.}^p{C}_k\right)\right)=$

1. 
2. 
3. 
4. 

Q. The value of ${(}^{21}{C}_1{-}^{10}{C}_1)+{(}^{21}{C}_2{-}^{10}{C}_2)+{(}^{21}{C}_3{-}^{10}{C}_3)+{(}^{21}{C}_4{-}^{10}{C}_4)+...+{(}^{21}{C}_{10}{-}^{10}{C}_{10})$ is

1. $2^{21}-2^{11}$
2. $2^{20}-2^9$
3. $2^{21}-2^{10}$
4. $2^{20}-2^{10}$

Q.

If the sum of the coefficients in the expansion of $(x+y{)}^n$ is 8192, then the greatest coefficient in the expansion is

1. 

2. 

3. 

4. 

Q.

$\sum _{r=1}^n$${}^{n-1}{C}_{r-1}$ =

1. 

2. 

3. 

4. 

Q. If the sum of the coefficients in the expansion of $(a+b{)}^n$ is 4096, then the greatest coefficient in the expansion is .

1. 1594
2. 792
3. 924
4. 2924

Q.

If the sum of the coefficients in the expansion of $(a+b{)}^n$ is 4096, then the greatest coefficient in the expansion is

1. 792

2. 1594

3. 2924

4. 924

Q.

Number of middle terms in the expansion of $(a+b{)}^{20}$ is:

___

Q.

If the sum of the coefficients in the expansion of $(a+b{)}^n$ is 4096, then the greatest coefficient in the expansion is

1. 1594

2. 2924

3. 792

4. 924

Q.

If the sum of the coeficients in the expansion of $(a+b{)}^n$ is 4096, then the greatest coefficient in the

expansion is.

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