Sum of binomial coefficients of odd numbered terms

Q. The sum of the coefficients of the binomial expansion of ${(\frac{1}{x}+2x)}^n$ is equal to 6561. The constant term in the expansion is

1. \(None~of~these
2. 
3. 
4. 

Q.

The value of $1.C_1+3.C_3+5.C_5+7.C_7+....where{C}_0,C_1,C_2.....C_n$ are binomial coefficients in the expansion of $(1+x{)}^n$ is:

1. n∙2^n-1

2. n∙2^n-2

3. n(n-1)2^n-1

4. None of these

Q.

The number of terms which are free from radical

signs in the expansion of $(y^{\frac{1}{5}}+x^{\frac{1}{10}}{)}^{55}$ is

1. 5

2. 6

3. None of these

4. 7

Q. In the expansion of $(1+a{)}^{m+n}$, prove that coefficients of $a^m$ and $a^n$ are equal.

Q. If $A_{(i,j)}$ be the coefficient of $a^i{b}^j{c}^{2010-i-j}$ in the expansion of $(a+b-c{)}^{2010}$ then

1. A._2i, _3i is defined for i ?405
2. A_i, _i is defined for i ?1010
3. A_i, _j = A_j, _i
4. A₀, ₁ = 2000

Q.

If the number of terms in the expansion of $(x+1+\frac{1}{x}{)}^n$ is 501, then n =

1. 250

2. 500

3. 251

4. 249

Q.

If number of terms in the expansion of

$(x-2y+3z{)}^n$ are 45, then n =

1. 7

2. 8

3. 9

4. None of these

Q.

Find the number of dissimilar terms in the expansion of $(a+b{)}^{100}$

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Q. The coefficient of $ab{c}^{3}d{e}^2$ in the expansion of $(a+b+c+d+e{)}^8$ is equal to

1. none of these
2. 3630
3. 3600
4. 3360

Q.

If T=${}^{2n+1}{C}_1{+}^{2n+1}{C}_2+......{+}^{2n+1}{C}_n=255$. Find the value of n.

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Q. Find the coefficient of $x^n$ in the expansion of $(1+x{)}^{2n}$

1. ²ⁿC_n

2. ²ⁿC_2n

3. 2n

4. ²ⁿC_{n - 1}

Q.

Find the total number of terms in the expansion of $(x+a{)}^{100}+(x-a{)}^{100}$

Q.

Find the number of dissimilar terms in the expansion of $(x+y{)}^{32}$

1. 20

2. 21

3. 23

4. 22

Q.

Find the $(r+1{)}^{th}$ term in the expansion of $(x+y{)}^n$

1. 

2. 

3. 

4. 

Q.

The number of terms in the expansion of $(a+b+c{)}^n$

will be

1. 

2. 

3. 

4. None of these

Q.

How many dissimilar terms are there in the expansion of $(x+y{)}^{25}$

1. 26

2. 25

3. 24

4. 27

Q.

The number of terms in the expansion of $(x+y+z+u{)}^5$ is:

1. 56

2. 70

3. 189

4. None

Q.

One of the terms in the expansion of $(x+y{)}^n$ is $k{x}^8{y}^{13}$. Find the number of terms in the expansion.

__

Q.

If number of terms in the expansion of $(x-2y+3z{)}^n$ are 45, then n =

1. 7

2. 8

3. 9

4. None of these

Q. If the number of terms in the expansion of ${(1-\frac{2}{x}+\frac{4}{x^2})}^n,x\ne 0$, is 28, then the sum of the coefficients of all the terms in this expansions, is

1. 64
2. 2187
3. 729
4. 243

Q. If the number of terms in the expansion of ${(1-\frac{2}{x}+\frac{4}{x^2})}^n$, $x\ne 0$, is $28$, then the sum of the coefficients of all the terms in this expansion, is:

1. 243
2. 729
3. 64
4. 2187

Q.

Find the number of dissimilar terms in the expansion of $(a^3+b^3+3ab(a+b){)}^{50}$

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