Index of (r+1)th Term from End When Counted from Beginning

Q.

If the coefficient of $x^2$ and $x^3$ in the expansion of $(3+ax{)}^9$ are the same, then the value of a is

1. $-\frac{7}{9}$

2. $\frac{7}{9}$

3. $-\frac{9}{7}$

4. $\frac{9}{7}$

Q.

If in the expansion of $(1+x{)}^{15}$, the coefficient of $(2r+3{)}^{th}$ and $(r-1{)}^{th}$ terms are equal, then the value of r is

1. 5

2. 4

3. 3

4. 6

Q.

The coefficients of 5th, 6th and 7th terms in the expansion of $(1+x{)}^n$ are in A.P., find n.

Q.

Find n in the binomial ${(\sqrt[3]{32}+\frac{1}{\sqrt[3]{33}})}^n$, if the ratio of $7^{th}$ term from the beginning to the $7^{th}$ term from the end is $\frac{1}{6}.$

Q.

The coefficient of $x^{-3}$ in the expansion of ${(x-\frac{m}{x})}^{11}$ is

1. $-792m^5$

2. $-792m^6$

3. $-924m^7$

4. $-330m^7$

Q.

If the coefficient of the $5th,6th$ and $7th$ terms of the expansion of $(1+x{)}^n$ are in A.P then the value of $n$may be?

1. $5$

2. $6$

3. $7$

4. $8$

Q.

If 3rd, 4th, 5th and 6th terms in the expansion of $(x+\alpha {)}^n$ be respectively a, b, c and d. prove that $\frac{b^2-ac}{c^2-bd}=\frac{5a}{3c}.$

Q.

If the coefficients of three consecutive terms in the expansion of $(1+x{)}^n$ be 76, 95 and 76, find n.

Q.

Find the 11th term from the beginning and the 11th term from the end in the expansion of $(2x-{\frac{1}{x^2}}^{25})$

Q.

If in the expansion of $(1+y{)}^n$, the coefficients of $5^{th}$, $6^{th}$ and $7^{th}$ terms are in A.P., then n is equal to

1. 7, 14

2. 8, 16

3. None of these

4. 7, 11

Q.

If the coefficients of (2r+1)th term and (r+2)th terms in the expansion of $(1+x{)}^{43}$ are equal, find r.

Q.

If in the expansion of $(1+x{)}^n$, the coefficients of three consecutive terms are 56, 70 and 56, then find n and the position of the terms of these coefficients.

Q.

Find the 7th term in the expansion of ${(\frac{4x}{5}+\frac{5}{2x})}^8$

Q.

If in the expansion of $(1+x{)}^n$, the coefficients of pth and qth terms are equal, prove that p+q =n+2, where $p\ne q.$

Q.

If in the expansion of ${(x^4-\frac{1}{x^3})}^{15},x^{-17}$ occurs in rth term, then

1. r=10

2. r=11

3. r=13

4. r=12

Q.

If the coefficient of the $(n+1{)}^{th}$ term and the $(n+3{)}^{th}$ termin the expansion of $(1+x{)}^{20}$ are equal, then the value of n is

1. 10

2. 9

3. None of these

4. 8

Q.

If the coefficient of x in ${(x^2+\frac{\lambda }{x})}^5$ is 270, then $\lambda =$

1. 5

2. 4

3. 3

4. None of these

Q.

If the coefficients of $2^{nd}$, $3^{rd}$ and $4^{th}$ terms in the expansion of $(1+x{)}^n,n\in N$ are in A.P., then n =

1. 7

2. 14

3. 2

4. None of these

Q.

If the expansion of $(1+x{)}^{20}$, then coefficients of rth and (r+4)th terms are equal, then r is equal to

1. 7

2. 9

3. 10

4. 8

Q.

Find the 4th term from the beginning and 4th term from the end in the expansion of ${(x+\frac{2}{x})}^9$

Q.

If the 2nd, 3rd and 4th terms in the expansion of $(x+a{)}^n$ and 240, 720 and 1080, find x, a, n.

Q.

How do you do cofactor expansion?

Q.

Find the 4th term from the end in the expansion of ${(\frac{4x}{5}-\frac{5}{2x})}^9$

Q.

Find a, if the coefficients of $x^2$ and $x^3$ in the expansion of $(3+ax{)}^9$ are equal.

Q.

Find the ratio of the coefficients of $x^n$ and $x^q$ in the expansion of $(1+x{)}^{p+q}.$

Q.

Find the 7^{th} term from the end in the expansion of ${(2x^2-\frac{3}{2x})}^8$

Q.

If in the expansion of $(a+b{)}^n$ and $(a+b{)}^{n+3}$, the ratio of the coefficients of second and third terms, and third and fourth terms respectively are equal, then n is

1. 6

2. 3

3. 4

4. 5

Q. The sum of the numerical coefficients in the expansion of ${(1+\frac{x}{3}+\frac{2y}{3})}^{12}$ is

1. 
2. 
3. 
4. 

Q.

Find the 5th term from the end in the expansion of $(3x-\frac{1}{x^2})$

Q.

If the 6th, 7th and 8th terms in the expansion $(x+a{)}^n$ are respectivley 112, 7 and $\frac{1}{4}$, find x, a, n.