General Term of Binomial Expansion

Q.

If the coefficient of $x^7$ in $(a{x}^2+\frac{1}{bx}{)}^{11}$ is equal to the coefficient of $x^{-7}$ in $(ax-\frac{1}{b{x}^2}{)}^{11}$, then ab =

1. 1

2. 1/2

3. 2

4. 3

Q.

If the ratio of the coefficient of third and fourth term in the expansion of $(x-\frac{1}{2x}{)}^n$ is $1:2$, then the value of $n$ will be

1. $16$

2. $12$

3. $-10$

4. $18$

Q.

Factorise $\frac{64}{125}{a}^3-\frac{96}{25}{a}^2+\frac{48}{5}a-8$.

Q. The coefficients of three consecutive terms of $(1+x{)}^{n+5}$ are in the ratio 5 : 10 : 14. Then, n is equal to

1. 3
2. 4
3. 5
4. 6

Q.

The number of terms in the expansion of ${(x^2+1+\frac{1}{x^2})}^n,n\in$ N, is

1. 2n

2. 3n

3. 2n+1

4. 3n+1

Q. Find the coefficient of $x^7$ in $(a{x}^2+\frac{1}{bx})$ and $x^{-7}$ in $(ax-\frac{1}{b{x}^2})$ and find the relation between a and b, so that these coefficients are equal.

Or

In the binomial expansion of $(1+x{)}^n$, the coefficients of the fifth, sixth and seventh terms are in AP. Find all values of n for which this can happen.

Q.

If the coefficients of $r^{th}$ term and $(r+4{)}^{th}$ term are equal in the expansion of $(1+x{)}^{20}$, then the value of r will be

1. 7

2. 8

3. 9

4. 10

Q.

If the third term in the binomial expansion of $(1+x{)}^m$ is $-\frac{1}{8}{x}^2$, then the rational value of m is

1. 2

2. 3

3. 4

4. $\frac{1}{2}$

Q.

The coefficient of $x^n$ in the expansion of $(1+2x+3x^2+...{)}^{1/2}$ is equal to:

1. 1

2. n

3. -n

4. None

Q.

If n is positive integer and three consecutive

coefficients in the expansion of $(1+x{)}^n$ are in the

ratio 6 : 33 : 110, then n =

1. 4

2. 6

3. 12

4. 16

Q.

Find the coefficient of $x^8{y}^{12}$ in the expansion of $(x+2y{)}^{20}$

1. 

2. 

3. 

4. 

Q.

The coefficient of $x^8$ in the expansion of ${(3x^2+\frac{5}{x^3})}^9$ is

1. 

2. 

3. 

4. 

Q.

Find the coefficient of abcd in the expansion of $(a+b+c+d{)}^4$

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Q.

If in the expansion of (1+x)ⁿ, the coefficients of r^thand (r+2)^th terms be equal, then r is equal to :

1. 2n

2. 

3. 

4. 

Q.

If the ratio of the 5th term from the beginning to the 5th term from the end in the expansion of ${(4\sqrt{2}+\frac{1}{4\sqrt{3}})}^n$
is $\sqrt{6}:1$ then find the value of n.

Q.

If A + B = ${45}^{\circ }$, find tanA + tanB

1. TanAtanB

2. 1 - tanAtanB

3. 1+tanAtanB

4. TanAtanB-1

Q.

If the coefficients of 7^th and 13^th terms in the expansion of (1 + x)ⁿ are equal, then n is equal to

1. 20

2. 10

3. 15

4. 18

Q.

In an A. P., $S_m:S_n=m^2:n^2$ . The ratio of $p^{2}th$ term to $q^{2}th$ term is:

1. $\frac{2p^2+1}{2q^2+1}$

2. $\frac{2p^2-1}{2q^2-1}$

3. $\frac{2p-1}{2q-1}$

4. $\frac{p^2-2}{q^2-2}$

Q.

The coefficient of y in expansion of $(y^2+\frac{c}{y}{)}^5$ is :

1. 29c

2. 10c

3. 10c³

4. 20c²

Q.

The number of terms in the expansion of (x - y + 2z)⁷ are:

1. 35

2. 38

3. 37

4. 36

Q.

If the coefficient of $(2r+4{)}^{th}$ and $(r-2{)}^{th}$ terms in the

expansion of ($1+x{)}^{18}$ are equal, then r =

1. 10

2. 8

3. 12

4. 6

Q.

If the ratio of the coefficient of third and fourth term in the expansion of $(x-\frac{1}{2x}{)}^n$ is 1:2, then the value of n will be

1. 18

2. 16

3. 12

4. -10

Q.

If the ratio of the coefficient of third and fourth term in the

expansion of $(x-\frac{1}{2x}{)}^n$ is 1:2, then the value of n will be

1. 18

2. 12

3. 16

4. -10

Q. The remainder when }7^{63} is divided by }25 is , explain in detail .}

Q.

In the expansion of (x+y)ⁿ , the coefficients of 4^th and 13^th terms are equal, Then the value of n is :

1. 15

2. 12

3. 9

4. 21

Q. The smallest natural number $n,$ such that the cofficient of $x$ in the expansion of ${(x^2+\frac{1}{x^3})}^n$is ${}^n{C}_{23}$, is :

1. $23$
2. $38$
3. $35$
4. $58$

Q. which of the following cannot be the sum of n terms of an AP ? (a) 3n^2+5n (b) n^2+5n (c) \lbrack(n)(n+1)(2n+1)\rbrack/6 (d) n(n+1) /2 . Explain in detail

Q.

If A = ${20}^{\circ }$ and B = ${25}^{\circ }$, Find the value of tanA + tanB + tanAtanB.

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Q. ${10}^{\text{th}}$ term in the expansion of ${(3-\sqrt{\frac{17}{4}+3\sqrt{2}})}^{20}$ is

1. an irrational number
2. a rational number
3. a positive integer
4. a negative integer

Q.

In the expansion of (a+b)ⁿ, n Є N the number of terms is:

1. n + 1

2. n - 1

3. aⁿ

4. n