# NCERT Class 11-Math՚s: Chapter – 8 Binomial Theorem Part 6 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 21**:

The ratio of the coefficient of to the term independent of in is

(A)

(B)

(C)

(D)

**Answer**:

(B) Is the correct choice.

Let be the general term of , so

Now, for the coefficient of term containing ,

Therefore, is the coefficient of (from (1) )

To find the term independent of , put

Thus is the term independent of (from (1) )

Now the ratio is

**Question 22**:

If , then

(A)

(B)

(C)

(D)

**Answer**:

B is the correct choice. On simplification, we get

Since and , will not contain any *i* and hence .

## 8.3 EXERCISE

## Short Answer Type

**Question 1**:

Find the term independent of , , in the expansion of

**Answer**:

**Question 2**:

If the term free from in the expansion of is , find the value of *k*.

**Answer**:

**Question 3**:

Find the coefficient of *x* in the expansion of .

**Answer**:

**Question 4**:

Find the term independent of *x* in the expansion of,

**Answer**:

**Question 5**:

Find the middle term (terms) in the expansion of

(i) (ii)

**Answer**:

(i) (ii)

**Question 6**:

Find the coefficient of in the expansion of .

**Answer**:

**Question 7**:

Find the coefficient of in the expansion of

**Answer**:

**Question 8**:

Find the sixth term of the expansion , if the binomial coefficient of the third term from the end is 45.

[**Hint**: Binomial coefficient of third term from the end Binomial coefficient of third term from beginning .]

**Answer**:

**Question 9**:

Find the value of , if the coefficients of and terms in the expansion of are equal.

**Answer**: