# NCERT Class 11-Math's: Chapter –8 Binomial Theorem Part 6

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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:**