# NCERT Class 11-Math՚s: Chapter – 8 Binomial Theorem Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 14**:

Find in the binomial f the ratio of 7^{th} term from the beginning to the 7^{th} term from the end is .

**Answer**:

The given expression is

General Term

7^{th} term from the end term from the beginning

term from the beginning

So,

According to the question, we get

Hence, the required value of is

**Question 15**:

In the expansion of if the sum of odd terms is denoted by and the sum of even term by E.

Then prove that

(i)

(ii)

**Answer**:

Given expression is

Sum of odd terms

And the sum of even terms,

Now

Similarly

Multiplying eq. (i) and eq. (ii) , we get

Hence

(ii)

Hence,

**Question 16**:

If occurs in the expansion of , prove that its coefficient is

**Answer**:

Given expression is

General terms,

If occurs in

Then

Hence, the coefficient of