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

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Question 14:

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

Answer:

The given expression is

General Term

7th 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