# NCERT Class 11 Mathematics Solutions: Chapter 8 – Binomial Theorem Miscellaneous Exercise Part 5 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. Find an approximation of using the first three terms of its expansion.

Answer:

(Approximately)

So, the value of is approximately .

2. Find , if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of

Answer:

In the expansion,

Fifth term from the beginning

So, it is evident that in the expansion of the fifth term from the

… . eq (1)

… eq (2)

It is given that the ratio of the fifth term from the beginning to the fifth term from the end is .

Therefore, from (1) and (2) ,

So, the value of is .