# 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.

(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

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 .