NCERT Class 11-Math's: Chapter –8 Binomial Theorem Part 3

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Question 8:

Find the middle term in the expansion of

Answer:

Since the power of binomial is even, it has one middle term which is the term and it is given by

Question 9:

Find the middle term (terms) in the expansion of

Answer:

Since the power of binomial is odd. Therefore, we have two middle terms which are 5th and 6th terms. These are given by

And

Question 10:

Show that , where is divisible by .

Answer:

We have

Thus, is divisible by .

Long Answer Type

Question 11:

Find numerically the greatest term in the expansion of , where .

Answer:

We have

Therefore,

Thus the maximum value of is . Therefore, the greatest term is

Hence, where

Question 12:

If is a positive integer, find the coefficient of in the expansion of

Answer:

We have

Now to find the coefficient of in it is equivalent to finding coefficient of in which in turn is equal to the coefficient of in the expansion of .

Since

Thus the coefficient of is

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