NCERT Class 11-Math՚S: Chapter – 8 Binomial Theorem Part 4 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 13:

Which of the following is larger?

Answer:

We have

Similarly

Subtracting (2) from (1) , we get

Hence

Question 14:

Find the coefficient of after simplifying and collecting the like terms in the expansion of

Answer:

Since the above series is a geometric series with the common ratio its sum is

Hence, coefficient of is given by

Question 15:

If and are the coefficient of any four consecutive terms in the expansion of , prove that

Answer:

Let and be the coefficient of four consecutive terms and respectively. Then

And

Thus

Similarly,

Hence,

And

Objective Type Questions (M. C. Q)

Question 16:

The total number of terms in the expansion of after simplification is

(a)

(b)

(c)

(d) None of these

Answer:

C is the correct choice since the total number of terms are of which terms get cancelled.