NCERT Class 11-Math՚s: Chapter – 8 Binomial Theorem Part 5 (For CBSE, ICSE, IAS, NET, NRA 2023)

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Question 17:

If the coefficients of in are equal, then is

(a)

(b)

(c)

(d)

Answer:

B is the correct choice.

in expansion of ,

Therefore,

And

Therefore, (since it is given that coefficient of coefficient )

Question 18:

If then equals

(A)

(B)

(C)

(D)

Answer:

A is the correct choice. Putting and in

We get

and (2)

Adding (1) and (2) , we get

Therefore

Question 19:

The coefficient of and ( and are positive integers) in the expansion of are

(A) Equal

(B) Equal with opposite signs

(C) Reciprocal of each other

(D) None of these

Answer:

A is the correct choice. Coefficient of and in the expansion of are and

And

Hence (a) is the correct answer.

Question 20:

The number of terms in the expansion of , where is

(A)

(B)

(C)

(D)

Answer:

A is the correct choice. We have

Further, expanding each term of R. H. S. , we note that

First term consist of term.

Second term on simplification gives terms.

Third term on expansion gives terms.

Similarly, fourth term on expansion gives 4 terms and so on.

The total number of terms