NCERT Class 11-Math's: Chapter –8 Binomial Theorem Part 5

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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