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