Question

What is the middle term of (xyz + 3)^80?

(a) ^80C41 (xyz)^41 (3)^39

(b) ^80C40 (xyz)^40 (3)^40

(c) ^80C39 (xyz)^39 (3)^40

(d) ^80C41 (xyz)^41 (3)^40

The question was asked in an interview.

I need to ask this question from Binomial Theorem topic in section Binomial Theorem of Mathematics – Class 11

Answer 1

Correct choice is (b) ^80C40 (xyz)^40 (3)^40

Explanation: Since the power is even, there are odd number of terms.

The middle term is the \((\frac{n}{2} + 1)^{th}\) term.

= \((\frac{80}{2} + 1)^{th}\) term

= 41^st term

The 41^st term = ^80C40 (xyz)^40 (3)^40