Question

What is the value of \(\frac{101^3-99^3+2969703–3029697}{ 101^2 – 99^2}\)?

(a) 1

(b) 1/200

(c) 1/100

(d) 1/50

This question was addressed to me in a national level competition.

Enquiry is from Binomial Theorem for Positive Integral Index in chapter Binomial Theorem of Mathematics – Class 11

Answer 1

The correct choice is (d) 1/50

To explain I would say: The numerator when simplified is of the form (101 – 99)^3

The denominator can be simplified as (101 – 99)(101 + 99)

When we substitute in the numerator and denominator we get (2 x 2 x 2) / (2 x 200)

= 1/50.