ExamHabit
Practise free

JEE Main 2019 · 9 Jan · Shift I

JEE Main 2019 Mathematics question on Binomial Theorem

If the fractional part of the number 240315\frac{2^{403}}{15} is k15\frac{k}{15}, then kk is equal to
  1. A.
    14
  2. B.
    6
  3. C.
    4
  4. D.
    8
Show answer and solution

Correct option: D

Solution

2403 = 2^(4·100 + 3) = (24)100 · 23 = 16100 · 8.

Now 16 ≡ 1 (mod 15), so 16100 ≡ 1 (mod 15), giving 2403 ≡ 8 (mod 15).

So 2403 = 15m + 8 for some integer m, meaning 2403/15 = m + 8/15, and the fractional part is 8/15. Thus k = 8.

[JEE Main 2019 · 9 Jan · Shift I]

Practise Binomial Theorem the way it is asked

A timed set of real JEE Main Binomial Theorem questions, graded as the exam grades. No sign-up.

Start a Binomial Theorem test

More: all JEE Main Binomial Theorem questions · JEE Main 2019 · Mathematics chapter list