ExamHabit
Practise free

1999

JEE Main 1999 Mathematics question on Binomial Theorem

If in the expansion of (1+x)m(1−x)n(1 + x)^m (1 - x)^n, the coefficients of xx and x2x^2 are 3 and −6-6 respectively, then mm is equal to
  1. A.
    6
  2. B.
    9
  3. C.
    12
  4. D.
    24
Show answer and solution

Correct option: C

Solution

From (1+x)m(1-x)n, collect coefficients of x and x²:

Coefficient of x: mC1 - nC1 = m - n = 3

Coefficient of x²: mC2 - mC1·nC1 + nC2 = m(m-1)/2 - mn + n(n-1)/2 = -6

Substituting m = n + 3 into the second equation:
(n+3)(n+2)/2 - (n+3)n + n(n-1)/2 = -6

Expanding: (n²+5n+6)/2 - n²-3n + (n²-n)/2 = -6

= (n²+5n+6 + n²-n)/2 - n²-3n = -6

= (2n²+4n+6)/2 - n²-3n = -6

= n²+2n+3 - n²-3n = -6

= -n+3 = -6

So n = 9, and m = n + 3 = 12.

[1999]

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 1999 · Mathematics chapter list