ExamHabit
Practise free

2000

JEE Main 2000 Mathematics question on Binomial Theorem

For 2≤r≤n2 \leq r \leq n, (nr)+2(nr−1)+(nr−2)\binom{n}{r} + 2\binom{n}{r-1} + \binom{n}{r-2} is equal to
  1. A.
    (n+1r−1)\binom{n+1}{r-1}
  2. B.
    2(n+1r+1)2\binom{n+1}{r+1}
  3. C.
    2(n+2r)2\binom{n+2}{r}
  4. D.
    (n+2r)\binom{n+2}{r}
Show answer and solution

Correct option: D

Solution

Using Pascal's identity C(n,r) + C(n,r-1) = C(n+1,r), group the expression in two steps:

C(n,r) + 2·C(n,r-1) + C(n,r-2)
= [C(n,r) + C(n,r-1)] + [C(n,r-1) + C(n,r-2)]
= C(n+1,r) + C(n+1,r-1)
= C(n+2,r).

[2000]

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 2000 · Mathematics chapter list