For 2≤ r≤ n, nr+2 n r-1 + n r-2 = (a) n+1 r-1 (b) 2 n+1 r+1 (c) 2 n+2 r (d) n+2 r

Correct answer: (d) n+2 r Pairing via Pascal's rule twice gives n+1 r+ n+1 r-1 = n+2 r. JEE Advanced 2000 · Binomial Theorem — verified solution by the Vidaara Team.

JEE PYQ

[JEE Advanced 2000] for 2 r n binom nr 2 binom n r 1 binom n r

VAVidaara Admin Asked 4d ago 0 views 1 answer

#PYQJEE #JEE #JEE Advanced #2000 #binomial-sums #Binomial Theorem

For $2\le r\le n$, $\binom nr+2\binom n{r-1}+\binom n{r-2}=$

(a) $\binom{n+1}{r-1}$
(b) $2\binom{n+1}{r+1}$
(c) $2\binom{n+2}r$
(d) $\binom{n+2}r$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 4d ago ▲ 0

Correct answer: (d) $\binom{n+2}r$

Pairing via Pascal's rule twice gives $\binom{n+1}r+\binom{n+1}{r-1}=\binom{n+2}r$.

JEE Advanced 2000 · Binomial Theorem — verified solution by the Vidaara Team.

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