Binomial Theorem Ques 6
- For $2 \leq r \leq n,\binom{n}{r}+2\binom{n}{r-1}+\binom{n}{r-2}$ is equal to
(a) $\binom{n+1}{r-1}$
(b) $2\binom{n+1}{r+1}$
(c) $2\binom{n+2}{r}$
(d) $\binom{n+2}{r}$
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Answer:
Correct Answer: 6.(d)
Solution: (d) $\binom{n}{r}+2\binom{n}{r-1}+\binom{n}{r-2}=\left[\binom{n}{r}+\binom{n}{r-1}\right] $
$+\left[\binom{n}{r-1}+\binom{n}{r-2}\right]=\binom{n+1}{r}+\binom{n+1}{r-1}=\binom{n+2}{r} $
${\left[\because \quad { }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r\right]}$
BETA
