The correct option is A 12/(α+1)(α 2) =^αC_2^α + 1C_4 =α !4!(α 3)!(α 2)!2!(α +1)! =α !4.3.2!(α 3)!(α 2)(α 3)!2!(α +1)α ! =12(α 2 ...

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Chain Rule of Differentiation

αC2/α + 1C4 =

Question

$\frac{^{α} C_{2}}{^{α + 1} C_{4}}$ =

\frac{1}{3}

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\frac{12}{(α + 1) (α - 2)}

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\frac{4}{(α + 1) (α - 3)}

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\frac{12}{(α + 1) (α - 2) (α - 3)}

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Solution

The correct option is A $\frac{12}{(α + 1) (α - 2)}$
$= \frac{^{α} C_{2}}{^{α + 1} C_{4}}$
$= \frac{α! 4! (α - 3)!}{(α - 2)! 2! (α + 1)!}$
$= \frac{α! 4.3.2! (α - 3)!}{(α - 2) (α - 3)! 2! (α + 1) α!}$
$= \frac{12}{(α - 2) (α + 1)}$
Hence, option 'B' is correct.

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