Assertion :A polygon has 44 diagonals and number of sides are 11. Reason: From n distinct objects r objects can be selected in $^{n} C_{r}$ ways.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Assertion is incorrect but Reason is correct

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Let no of sides be $n$
$\Rightarrow^{n} C_{2} - n = 44$
$\Rightarrow n = - 8$ or $\Rightarrow n = 11$ .
$r$ objects can be selected from $n$ objects in $^{n} C_{r}$ ways
Hence, both assertion and reason are correct and reason is the correct explanation for assertion.

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Assertion :A polygon has 44 diagonals and number of sides are 11. Reason: From n distinct objects r objects can be selected in nCr ways.

Assertion :A polygon has 44 diagonals and number of sides are 11. Reason: From n distinct objects r objects can be selected in $^{n} C_{r}$ ways.