Assertion : $11$ sides of the polygon has $44$ diagonals. Reason: The number of diagonals in the polygon by $\frac{n (n - 3)}{2},$ where $n$ is the number of sides of the polygon.

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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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Number of ways of selecting 2 out of n $= {^{n} C}_{2}$
Out of these lines, n lines are the sides of the polygon. Thus ${^{n} C}_{2} - n = \frac{n (n - 3)}{2}$
If $n = 11$ , then the number of diagonals is $= \frac{11 (11 - 3)}{2} = 44$
So both Assertion and Reason are true and Assertion follows from the Reason.

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