• # question_answer Direction: For the following questions, choose the correct answers from the codes [a], [b], [c] and [d] defined as follows. Let $f(x)$ be a function such that $f'(x)\,=\,\prod\limits_{n\,=\,1}^{10}{{{(x-n)}^{n}}}$. Statement I The sum of all values of $x$at which $f(x)$ attains minima is 15. Statement II$f(x)$ has inflectional points at $x=2,\,4,\,6,\,\,8,\,\,10$ A)  Statement I is true. Statement II is also true and Statement n is the correct explanation of Statement I. B)  Statement I is true. Statement II is also true and Statement n is not the correct explanation of Statement I. C)  Statement I is true. Statement II is false. D)  Statement I is false. Statement II is true.

Correct Answer: A

Solution :

$f(x)$ has inflectional points at $x=2,\,4,\,6,\,8,\,10$. Maximum at $x=3,\,7$ and minimum at $x=1,\,\,5,\,\,9$. $\therefore$ Sum of minimum values of $x=1+5+9=15$

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