Let $f (1 + x) = f (1 - x) and f (4 + x) = f (4 - x)$
Statement 1 : f (x) is periodic with period 6
Statement 2: 6 is not necessarily fundamental period of f(x)

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Statement -1 is True Statement-2 is true and Statement-2 is not a correct explanation of Statement -1.

Statement -1 is True and Statement-2 is False

Statement -1 is False and Statement-2 is True

Statement -1 is True Statement-2 is True and Statement-2 is correct explanation of Statement-1

answer is B.

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Detailed Solution

$f (1 + x) = f (1 - x) \Rightarrow f (2 - x) = f (x) . . . . . . . . . . (i)$
$& f (4 + x) = f (4 - x)$
$\Rightarrow f (8 - x) = f (x) . . . . . . . . . . (ii)$
From (i) & (ii) we have
$\begin{array}{l} f (8 - x) = f (2 - x) replace x by 2 - x \\ f (8 - (2 - x)) = f (2 - (2 - x)) \\ f (6 + x) = f (x) \end{array}$
f is periodic but 6 need not be the fundamental periodic.