Question
Let $$f\left( x \right) = \cos \sqrt {p}x ,$$ where $$p = \left[ a \right] = $$ the greatest integer less than or equal to $$a.$$ If the period of $$f\left( x \right)$$ is $$\pi $$ then :
A.
$$a\, \in \,\,\left[ {4,\,5} \right]$$
B.
$$a=4,\,5$$
C.
$$a\, \in \,\,\left[ {4,\,5} \right)$$
D.
none of these
Answer :
$$a\, \in \,\,\left[ {4,\,5} \right)$$
Solution :
The period of $$f\left( x \right) = \frac{{2\pi }}{{\sqrt p }} = \pi $$ (from the question).
$$\eqalign{
& \therefore \sqrt p = 2{\text{ or }}p = 4 \cr
& \therefore \left[ a \right] = 4 \cr
& \therefore \,\,4 \leqslant a < 5 \cr} $$