Question

$f\left(x\right)=\sin \left(2\left(\sqrt{\left[a\right]}\right)x\right)$, where [ ] denotes the greatest integer function, has fundamental period $\pi$ for

• A. $a=\frac{3}{2}$
• B. $a=\frac{5}{4}$
• C. $a=\frac{2}{3}$
• D. $a=\frac{4}{5}$

Answer 1

Answer: (A), (B)

The correct options are
A $a=\frac{3}{2}$
B $a=\frac{5}{4}$

The fundamental period for $\sin \left(ax\right)$ is $\frac{2\pi }{a}$

Hence it will be $\pi$ for $a=2$

Hence $f\left(x\right)=\sin 2x$

So $\sqrt{\left[a\right]}=1$

Hence a must be a number between 1 and 2.

Option A and B are correct.