Which one of the following conditions is incorrect for a well-behaved wave function $(\psi)$?

An ideal transformer has $100$ turns in the primary and $250$ turns in the secondary. The peak value of the $AC$ voltage in the primary is $28\ V$. The $r.m.s.$ secondary voltage is nearest to $....V$.

In algae with a haplontic life cycle,which of the following processes involves mitosis?

If $f(0)=0, f(1)=1, f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3, 4, 5, \ldots$, then $f(9)$ is equal to

If $\log _{27}(\log _3 x) = \frac{1}{3}$, then the value of $x$ is

In a compound microscope,the focal lengths of two lenses are $1.5 \, cm$ and $6.25 \, cm$. An object is placed at $2 \, cm$ from the objective lens and the final image is formed at $25 \, cm$ from the eye lens. The distance between the two lenses is.......$cm$.