$a^{m \log_a n} = $

An air column in a tube $32 ~cm$ long,closed at one end,is in resonance with a tuning fork. The air column in another tube,open at both ends,of length $66 ~cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together,they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

The proposition $(\sim p) \vee (p \wedge \sim q)$ is equivalent to:

The specific resistance (resistivity) of material $B$ is twice that of material $A$. The diameter of a circular wire made of $B$ is twice that of a wire made of $A$. If the resistances of both wires are equal,then the ratio of their lengths $l_B/l_A$ will be .......

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

Resonance is an example of