If $a = \log_{24} 12$,$b = \log_{36} 24$,and $c = \log_{48} 36$,then $1 + abc$ is equal to:

Which one of the following is correctly matched?

Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 >> R_2$,the mutual inductance $M$ between them will be directly proportional to

An inductive circuit contains a resistance of $10\,\Omega$ and an inductance of $2.0\,H$. If an $AC$ voltage of $120\,V$ and frequency $60\,Hz$ is applied to this circuit,the current would be nearly ................$A$.

If $\vec{a}, \vec{b}, \text{ and } \vec{c}$ are unit vectors,then $|\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2$ does not exceed:

The surface of water in a water tank of cross-sectional area $750 \, cm^2$ on the top of a house is $h \, m$ above the tap level. The speed of water coming out through the tap of cross-sectional area $500 \, mm^2$ is $30 \, cm/s$. At that instant,$\frac{dh}{dt}$ is $x \times 10^{-3} \, m/s$. The value of $x$ will be $.............$.