If $(a \times b)^2 + (a \cdot b)^2 = 144$ and $|a| = 4$,then $|b| = $

Let $A$ and $B$ be two sets. Then $(A \cup B)' \cup (A' \cap B)$ is equal to:

$A$ metal disc of radius $R$ rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction $B$ acting perpendicular to the plane of the disc. The magnitude of the induced e.m.f. between the rim and the axis of the disc is:

If $\cos (x-y), \cos x, \cos (x+y)$ are three distinct numbers which are in harmonic progression and $\cos x \neq \cos y$,then $1+\cos y$ is equal to

The quantum number which explains the line spectra observed as doublets in the case of hydrogen and alkali metals and doublets and triplets in the case of alkaline earth metals is

$A$ capacitor of capacitance $C_0$ is charged to a potential $V_0$ and is connected with another capacitor of capacitance $C$ as shown. After closing the switch $S$,the common potential across the two capacitors becomes $V$. The capacitance $C$ is given by