If $A$ and $B$ are any two events,then $P(A \cup B) = $

$A$ nucleus with $Z = 92$ emits the following in a sequence: $\alpha, \alpha, \beta^-, \beta^-, \alpha, \alpha, \alpha, \alpha, \beta^-, \beta^-, \alpha, \beta^-, \beta^-, \alpha$. The $Z$ of the resulting nucleus is

For a cell,the terminal potential difference $(P.D.)$ is $2.2 \, V$ when the circuit is open and reduces to $1.8 \, V$ when the cell is connected to an external resistance of $R = 5 \, \Omega$. Determine the internal resistance of the cell $(r)$.

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

Two bodies have their moments of inertia $I$ and $2I$ respectively about their axis of rotation. If their kinetic energies of rotation are equal,their angular momenta will be in the ratio

$A$ wire in the form of a square of side $a$ carries a current $i$. Then,the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)