When $MgCl_2 \cdot 6H_2O$ is strongly heated,then it forms

The wavelength of radiation emitted is $\lambda_0$ when an electron jumps from the third to the second orbit of a hydrogen atom. For the electron to jump from the fourth to the second orbit of the hydrogen atom,the wavelength of radiation emitted will be

$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires $AB$ and $CD$ are

In the given figure,what does the part labeled '$a$' represent?

Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R$. At time $t = 0$,the number of $P$ species is $4N_0$ and that of $Q$ is $N_0$. The half-life of $P$ is $1$ minute,while that of $Q$ is $2$ minutes. Initially,there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ are equal,the number of nuclei of $R$ present in the sample would be:

The resultant gate and its Boolean expression in the given circuit is