$A$ radioactive sample consists of two distinct species having an equal number of atoms $N_0$ initially. The mean-life of one species is $\tau$ and of the other is $5\tau$. The decay products in both cases are stable. The total number of radioactive nuclei at $t = 5\tau$ is:

$A$ long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B$. It is then bent into a circular loop of $n$ turns. The magnetic field at the centre of the coil will be

Typhoid fever is caused by which of the following?

Match the following columns:

Column-$I$	Column-$II$
$(a)$ $Oscillatoria$	$(p)$ $Prothallus$
$(b)$ $Cycas$	$(q)$ $Cell$ $wall$ $contains$ $chitin$ $mixed$ $with$ $cellulose$
$(c)$ $Dryopteris$	$(r)$ $Primitive$ $flowers$
$(d)$ $Yeast$	$(s)$ $Food$ $stored$ $as$ $starch$

Consider a block of conducting material of resistivity ' $\rho$ ' as described. Current ' $I$ ' enters at ' $A$ ' and leaves from ' $D$ '. We apply the superposition principle to find the voltage ' $\Delta V$ ' developed between ' $B$ ' and ' $C$ '. The calculation is done in the following steps:
$(i)$ Take current ' $I$ ' entering from ' $A$ ' and assume it to spread over a hemispherical surface in the block.
(ii) Calculate the field $E(r)$ at distance ' $r$ ' from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at ' $r$ '.
(iii) From the ' $r$ ' dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
(iv) Repeat $(i)$,(ii),and (iii) for current ' $I$ ' leaving ' $D$ ' and superpose results for ' $A$ ' and ' $D$ '.
For current entering at $A$,the electric field at a distance ' $r$ ' from $A$ is:

$A$ $100\%$ efficient transformer has $100$ turns in the primary and $25$ turns in its secondary coil. If the current in the secondary coil is $4\, A$,then the current in the primary coil is.....$A$.