If $n(A) = 3$ and $n(B) = 6$ and $A \subseteq B$,then the number of elements in $A \cap B$ is equal to

The equation of a straight line passing through the point $(1,2)$ and inclined at $45^{\circ}$ to the line $y=2x+1$ is

The enthalpy of the reaction,$H_{2(g)} + \frac{1}{2}O_{2(g)} \to H_2O_{(g)}$ is $\Delta H_1$ and that of $H_{2(g)} + \frac{1}{2}O_{2(g)} \to H_2O_{(l)}$ is $\Delta H_2$,then:

The three-domain system of classification is based on which of the following criteria?

$A$ wire carrying a current $i$ is placed in a uniform magnetic field in the form of the curve $y = a \sin \left( \frac{\pi x}{L} \right)$ for $0 \le x \le 2L$. The force acting on the wire is

$A$ long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of windings of $N$ turns each. If it carries a current $i$,the magnetic field at its centre will be