The truth table for the system of four $NAND$ gates as shown in the figure is:

If $\frac{3+2i \sin \theta}{1-2i \sin \theta}$ is a real number and $0 < \theta < 2\pi$,then $\theta$ is equal to

Calculate the heat of combustion (in $kJ$) of methane from the following data:
$(I)$ $C_{(graphite)} + 2H_{2(g)} \rightarrow CH_{4(g)} \quad \Delta H = -74.8 \ kJ$
$(II)$ $C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)} \quad \Delta H = -393.5 \ kJ$
$(III)$ $H_{2(g)} + 1/2 O_{2(g)} \rightarrow H_2O_{(l)} \quad \Delta H = -286.2 \ kJ$

$A$ biological catalyst is essentially

The point of intersection of tangents at the ends of the latus-rectum of the parabola $y^2 = 4x$ is

$A$ variable circle passes through the fixed point $A(p, q)$ and touches the $X$-axis. The locus of the other end of the diameter through $A$ is