In Whittaker's classification system,which kingdom acts as the primary producer?

$A$ black body at a temperature of $227^{\circ}C$ radiates heat energy at the rate of $5 \ cal/cm^2-sec$. At a temperature of $727^{\circ}C$,the rate of heat radiated per unit area in $cal/cm^2-sec$ will be:

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x \, dx$ is equal to

The maximum value of $\frac{\log x}{x}, 0 < x < \infty$ is

If $\cos \theta - 4 \sin \theta = 1$,then $\sin \theta + 4 \cos \theta$ is equal to

The locus of the centre of the circle,which cuts the circle $x^2+y^2-20x+4=0$ orthogonally and touches the line $x=2$,is