What is the objective of Systematics?

In a region of uniform magnetic induction $B = 10^{-2} \, T$,a circular coil of radius $30 \, cm$ and resistance $\pi^2 \, \Omega$ is rotated about an axis which is perpendicular to the direction of $B$ and which forms a diameter of the coil. If the coil rotates at $200 \, rpm$,the amplitude of the alternating current induced in the coil is ...... $mA$.

In the standing wave shown,particles at the positions $A$ and $B$ have a phase difference of

$\frac{d}{dx}{\left( \sqrt{x} + \frac{1}{\sqrt{x}} \right)^2} = $

$A$ coil of $50$ turns and $4\,cm$ radius carries $2\,A$ current. The magnetic field at its centre is......$mT$.

In an industrial process,$10\, kg$ of water per hour is to be heated from $20^\circ C$ to $80^\circ C$. To do this,steam at $200^\circ C$ is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at $90^\circ C$. How many $kg$ of steam is required per hour? (Specific heat of steam $= 0.5\, cal/g^\circ C$,Latent heat of vaporisation $= 540\, cal/g$,Specific heat of water $= 1\, cal/g^\circ C$)