The plates of a parallel plate capacitor are charged up to $100 \, V$. $A$ $2 \, mm$ thick plate is inserted between the plates. To maintain the same potential difference,the distance between the capacitor plates is increased by $1.6 \, mm$. The dielectric constant of the plate is:

The foot of the perpendicular from $(0,2,3)$ to the line $\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

If $x=e^{y+e^{y+e^{y+\ldots}}}$,then $\frac{d y}{d x}=$

Which of the following metals is a water pollutant and causes sterility in human beings?

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 $= 1\, cal/g^\circ C$)