The equation of a plane containing the line of intersection of the planes $2x - y - 4 = 0$ and $y + 2z - 4 = 0$ and passing through the point $(1, 1, 0)$ is:

At temperature $T \ K$,the $rms$ speed of $CO_2$ gas is $x \ cm/s$. At what temperature (in $Kelvin$) will the $rms$ speed of nitrous oxide $(N_2O)$ be $4x \ cm/s$ (in $T$)?

Two sources $A$ and $B$ are sending notes of frequency $680 \, Hz$. A listener moves from $A$ towards $B$ with a constant velocity $u$. If the speed of sound in air is $340 \, ms^{-1}$, what must be the value of $u$ so that the listener hears $10$ beats per second (in $ \, ms^{-1}$)?

$A$ telescope has an objective lens of focal length $144\, cm$ and an eyepiece of focal length $6\, cm$. Find the magnifying power of the telescope for normal adjustment.

The figure shows a system of logic gates. From the study of the truth table,it can be found that to produce a high output $(1)$ at $R$,we must have

The maximum value of $xy$ subject to $x+y=7$ is