$A$ $p-n$ photodiode is made of a material with a band gap of $2.0\, eV$. The minimum frequency of the radiation that can be absorbed by the material is nearly

If $x^2+y^2+z^2 \neq 0, \quad x=c y+b z, \quad y=a z+c x$ and $z=b x+a y$,then $a^2+b^2+c^2+2 a b c$ is equal to

Consider the situation shown in the figure. Water $(\mu = 4/3)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ from the surface of the water. The distance of the image from the mirror after reflection from it of an object $O$ at the bottom of the beaker is ..... $cm$.

$A$ wire elongates by $l \, mm$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends,the elongation of the wire will be (in $mm$):

What is $X$ in the following reaction?
$2 CH_3COCH_3 \stackrel{Ba(OH)_2}{\longrightarrow} X$

$A$ vibration magnetometer consists of two identical bar magnets placed one over the other such that they are perpendicular and bisect each other. The time period of oscillation in a horizontal magnetic field is $2^{5/4} \ s$. One of the magnets is removed and if the other magnet oscillates in the same field,then the time period in seconds is: