$A$ vessel contains oil (density $= 0.8 \, g/cm^3$) over mercury (density $= 13.6 \, g/cm^3$). $A$ homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $g/cm^3$ is

$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced electromotive forces (emf) in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.

When electric current is passed through acidified water for $1930 \ s$,$1120 \ mL$ of $H_2$ gas is collected (at $STP$) at the cathode. What is the current passed in amperes?

What is the coordination number of the metal in $[Co(en)_2Cl_2]^+$?

If an electron in a hydrogen atom jumps from an orbit of level $n=3$ to an orbit of level $n=2$,then the emitted radiation frequency is (where $R=$ Rydberg's constant,$C=$ velocity of light).

For preparing a $0.1 \, N$ solution of a compound from its impure sample,of which the percentage purity is known,the weight of the substance required will be