$CrO_3$ dissolves in aqueous $NaOH$ to give:

If $p$ and $q$ are distinct prime numbers and if the equation $x^2 - px + q = 0$ has positive integers as its roots,then the roots of the equation are

During the electrolysis of cryolite,aluminium and fluorine are formed in ........ molar ratio :

$A$ plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If the lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses,then the focal length of the combination is

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = Young's modulus,$\rho$ = density,$\alpha$ = coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

$A$ meter bridge is set up as shown,to determine an unknown resistance '$X$' using a standard $10 \, \Omega$ resistor. The galvanometer shows a null point when the tapping-key is at the $52 \, cm$ mark. The end corrections are $1 \, cm$ and $2 \, cm$ respectively for the ends $A$ and $B$. The determined value of '$X$' is $.......... \Omega$.