$A$ convex lens $A$ of focal length $20 \ cm$ and a concave lens $B$ of focal length $5 \ cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam,then the distance $d$ in $cm$ will be

$A$ solution containing $10 \ g$ per $dm^3$ of urea (molecular mass $= 60 \ g \ mol^{-1}$) is isotonic with a $5 \%$ solution of a non-volatile solute. The molecular mass of the non-volatile solute is ........ $g \ mol^{-1}$.

For a gas,$\frac{R}{C_{V}}=0.4$,where $R$ is the universal gas constant and $C_{V}$ is the molar specific heat at constant volume. The gas is made up of molecules which are

$A$ hyperbola passes through a focus of the ellipse $\frac{x^2}{169} + \frac{y^2}{25} = 1$. Its transverse and conjugate axes coincide respectively with the major and minor axes of the ellipse. The product of their eccentricities is $1$. Then,the equation of the hyperbola is:

$A$ circular disc of radius $R$ and thickness $\frac{R}{6}$ has a moment of inertia $I$ about an axis passing through its center and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of this sphere about its diameter is:

Two slits separated by a distance of $1\, mm$ are illuminated with red light of wavelength $6.5 \times 10^{-7}\, m$. The interference fringes are observed on a screen placed $1\, m$ from the slits. Find the distance between the third dark fringe and the fifth bright fringe on the same side of the central maxima.