$A$ plano-convex lens is made of glass with a refractive index of $1.5$. The radius of curvature of its convex surface is $R$. What is its focal length?

For all values of $a$ and $b$,the line $(a+2b)x + (a-b)y + (a+5b) = 0$ passes through a fixed point. Find that point.

The velocities of three particles of masses $20 \ g$,$30 \ g$ and $50 \ g$ are $10 \hat{i}$,$10 \hat{j}$ and $10 \hat{k}$,respectively. The velocity of the centre of mass of the three particles is

Initially a photon of wavelength $\lambda_1$ falls on a photocathode and emits an electron of maximum energy $E_1$. If the wavelength of the incident photon is changed to $\lambda_2$,the maximum energy of the electron emitted becomes $E_2$. Then the value of $hc$ ($h=$ Planck's constant,$c=$ velocity of light) is

$A$ bimetallic strip consists of metals $X$ and $Y$. It is mounted rigidly at the base as shown in the figure. The metal $X$ has a higher coefficient of linear expansion compared to that of metal $Y$. When the bimetallic strip is placed in a cold bath, what happens?

Which of the following is a scalar quantity?