$A$ point source of light is placed $4 \, m$ below the surface of water of refractive index $5/3$. The minimum diameter of a disc that should be placed over the source on the surface of water to cut off all light coming out of the water is ...... $m$.

$A$ short magnetic needle is pivoted in a uniform magnetic field of induction $1 ~T$. Now,simultaneously another magnetic field of induction $\sqrt{3} ~T$ is applied at right angles to the first field; the needle deflects through an angle $\theta$ whose value is (in $^{\circ}$)

An iron rod of length $2 \, m$ and cross-sectional area of $50 \, mm^2$ is stretched by $0.5 \, mm$ when a mass of $250 \, kg$ is hung from its lower end. The Young's modulus of the iron rod is:

Where is the very rich museum located in Gujarat?

In the adjacent circuit,a voltmeter of internal resistance $R$,when connected across $B$ and $C$,reads $\frac{100}{3} \text{ V}$. Neglecting the internal resistance of the battery,the value of $R$ is

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge as shown in the figure. The bridge is balanced when $C = 100 \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \Omega$. The value of $D$ is (in $\Omega$)