An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and \(2 \sqrt{3}\) (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is _________ .

A charge particle is moving in a uniform magnetic field \((2 \hat{i}+3 \hat{j}) T\). If it has an acceleration of \((\alpha \hat{i}-4 \hat{j}) m / s ^{2}\), then the value of \(\alpha\) will be.

As show in the figure, in steady state, the charge stored in the capacitor is....... \(\times 10^{-6}\,C\).

The graph between two temperature scales \(P\) and \(Q\) is shown in the figure. Between upper fixed point and lower fixed point there are \(150\) equal divisions of scale \(P\) and \(100\) divisions on scale \(Q\). The relationship for conversion between the two scales is given by :

The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\)

A uniformly charged ring of radius \(3a\) and total charge \(q\) is placed in \(xy-\) plane centered at origin. A point charge \(q\) is moving towards the ring along the \(z-\) axis and has speed \(v\) at \(z = 4a\). The minimum value of \(v\) such that it crosses the origin is

In the circuit shown below, maximum zener diode current will be \(.....mA\)

Let \(f(x)=\log _{\mathrm{e}} x\) and \(g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}\). Then the domain of \(f \circ g\) is

Let \(S=\left\{z \in C : z^{2}+\bar{z}=0\right\}\). Then \(\sum \limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))\) is equal to\(......\)

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt{3}\) times of amplitude of individual motions. The phase difference between the two motions is \(.....(degree)\)

A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

The material filled between the plates of a parallel plate capacitor has resistivity \(200 \Omega \, {m}\). The value of capacitance of the capacitor is \(2\, {pF}\). If a potential difference of \(40 \,{V}\) is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is (given the value of relative permitivity of material is \(50\) )

Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is \(0.7\; \mathrm{V} .\) For the input voltages shown in the figure, the voltage (in \(Volts\)) at point \(A\) is