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 _________ .

Find the equivalent resistance between two ends of the following circuit

Match List \(- I\) (Electromagnetic wave type) with List \(- II\) (Its association/application) and select the correct option from the choices given below the lists

લિસ્ટ\(-I\)	લિસ્ટ\(-II\)
\(a\). Infrared waves	\(i\). To treat muscular strain
\(b\). Radio waves	\(ii\). For broadcasting
\(c\). \(X-\)rays	\(iii\). To detect fracture of bones
\(d\). Ultraviolet rays	\(iv\). Absorbed by the ozone layer of the atmosphere

\(a\)         \(b\)         \(c\)         \(d\)

Ge and Si diodes conduct at \(0.3 \,V\) and \(0.7\, V\) respectively. In the following figure if Ge diode connection are reversed, the valve of \(V0\) changes by.....\(V\)

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be..... \(\%\).

Find the truth table for the function \(Y\) and \(A\) and \(B\) represented in the following figure.

The maximum speed of a boat in still water is \(27 \mathrm{~km} / \mathrm{h}\). Now this boat is moving downstream in a river flowing at \(9 \mathrm{~km} / \mathrm{h}\). A man in the boat throws a ball vertically upwards with speed of \(10 \mathrm{~m} / \mathrm{s}\). Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\))

The space between the plates of a parallel plate capacitor is filled with a 'dielectric' whose 'dielectric constant' varies with distance as per the relation: \(K(x) = K_0 + \lambda x\) ( \(\lambda  =\) constant) The capacitance \(C,\) of the capacitor, would be related to its vacuum capacitance \(C_0\) for the relation

An object of mass ' m ' is projected from origin in a vertical \(x y\) plane at an angle \(45^{\circ}\) with the x axis with an initial velocity \(\mathrm{v}_0\). The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]

A bead of mass ' \(m\) ' slides without friction on the wall of a vertical circular hoop of radius ' \(R\) ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' \(R\) '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)

If \(\in\), \( E \) and \( t \) represent the free space permittivity, electric field and time respectively, then the unit of \( \frac{eE}{t} \) will be :

A block of mass \(10\, kg\) starts sliding on a surface with an initial velocity of \(9.8\, ms ^{-1}\). The coefficient of friction between the surface and bock is \(0.5\). The distance covered by the block before coming to rest is: [use \(g =9.8\, ms ^{-2}\) ].........\(m\)

An electron of mass \(m\) is moving in an electric field \(\vec{E} = -2E_0\hat{i}\) (\(E_0 =\) constant \(> 0\)), with an initial velocity \(\vec{V} = v_0\hat{i}\) (\(v_0 =\) constant \(> 0\)). If \(\lambda_0 = \dfrac{h}{4mv_0}\), its de Broglie wavelength at time \(t\) is __________.
(\(e =\) charge of electron)