A thin prism of angle \(6^{\circ}\) and refractive index for yellow light \(\left(n_{Y}\right) 1.5\) is combined with another prism of angle \(5^{\circ}\) and \(n _{ Y }=1.55\). The combination produces no dispersion. The net average deviation ( \(\delta\) ) produced by the combination is \(\left(\frac{1}{x}\right)^{\circ}\). The value of \(x\) is.......

A charge \(q\)  is spread uniformly over an insulated loop of radius \(r\) . If it is rotated with an angular velocity \(\omega \) with respect to normal axis then the magnetic moment of the loop is

Three blocks \(A, B\) and \(C\) are lying on a smooth horizontal surface, as shown in the figure. \(A\) and \(B\) have equal masses, \(m\) while \(C\) has mass \(M\). Block \(A\) is given an initial speed \(v\) towards \(B\) due to which it collides with \(B\) perfectly inelastically. The combined mass collides with \(C\), also perfectly inelastically. The combined mass collides with \(C\), also perfectly inelastically if \(\frac{5}{6}^{th}\) of the initial kinetic energy is lost in whole process. What is value of \(M/m\) ?

A uniform disc of radius \(R\) and mass \(M\) is free to rotate only about its axis. A string is wrapped over its rim and a body of mass \(m\) is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is

A metallic surface is illuminated with radiation of wavelength \(\lambda\), the stopping potential is \(V_0\). If the same surface is illuminated with radiation of wavelength \(2 \lambda\), the stopping potential becomes \(\frac{V_0}{4}\). The threshold wavelength for this metallic surface will be -

A bob of mass \(m\) attached to an inextensible string of length \(l\) is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed \(\omega\ rad/s\) about the vertical. About the point of suspension:

A uniformly tapering conical wire is made from a material of Young's modulus \(Y\)  and has a normal, unextended length \(L.\) The radii, at the upper and lower ends of this conical wire, have values \(R\) and \(3R,\)  respectively. The upper end of the wire is fixed to a rigid support and a mass \(M\) is suspended from its lower end. The equilibrium extended length, of this wire, would equal 

Conductivity of a photodiode starts changing only if the wavelength of incident light is less than \(660 \mathrm{~nm}\). The band gap of photodiode is found to be \(\left(\frac{x}{8}\right) \mathrm{eV}\). The value of \(x\) is _______. (Given, \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) )

The number of solutions of the equation \(\sin ^{-1}\left[x^{2}+\frac{1}{3}\right]+\cos ^{-1}\left[x^{2}-\frac{2}{3}\right]=x^{2}\) for \(x \in[-1,1],\) and \([x]\) denotes the greatest integer less than or equal to \(x\), is ...... .

Identify the correct statements :
A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination.
B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric.
C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance.
D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces.
Choose the correct answer from the options given below.

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first drop strikes the ground is ___________ m.
\(\left( g =10 m / s ^2\right)\)

Following gates section is connected in a complete suitable circuit. For which of the following combination, bulb will glow \((ON)\)?

Two projectiles \(A\) and \(B\) are thrown with initial velocities of \(40\,m / s\) and \(60\,m / s\) at angles \(30^{\circ}\) and \(60^{\circ}\) with the horizontal respectively. The ratio of their ranges respectively is \(\left( g =10\,m / s ^2\right)\)