A double convex lens has power \(P\) and same radii of curvature \(R\) of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power \(1.5P\) is ......\(R\)

A \(0.07\,{H}\) inductor and a \(12 \,\Omega\) resistor are connected in series to a \(220 \,{V}, 50 \,{Hz}\) ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take \(\pi\) as \(\left.\frac{22}{7}\right]\)

The angular momentum of a planet of mass \(M\) moving around the sun in an elliptical orbit is \(\overrightarrow{ L }\). The magnitude of the areal velocity of the planet is:

Water boils in an electric kettle in \(20\) minutes after being switched on. Using the same main supply, the length of the heating element should be _______ to _______ times of its initial length if the water is to be boiled in \(15\) minutes.

A balloon is moving up in air vertically above a point \(A\) on the ground. When it is at a height \(h _{1},\) a girl standing at a distance \(d\) (point \(B\) ) from \(A\) (see figure) sees it at an angle \(45^{\circ}\) with respect to the vertical. When the balloon climbs up a further height \(h _{2},\) it is seen at an angle \(60^{\circ}\) with respect to the vertical if the girl moves further by a distance \(2.464\, d\) (point \(C\) ). Then the height \(h _{2}\) is (given tan \(\left.30^{\circ}=0.5774\right)\)\(.......\)

Two simple harmonic waves having equal amplitudes of \(8\,cm\) and equal frequency of \(10\,Hz\) are moving along the same direction. The resultant amplitude is also \(8\,cm\). The phase difference between the individual waves is \(..................\) degree.

As shown in the figure, a particle is moving with constant speed \(\pi\,m / s\). Considering its motion from \(A\) to \(B\), the magnitude of the average velocity is:

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are \(10^{15}\text{ atoms/cm}^3\) and \(10^{18}\text{ atoms/cm}^3\), respectively. Which one of the following statements is true ?

A metal block of base area \(0.20\,m ^2\) is placed on a table, as shown in figure. A liquid film of thickness \(0.25\,mm\) is inserted between the block and the table. The block is pushed by a horizontal force of \(0.1\,N\) and moves with a constant speed. If the viscosity of the liquid is \(5.0 \times 10^{-3} \;Pa-s\), the speed of block is \(.........\times 10^{-3}\,m / s\)

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability \(\mu=2\mu_{0}\), is
( \(\mu_0=\) permeability of vacuum)

A \(10\, \mu F\) capacitor is fully charged to a potential difference of \(50\, V\). After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes \(20\, V\). The capacitance of the second capacitor is......\(\mu F\)

A \(20\, Henry\) inductor coil is connected to a \(10\, ohm\) resistance in series as shown in figure. The time at which rate of dissipation of energy (Joule’s heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor, is