The root mean square velocity of molecules of gas is

A power transmission line feeds input power at \(2300\,V\) to a step down transfonner with its primary windings having  \(4000\) turns, giving the output power at \(230\,V.\)  If the current in the primary of the transformer is  \(5\,A,\) and its efficiency is \(90\%,\)  the output current would be......\(A\)

Match List\(-I\) with List\(-II\)

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( \(k _1\) and \(k _2\) ) in the following fashion. Which of the following is true? \(\left( k _1> k _2\right)\)

The electric current in the circuit is given as \(i=i_{ o }(t / T)\). The r.m.s current for the period \(t=0\) to \(t=T\) is ___________

In a meter bridge experiment to determine the value of unknown resistance, first the resistances \(2 \Omega\) and \(3 \Omega\) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \(l cm\) from the left. Now when an unknown resistance \(x \Omega\) is connected in parallel to \(3 \Omega\) resistance, the null point is shifted by 10 cm to the right of wire. The value of unknown resistance \(x\) is _________ \(\Omega\).

In an experiment for determining the gravitational acceleration \(g\) of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure. What is the value of \(g\) at the place? ...... \(m/s^2\)

Electric field in a region is given by \( \vec{E}=Ax\hat{i}+By\hat{j} \), where \( A=10~V/m^{2} \) and \( B=5~V/m^{2} \). If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is __________ V.

The radii of two soap bubbles are \(r_1\) and \(r_2\). In isothermal conditions, two meet together in vaccum. Then the radius of the resultant bubble is given by

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 \(\left.\frac{22}{7}\right]\)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason \(\mathrm{R}\)
Assertion A: In photoelectric effect, on increasing the intensity of incident light the stopping potential increases.
Reason R : Increase in intensity of light increases the rate of photoelectrons emitted, provided the frequency of incident light is greater than threshold frequency.
In the light of the above statements, choose the correct answer from the options given below

A block of mass \(m\) slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is : Given \({m}=8 \,{kg}, {M}=16\, {kg}\) Assume all the surfaces shown in the figure to be frictionless.