A combination of parallel plate capacitors is maintained at a certain potential difference When a \(3\, mm\) thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by \(2.4\, mm\). Find the dielectric constant of the slab. 

The equation of a wave travelling on a string is \(\mathrm{y}=\sin [20 \pi \mathrm{x}+10 \pi \mathrm{t}]\), where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

Read the following statements: \(A.\) When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. \(B.\) Two bodies \(P\) and \(Q\) having equal surface areas are maintained at temperature \(10^{\circ}\,C\) and \(20^{\circ}\,C\). The thermal radiation emitted in a given time by \(P\) and \(Q\) are in the ratio \(1: 1.15\) \(C.\) A carnot Engine working between \(100\,K\) and \(400\,K\) has an efficiency of \(75 \%\) \(D.\) When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) propagates along the positive \(z-\) direction in free space. The peak value of the electric field is \(60\, V/m\). Which among the following is the acceptable magnetic field component in the electromagnetic wave?

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is \(7 \times 10^8 \mathrm{~V} / \mathrm{s}\) then the integer value of the distance between the parallel plates is \(\left(\right.\) Take, \(\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)\) ________ \(\mu \mathrm{m}\).

A radioactive nuclei with decay constant \(0.5/s\) is being produced at a constant rate of \(100\, nuclei/s\). If at \(t\, = 0\) there were no nuclei, the time when there are \(50\, nuclei\) is

At time \(t =0\) a particle starts travelling from a height \(7\,\hat{z} cm\) in a plane keeping \(z\) coordinate constant. At any instant of time it's position along the \(x\) and \(y\) directions are defined as \(3\,t\) and \(5\,t^{3}\) respectively. At \(t =1\,s\) acceleration of the particle will be.

The equivalent resistance between the points \(A\) and \(B\) in the following circuit is \(\frac{x}{5} \Omega\). The value of \(x\) is ___________.

A convex mirror of radius of curvature \(30 \mathrm{~cm}\) forms an image that is half the size of the object. The object distance is :

The value of \(\cos \,\frac{\pi }{{{2^2}}}.\cos \,\frac{\pi }{{{2^3}}}{._{..................}}.\cos \,\frac{\pi }{{{2^{10}}}}.\,\sin \,\frac{\pi }{{{2^{10}}}}\) is

In a series \(L R\) circuit \(X_{L}=R\) and power factor of the circuit is \(P _{1}\). When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P_{2}\). The ratio \(\frac{ P _{1}}{ P _{2}}\) is

Number of \(4-\)digit numbers that are less than or equal to \(2800\) and either divisible by \(3\) or by \(11\) , is equal to \(............\).

A boy pushes a box of mass \(2\, kg\) with a force \(\overrightarrow{ F }=(20 \hat{ i }+10 \hat{ j }) N\) on a frictionless surface. If the box was initially at rest, then ...........  \(m\) is displacement along the \(x-\)axis after \(10\, s\).