A point charge of \(10\,\mu C\) is placed at the origin. At what location on the \(X\)-axis should a point charge of \(40\,\mu\,C\) be placed so that the net electric field is zero at \(x =2\,cm\) on the \(X\)-axis ?

Your friend is having eye sight problem. She is not able lo see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as

A particle executes simple harmonic motion and is located at \(x = a, b\)  and  \(c\) at times \(t_0, 2t_0\) and \(3t_0\) respectively. The frequency of the oscillation is

The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy: (Assume \(m_p=m_e \times 1849\) )

A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir raised by \(x\), its efficiency decreases to \(\frac{1}{6}\). The value of \(x\), if the temperature of hot reservoir is \(99^{\circ}\,C\), will be \(........\,K\)

Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a, b\) and \(c (a < b < c)\) have surface charge densities \(+\sigma,-\sigma\) and \(+\sigma\) respectively. The potential of shell \(B\) is

A raindrop with radius \(R=0.2\, {mm}\) fells from a cloud at a height \(h=2000\, {m}\) above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attainde by the raindrop is : (In \({ms}^{-1}\)) [Density of water \(f_{{w}}=1000\;{kg} {m}^{-3}\) and density of air \(f_{{a}}=1.2\; {kg} {m}^{-3}, {g}=10 \;{m} / {s}^{2}\) Coefficient of viscosity of air \(=18 \times 10^{-5} \;{Nsm}^{-2}\) ]

Match List-I with List-II.

	List-I		List-II
A.	Coefficient of viscosity	I.	\(\left[ ML ^{-1} T^{-2}\right]\)
B.	Surface tension	II.	\(\left[ ML ^2 T^{-2}\right]\)
C.	Pressure	III.	\(\left[ ML ^0 T^{-2}\right]\)
D.	Surface energy	IV.	\(\left[ ML ^{-1} T^{-1}\right]\)

Choose the correct answer from the options given below :

A particle moving with kinetic energy \(E\) has de Broglie wavelength \(\lambda\). If energy \(\Delta \mathrm{E}\) is added to its energy, the wavelength become \(\frac {\lambda}{2} .\) Value of \(\Delta \mathrm{E},\) is 

Half-lives of two radioactive elements \(A\) and \(B\) are \(20\) minutes and \(40\) minutes, respectively. Initially, the samples have equal number of nuclei. After \(80\) minutes, the ratio of decayed number of \(A\) and \(B\) nuclei will be

A body of mass \(2\) kg begins to move under the influence of time dependent force \(\vec{F} = (2t\hat{i} + 6t^2\hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along \(x\) and \(y\)-axis respectively. The power produced by the force at \(t = 2\) s is _____ W.