A radioactive sample is undergoing \(\alpha\) decay. At any time \(t_{1}\), its activity is \(A\) and another time \(t _{2}\), the activity is \(\frac{ A }{5}\). What is the average life time for the sample?

A vertical closed cylinder is separated into two parts by a frictionless piston of mass \(m\) and of negligible thickness. The piston is free to move along the length of the cylinder .The length of the cylinder above the piston is \(l_1,\) and that below the piston is \(l_2,\) such that \(l_1 > l_2.\) Each part of the cylinder contains \(n\) moles of an ideal gas at equal temperature \(T.\) If the piston is stationary, its mass, \(m,\) will be given by: ( \(R\) is universal gas constant and \(g\) is the acceleration due to gravity)

The maximum velocity of the photoelectrons emitted from the surface is \(v\) when light of frequency \(n\) falls on a metal surface. If the incident frequency is increased to \(3n\) , the maximum velocity of the ejected photoelectrons will be 

The parameter that remains the same for molecules of all gases at a given temperature is _______.

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

The diameter of the objective lens of microscope makes an angle \(\beta \) at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index \(n\). Then the resolving power of the microscope

A circular hole of radius \(\left(\frac{ a }{2}\right)\) is cut out of a circular disc of radius \('a'\) as shown in figure. The centroid of the remaining circular portion with respect to point \('O'\) will be :

A fully loaded boeing aircraft has a mass of \(5.4 \times 10^5\,kg\). Its total wing area is \(500\,m ^2\). It is in level flight with a speed of \(1080\,km / h\). If the density of air \(\rho\) is \(1.2\,kg\,m ^{-3}\), the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be \(\left( g =10\,m / s ^2\right)\)

A liquid column of height \(0.04 \mathrm{~cm}\) balances excess pressure of soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}\) and surface tension of soap solution is \(0.28 \mathrm{Nm}^{-1}\), then diameter of the soap bubble is _______ \(\mathrm{cm}\). \(\text { (if } g=10 \mathrm{~ms}^{-2} \text { ) }\)

In an experiment of \(CE\) configuration of \(n-p-n\) transistor, the transfer characteristics are observed as given in figure. If the input resistance is \(200 \Omega\) and output resistance is \(60 \Omega\) the voltage gain in this experiment will be..........

The effective current \(I\) in the given circuit at very high frequencies will be \(.......A\)

A biconvex lens of refractive index \(1.5\) has a focal length of \(20 \mathrm{~cm}\) in air. Its focal length when immersed in a liquid of refractive index \(1.6\) will be: