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

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below:

If a radioactive element having half-life of \(30\,min\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90\,min\). will be :

Three point charges of magnitude \(5 \mu C , 0.16 \mu C\) and \(0.3 \mu C\) are located at the vertices \(A , B , C\) of a right angled triangle whose sides are \(AB =3\,cm\), \(BC =3 \sqrt{2}\,cm\) and \(CA =3\,cm\) and point \(A\) is the right angle corner. Charge at point \(A\) experiences \(N\) of electrostatic force due to the other two charges.

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through \(O\) (the centre of mass) and \(O ^{\prime}(\) corner point \()\) is 

A air bubble of radius \(1\,cm\) in water has an upward acceleration \(9.8\, cm\, s ^{-2}\). The density of water is \(1\, gm\, cm ^{-3}\) and water offers negligible drag force on the bubble. The mass of the bubble is\(.......gm\) \(\left( g =980 \,cm / s ^{2}\right)\)

In finding out refractive index of glass slab the following observations were made through travelling microscope \(50\) vernier scale division \(=\) \(49 \mathrm{MSD} ; 20\) divisions on main scale in each \(\mathrm{cm}\) For mark on paper \(\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26\) For mark on paper seen through slab \(\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41\) For powder particle on the top surface of the glass slab \(\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1\) \((\mathrm{MSR}=\) Main Scale Reading, \(\mathrm{VC}=\) Vernier Coincidence) Refractive index of the glass slab is _______.

A particle is oscillating on the \(X-\) axis with an amplitude \(2\, cm\) about the point \(x_0 = 10\, cm\) with a frequency \(\omega \). A concave mirror of focal length \(5\,
cm\) is placed at the origin ( see figure) Identify the correct statements \((A)\) The image executes periodic motion \((B)\) The image executes non-periodic motion \((C)\) The turning points of the image are asymmetric w.r.t the image of the point at \(x =10\,cm\) \((D)\) The distance between the turning points of the oscillation of the image is \(\frac{{100}}{{21}}\)

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \(=500\, g\), Decay constant \(=20 \,g / s\) then ...... \(s\) time is required for the amplitude of the system to drop to half of its initial value ? \((\ln 2=0.693)\)

A body rotating with an angular speed of \(600\, {rpm}\) is uniformly accelerated to \(1800 \,{rpm}\) in \(10\; sec\). The number of rotations made in the process is ..... .

An element \(\Delta l=\Delta \mathrm{xi}\) is placed at the origin and carries a large current \(\mathrm{I}=10 \mathrm{~A}\). The magnetic field on the \(y\)-axis at a distance of \(0.5 \mathrm{~m}\) from the elements \(\Delta \mathrm{x}\) of \(1 \mathrm{~cm}\) length is _______.

If the function \(f(x)\, = \left\{ {\begin{array}{*{20}{c}}{ - x,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x < 1\,\,\,\,}\\{a + {{\cos }^{ - 1}}(x + b),\,\,\,\,\,\,\,\,\,1 \le x \le 2} \end{array}} \right.\)  is differentiable at \(x = 1 ,\) then \(\frac {a}{b}\) is equal to 

Photons of an electromagnetic radiation has an energy \(11\, keV\) each. To which region of electromagnetic spectrum does it belong ?

With reference to the observations in photo-electric effect, identify the correct statements from below: \(A.\) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. \(B.\) The value of saturation current increases on moving the source of light away from the metal surface. \(C.\) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. \(D.\) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. \(E.\) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below: