Calculate the limit of resolution of a telescope objective having a diameter of \(200\, cm\), if it has to detect light of wavelength \(500\, nm\) coming from a star

Match List-I with List-II.

LIST - I	LIST - II
(A) Isobaric	(I) ΔQ = ΔW
(B) Isochoric	(II) ΔQ = ΔU
(C) Adiabatic	(III) ΔQ = zero
(D) Isothermal	(IV) ΔQ = ΔU + PΔV

\(\Delta \mathrm{Q}=\) Heat supplied
\(\Delta \mathrm{W}=\) Work done by the system
\(\Delta \mathrm{U}=\) Change in internal energy
\(\mathrm{P}=\) Pressure of the system
\(\Delta \mathrm{V}=\) Change in volume of the system
Choose the correct answer from the options given below:

An object of uniform density rolls up the curved path with the initial velocity \(v_0\) as shown in the figure. If the maximum height attained by an object is \(\dfrac{7v_0^2}{10g}\) (\(g\) = acceleration due to gravity), the object is a _______.

The half-life of a radioactive element \(A\) is the same as the mean-life of another radioactive element \(B.\) Initially both substances have the same number of atoms, then

Surface of certain metal is first illuminated with light of wavelength \({\lambda _1} = 350\,nm\) and then, the light of wavelength \({\lambda _2} = 540\,nm\). It is found that the maximum speed of the photo electrons in the two cases differ by a factor of \(2\). The work function of the metal (in \(eV\)) is close to: (Energy of photon \( = \frac{{1240}}{{\lambda {\rm{(in\, nm)}}}}\,eV\))

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification \( m_{1} \), when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to \( m_{2} \).
The value of \(\left|\frac{m_1}{m_2}\right|\) is __________ .

Projectiles \(A\) and \(B\) are thrown at angles of \(45^{\circ}\) and \(60^{\circ}\) with vertical respectively from top of a \(400 \mathrm{~m}\) high tower. If their ranges and times of flight are same, the ratio of their speeds of projection \(v_A: v_B\) is _______.

Effective capacitance of parallel combination of two capacitors \(\mathrm{C}_{1}\) and \(\mathrm{C}_{2}\) is \(10\; \mu \mathrm{F}\). When these capacitors are individually connected to a voltage source of \(1\; \mathrm{V},\) the energy stored in the capacitor \(\mathrm{C}_{2}\) is \(4\) times that of \(\mathrm{C}_{1}\). If these capacitors are connected in series, their effective capacitance will be

The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object ? (Figure drawn as schematic and not to scale)

In the first configuration (1) as shown in the figure, four identical charges \(\left(q_0\right)\) are kept at the corners \(A, B, C\) and \(D\) of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points \(\mathrm{G}, \mathrm{E}, \mathrm{H}\) and F, of the square, If \(\mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\), the difference between the potential energies of configuration (2) and (1) is given by :

The number of molecules in one litre of an ideal gas at \(300 \,{K}\) and \(2\) atmospheric pressure with mean kinetic energy \(2 \times 10^{-9}\, {J}\) per molecules is \(....\, \times 10^{11}\)

Given below are two statements: Statement \((I)\) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement \((II)\) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below: