Calculate the amount of charge on capacitor of \(4\, \mu\, {F}\). The internal resistance of battery is \(1\, \Omega\) : (in \(\mu {C}\))

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)

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to: \(A\). pure inductor. \(B\). pure capacitor. \(C\). pure resistor. \(D\). combination of an inductor and capacitor. Choose the correct answer from the options given below:

The centre of a wheel rolling on a plane surface moves with a speed \(v_{0} .\) A particle on the rim of the wheel at the same level as the centre will be moving at a speed \(\sqrt{x}\, v_{0}\). Then the value of \(x\) is ...... .

A circular coil of radius \(8.0 \,{cm}\) and \(20\) turns is rotated about its vertical diameter with an angular speed of \(50\, {rad} {s}^{-1}\) in a uniform horizontal magnetic field of \(3.0 \times 10^{-2}\, {T}\). The maximum \(emf\) induced the coil will be \(\ldots \ldots \ldots \times 10^{-2}\) \(volt\) (rounded off to the nearest integer)

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of \(f_1\) in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of \(\mathrm{f}_2\) when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of \(f_1\) and \(f_2\) will be _______.

Electric potential at a point \(P\) due to a point charge of \(5 \times 10^{-9}\; C\) is \(50 \;V\). The distance of \(P\) from the point charge is ......... \(cm\) (Assume, \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^{+9}\; Nm ^2 C ^{-2}\))

A sound wave of frequency \(245 \,Hz\) travels with the speed of \(300\, ms ^{-1}\) along the positive \(x\)-axis. Each point of the wave moves to and fro through a total distance of \(6 \,cm\). What will be the mathematical expression of this travelling wave ?

A car covers \(A B\) distance with first one-third at velocity \(v _{1} ms ^{-1}\), second one-third at \(v _{2} ms ^{-1}\) and last one-third at \(v _{3} ms ^{-1}\). If \(v _{3}=3 v _{1}, v _{2}=2 v _{1}\) and \(v _{1}=11\,ms ^{-1}\) then the average velocity of the car is________ \(ms ^{-1} .\)

This question has Statement \(- 1\) and Statements \(- 2\). Of the four choices given after the Statements, choose the one that best describes the two Statements Statement \(-1\) : Out of radio waves and microwaves, the radio waves under go more diffraction Statement \(-2\) : Radio waves have greater frequency compared to microwaves

Average force exerted on a non-reflecting surface at normal incidence is \(2.4 \times 10^{-4} \mathrm{~N}\). If \(360 \mathrm{~W} / \mathrm{cm}^2\) is the light energy flux during span of \(1\) hour \(30\) minutes. Then the area of the surface is _______.