In a series LCR circuit, a resistor of \(300 \Omega\), a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ \(\times 10^4\) radians \(\mathrm{s}^{-1}\).

The logic gate equivalent to the given logic circuit is

To maintain a speed of \(80\,km / h\) by a bus of mass \(500\,kg\) on a plane rough road for \(4\,km\) distance, the work done by the engine of the bus will be \(........\,kJ\). [The coefficient of friction between tyre of bus and road is \(0.04]\).

A ray of light is incident at an angle of \(60^o\) on one face of a prism of angle \(30^o\) . The emergent ray of light makes an angle of \(30^o\)  with incident ray. The angle made by the emergent ray with second face of prism will be....\(^o\)

There is an air bubble of radius \(1.0\,mm\) in a liquid of surface tension \(0.075\,Nm ^{-1}\) and density \(1000\,kg\) \(m ^{-3}\) at a depth of \(10\,cm\) below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is \(....Pa \left( g =10\,ms ^{-2}\right)\)

A thin cylindrical rod of length \(10\,cm\) is placed horizontally on the principle axis of a concave mirror of focal length \(20\,cm\). The rod is placed in a such a way that mid point of the rod is at \(40\,cm\) from the pole of mirror. The length of the image formed by the mirror will be \(\frac{x}{3} cm\). The value of \(x\) is \(............\).

A capacitor is made of a tlat plate of area \(A\) and a second plate having a stair-like structure as shown in figure. If the area of each stair is \(\frac{A}{3}\) and the height is \(\mathrm{d}\), the capacitance of the arrangement is _______.

The maximum and minimum distances of a comet from the Sun are \(1.6 \times 10^{12}\, m\) and \(8.0 \times 10^{10}\, m\) respectively. If the speed of the comet at the nearest point is \(6 \times 10^{4}\, ms ^{-1},\) the speed at the farthest point is ......... \(\times 10^{3}\, m / s\)

For the given logic gate circuit, which of the following is the correct truth table?

Given below are two statements : \(Statement\) \((I)\) : Planck's constant and angular momentum have same dimensions. \(Statement\) \((II)\) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :

A ball of mass \(0.5 \; kg\) is dropped from the height of \(10 \; m\). The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is \(\dots \; m\). (Use \(g =10 \; m / s ^{2}\)).

A light wave is incident normally on a glass slab of refractive index \(1.5\). If \(4\%\) of light gets reflected and the amplitude of the electric field of the incident light is \(30\, V/m\), then the amplitude of the electric field for the wave propagating in the glass medium will be.......\( V/m\)

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below: