A small ball of mass \(m\) is thrown upward with velocity \(u\) from the ground. The ball experiences a resistive force \(mkv ^{2}\) where \(v\) is its speed. The maximum height attained by the ball is 

A parallel plate capacitor has charge \(5 \times 10^{-6} \mathrm{C}\). A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is \(4 \times 10^{-6} \mathrm{C}\) then the dielectric constant of the slab is ________.

A horse rider covers half the distance with \(5\,m / s\) speed. The remaining part of the distance was travelled with speed \(10\,m / s\) for half the time and with speed \(15 m / s\) for other half of the time. The mean speed of the rider averaged over the whole time of motion is \(\frac{x}{7}\,m / s\). The value of \(x\) is

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that \(\theta(t)=5 t^2-8 t\), where \(\theta(t)\) is the angular position of the rotating disc as a function of time \(t\). How much power is delivered by the applied torque, when \(t=2 s\) ?

If an electron is moving in the \(n ^{\text {th }}\) orbit of the hydrogen atom, then its velocity \(\left( v _{ n }\right)\) for the \(n ^{\text {th }}\) orbit is given as

The mean free path of molecules of a certain gas at \(STP\) is \(1500\,d\), where \(d\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373\,K\) is approximately \(..........\,d\)

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 \(\mathrm{s}^{-1}\).

Considering Bohr's atomic model for hydrogen atom :
(A) the energy of H atom in ground state is same as energy of \(\mathrm{He}^{+}\)ion in its first excited state.
(B) the energy of H atom in ground state is same as that for \(\mathrm{Li}^{++}\)ion in its second excited state.
(C) the energy of H atom in its ground state is same as that of \(\mathrm{He}^{+}\)ion for its ground state.
(D) the energy of \(\mathrm{He}^{+}\)ion in its first excited state is same as that for \(\mathrm{Li}^{++}\)ion in its ground state
Choose the correct answer from the options given below :

For the given circuit, comment on the type of transformer used:

Electric field in a certain region is given by \(\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)\). The \(SI\) unit of \(A\) and \(B\) are

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at \(30°\) and \(90°\), respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at \(60°\) with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ______.

Water flows through a horizontal tube as shown in the figure. The difference in height between the water columns in vertical tubes is 5 cm and the area of cross-sections at \(A\) and \(B\) are \(6 cm^2\) and \(3 cm^2\) respectively.
The rate of flow will be ___________ \(cm ^3 / s\). (take \(g =10 m / s ^2\) )