A curved in a level road has a radius \(75\, m\). The maximum speed of a car turning this curved road can be \(30 \,m / s\) without skidding. If radius of curved road is changed to \(48\, m\) and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be .........\(m / s\).

In a Young double slit experiment, the wavelength of incident light is \(6000\) Å, the separation between slits \(S_1\) and \(S_2\) is \(5\) cm and the distance between slits plane and screen is \(50\) cm, as shown in the figure below. If the resultant intensity at \(P\) is equal to the intensity due to individual slits, the path difference between interfering waves is __________ Å.

Two equal resistances when connected in series to a battery, consume electric power of \(60\,W.\) If these resistances are now connected in parallel combination to the same battery, the electric power consumed will be .............. \(W\)

A set of \(20\) tuning forks is arranged in a series of increasing frequencies. If each fork gives \(4\) beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is \(\dots \; Hz\).

A plane electromagnetic wave is propagating along the direction \(\frac{\hat{i}+\hat{j}}{\sqrt{2}},\) with its polarization along the direction \(\hat{\mathrm{k}}\). The correct form of the magnetic field of the wave would be (here \(\mathrm{B}_{0}\) is an appropriate constant)

A cylinder is rolling down on an inclined plane of inclination \(60^{\circ}\). It's acceleration during rolling down will be \(\frac{\mathrm{x}}{\sqrt{3}} \mathrm{~m} / \mathrm{s}^2\), where \(\mathrm{x}=\)___________. (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) ).

A body of mass \(m\) is moving in a circular orbit of radius \(R\) about a planet of mass \(M\). At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius \(\frac{R}{2}\) , and the other mass, in a circular orbit of radius \(\frac{3R}{2}\). The difference between the final and initial total energies is

A river is flowing from west to east direction with speed of \(9 \mathrm{~km} \mathrm{~h}^{-1}\). If a boat capable of moving at a maximum speed of \(27 \mathrm{~km} \mathrm{~h}^{-1}\) in still water, crosses the river in half a minute, while moving with maximum speed at an angle of \(150^{\circ}\) to direction of river flow, then the width of the river is :

For the network shown below, the value \(V _{ B }- V _{ A }\) is_______ \(V\)

Consider the following statements:
A. The junction area of solar cell is made very narrow compared to a photo diode.
B. Solar cells are not connected with any external bias.
C. LED is made of lightly doped p-n junction.
D. Increase of forward current results in continuous increase of LED light intensity.
E. LEDs have to be connected in forward bias for emission of light.
Choose the correct answer from the options given below:

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)

A train is moving with a speed of \(12 \mathrm{~m} / \mathrm{s}\) on rails which are \(1.5 \mathrm{~m}\) apart. To negotiate a curve radius \(400 \mathrm{~m}\), the height by which the outer rail should be raised with respect to the inner rail is (Given, \(g=\) \(10 \mathrm{~m} / \mathrm{s}^2\) ) :

In the given circuit, value of \(Y\) is