The magnifying power of a telescope with tube \(60\; \mathrm{cm}\) is \(5 .\) What is the focal length of its eye piece?......\(cm\)

A point particle of mass, moves along the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu\). The particle is released, from rest, from the point \(P\) and it comes to rest at a point \(R\). The energies, lost by the ball, over the parts, \(PQ\) and \(PR\), of the track, are equal to each other, and no energy is lost when particle changes direction from \(PQ\) to \(QR\). The values of the coefficient of friction \(\mu\) and the distance \(x(=QR)\) are, respecitvely close to

The mass defect in a particular reaction is \(0.4 \mathrm{~g}\). The amount of energy liberated is \(\mathrm{n} \times 10^7 \mathrm{kWh}\), where\(\mathrm{n}=\)________. (speed of light \(=3 \times 10^8 \mathrm{~m} / \mathrm{s}\) )

Abeam of unpolarised light of intensity \(I_0\) is passed through a polaroid \(A\) and then through another polaroid \(B\) which is oriented so that its principal plane makes an angle of \(45^{\circ}\) relative to that of \(A\). The intensity of emergent light is :

A fully loaded boeing aircraft has a mass of \(5.4 \times 10^5\,kg\). Its total wing area is \(500\,m ^2\). It is in level flight with a speed of \(1080\,km / h\). If the density of air \(\rho\) is \(1.2\,kg\,m ^{-3}\), the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be \(\left( g =10\,m / s ^2\right)\)

In the figure shown, after the switch \(‘S’\) is turned from position \(‘A’\) to position \(‘B’\), the energy dissipated in the circuit in terms of capacitance \(‘C’\) and total charge \(‘Q’\) is

In a Young's double slit experiment, slits are separated by \(0.5\ mm\), and the screen is placed \(150\ cm\) away. A beam of light consisting of two wavelengths, \(650\ nm\) and \(520\ nm\), is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is...... \(mm\)

If e is the electronic charge, \(c\) is the speed of light in free space and \(h\) is Planck's constant, the quantity \(\frac{1}{4 \pi \varepsilon_{0}} \frac{| e |^{2}}{h c}\) has dimensions of .......

\(n\) identical waves each of intensity \(I_0\) interfere with each other. The ratio of maximum intensities if the interference is \((i)\) coherent and \((ii)\) incoherent is :

If a copper wire is stretched to increase its length by \(20 \% \). The percentage increase in resistance of the wire is \(..........\%\)

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle \(\theta\) with each other. When suspended in water the angle remains the same. If density of the material of the sphere is \(1.5 \mathrm{~g} / \mathrm{cc}\), the dielectric constant of water will be _______. (Take density of water \(=1 \mathrm{~g} / \mathrm{cc}\) )