Which of the following physical quantities have the same dimensions?

For a thin symmetric prism made of glass (refractive index \(1.5\)), the ratio of incident angle and minimum deviation will be _______.

A monochromatic light of wavelength \(6000\)A is incident on the single slit of width \(0.01 \mathrm{~mm}\). If the diffraction pattern is formed at the focus of the convex lens of focal length \(20 \mathrm{~cm}\), the linear width of the central maximum is _______.

The increase in the pressure required to decrease the volume \((\Delta V)\) of water is \(6.3 \times 10^7\) N/m\(^2\). The percentage decrease in the volume is _____. (Bulk modulus of water \(= 2.1 \times 10^9\) N/m\(^2\).)

The \(I-V\) characteristics of a \(p - n\) junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltages of \(2 \; V\) and \(4 \; V\) respectively, is

A zener diode of power rating \(1.6\,W\) is to be used as voltage regulator. If the zener diode has a breakdown of \(8\,V\) and it has to regulate voltage fluctuating between \(3\,V\) and \(10 \,V\). The value of resistance \(R_5\) for safe operation of diode will be \(.........\Omega\)

A \(60\; pF\) capacitor is fully charged by a \(20\; \mathrm{V}\) supply. It is then disconnected from the supply and is connected to another uncharged \(60 \;pF\) capactior is parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in \(nJ\))

For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm. The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm) :

List\(-I\)	List\(-II\)
\(UV\) rays	\((i)\) Diagnostic tool in medicine
\(X-\) rays	\((ii)\) Water purification
Microwave	\((iii)\) Communication, Radar
Infrared wave	\((iv)\) Improving visibility in foggy days

Choose the correct answer from the options given below.

Moment of inertia of a dise of mass \(M\) and radius ' \(R\) ' about any of its diameter is \(\frac{ MR ^2}{4}\). The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, \(\frac{ x }{2} MR ^2\). The value of \(x\) is \(..........\).

\(\mathrm{A}, \mathrm{B}\) and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.

The moment of inertia of the given system about \(P Q\) is \(\frac{X}{15} I\), where \(I\) is the moment of inertia of the disc about its diameter. The value of x is _______.

A spring whose unstretched length is \(\ell \) has a force constant \(k\). The spring is cut into two pieces of unstretched lengths \(\ell_1\) and \(\ell_2\) where, \(\ell_1 = n\ell_2\) and \(n\) is an integer. The ratio \(k_1/k_2\) of the corresponding force constants, \(k_1\) and \(k_2\) will be

A block of mass \(m\), lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant \(k\). The other end of the spring is fixed, as shown in the figure. The block is initially at rest in a equilibrium position. If now the block is pulled with a constant force \(F\), the maximum speed of the block is