While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \(1 \mathrm{~mm}\) and circular scale reading is equal to \(42\) divisions. Pitch of screw gauge is \(1 \mathrm{~mm}\) and it has \(100\) divisions on circular scale. The diameter of the wire is \(\frac{x}{50} \mathrm{~mm}\). The value of \(x\) is _______.

Train A is moving along two parallel rail tracks towards north with speed \(72 \mathrm{~km} / \mathrm{h}\) and train B is moving towards south with speed \(108 \mathrm{~km} / \mathrm{h}\). Velocity of train \(B\) with respect to \(A\) and velocity of ground with respect to \(B\) are _______ (in \(\mathrm{ms}^{-1}\) ).

In the circuit diagram shown in figure given below, the current flowing through resistance \(3\, \Omega\) is \(\frac{ x }{3}\,A\). The value of \(x\) is \(...........\)

The \(V-I\) characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is

Assertion \(A\) : If \(A, B, C, D\) are four points on a semi-circular arc with centre at \('O'\) such that \(|\overrightarrow{{AB}}|=|\overrightarrow{{BC}}|=|\overrightarrow{{CD}}|\), then \(\overrightarrow{{AB}}+\overrightarrow{{AC}}+\overrightarrow{{AD}}=4 \overrightarrow{{AO}}+\overrightarrow{{OB}}+\overrightarrow{{OC}}\) Reason \(R\) : Polygon law of vector addition yields \(\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C D}+\overrightarrow{A D}=2 \overrightarrow{A O}\) In the light of the above statements, choose the most appropriate answer from the options given below

A body of mass \(m= 10^{-2}\) \(kg\) is moving in a medium and experiences a frictional force \(F= -kv^2\). Its initial speed is \(v_0= 10\) \(ms^{-1}\). If, after \(10\; s\), its energy is \(\frac{1}{8}\) \(mv_0^2\) the value of \(k\) will be

A monochromatic light wave with wavelength \(\lambda_1\) and frequency \(v_1\) in air enters another medium. If the angle of incidence and angle of refraction at the interface are \(45^{\circ}\) and \(30^{\circ}\) respectively, then the wavelength \(\lambda_2\) and frequency \(v_2\) of the refracted wave are :

A thin circular disc is in the \(xy\) plane as shown in the figure. The ratio of its moment of inertia about \(z\)  and \(z'\)  axes will be