A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm , respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be _______.

Given below are two statement : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a rod lying freely is heated, no thermal stress is developed in it. Reason \(R :\) On heating the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below

A compressive force, \(F\) is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta T\). The net change in its length is zero. Let \(l\) be the length of the rod, \(A\) its area of cross- section, \(Y\) its Young's modulus, and \(\alpha \) its coefficient of linear expansion. Then, \(F\) is equal to

For a given transistor amplifier circuit in \(CE\) configuration \(V_{C C}=1 V , R_c=1 k \Omega, R_b=100 k \Omega\) and \(\beta=100\). Value of base current \(I_b\) is

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature \(\mathrm{R}=2 \mathrm{~m}\). Another car approaches him from behind with a uniform speed of \(90 \mathrm{~km} / \mathrm{hr}\). When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ \(\mathrm{m} / \mathrm{s}^2\).

A bullet of mass \(0.1\, kg\) is fired on a wooden block to pierce through it, but it stops after moving a distance of \(50\, cm\) into it. If the velocity of bullet before hitting the wood is \(10\) \(m / s\) and it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is \('x' N.\) The value of \('x'\) to the nearest integer is................. \(N\)

What is the half-life (in years) period of a radioactive material if its activity drops to \(1 / 16^{\text {th }}\) of its initial value of \(30\) years?

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

XPQY is a vertical smooth long loop having a total resistance R where PX is parallel to QY and separation between them is \(l\). A constant magnetic field B perpendicular to the plane of the loop exists in the entire space. A rod CD of length L (L > \(l\)) and mass m is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is __________ m/s.
(g = acceleration due to gravity)

In an alpha particle scattering experiment distance of closest approach for the \(\alpha\) particle is \(4.5 \times 10^{-14} \mathrm{~m}\). If target nucleus has atomic number \(80\) , then maximum velocity of \(\alpha\)-particle is _______ \(\times 10^5\) \(\mathrm{m} / \mathrm{s}\) approximately. \(\left(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}\right.\) unit, mass of \(\alpha\) particle \(=\) \(\left.6.72 \times 10^{-27} \mathrm{~kg}\right)\)

As show in the figure, in steady state, the charge stored in the capacitor is....... \(\times 10^{-6}\,C\).