The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure. The estimated current gain from the figure is

Two spherical bodies of same materials having radius 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is _________. (assume, effect of the surrounding temperature to be negligible),

A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), where \(\hat i\) is along the ground and \(\hat j\) is along the vertical. If \(g = 10\ m/s^2\) , the equation of its trajectory is

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Knowing initial position \(x_0\) and initial momentum \(p_0\) is enough to determine the position and momentum at any time \(t\) for a simple harmonic motion with a given angular frequency \(\omega\).
Reason (R): The amplitude and phase can be expressed in terms of \(x_0\) and \(\mathrm{p}_0\).
In the light of the above statements, choose the correct answer from the options given below :

A tuning fork of frequency \(340\,Hz\) resonates in the fundamental mode with an air column of length \(125\,cm\) in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ \(cm\) (Velocity of sound in air is \(340\,ms ^{-1}\) )

An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(\mathrm{x}\) axis with frequency of \(\left(\frac{25}{\pi}\right) \mathrm{Hz}\). At the position \(\mathrm{x}=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) and potential energy \(0.4 \mathrm{~J}\) The amplitude of oscillation is _______ cm.

A straight wire \(AB\) of mass \(40\,g\) and length \(50\,cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40\,T\) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........\(A\). (Take \(g=10\,ms ^{-2}\) ).

The stopping potential in the context of photoelectric effect depends on the following property of incident electromagnetic radiation

Mass per unit area of a circular disc of radius \(\mathrm{a}\) depends on the distance \(\mathrm{r}\) from its centre as \(\sigma(\mathrm{r})=\mathrm{A}+\mathrm{Br} .\) The moment of inertia of the disc about the the axis, perpendicular to the plane and passing through its centre is

A body of mass \(m\) is projected with velocity \(\lambda v_{e}\) in vertically upward direction from the surface of the earth into space. It is given that \(v _{ e }\) is escape velocity and \(\lambda<1\). If air resistance is considered to the negligible, then the maximum height from the centre of earth, to which the body can go, will be. ( \(R\) : radius of earth)

Six equal resistances are connected between points \(P, Q\) and \(R\) as shown in figure. Then net resistance will be maximum between

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with \(3 m / s ^2\). At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is \(5 m / s\). The initial height of the aeroplane is ___________m.
\(\left( g =10 m / s ^2\right)\)