A \(12.5\) ev electron beam is used to bombard gaseous hydrogen at ground state. The energy level upto which the hydrogen atoms would be excited is

The velocity of a particle executing a simple harmonic motion is \(13 \mathrm{ms}^{-1}\), when its distance from the equilibrium position \((Q)\) is \(3 \mathrm{m}\) and its velocity is \(12 \mathrm{ms}^{-1},\) when it is \(5 \mathrm{m}\) away from \(Q .\) The frequency of the simple harmonic motion is

In a closed circuit there is only a coil of inductance \(L\) and resistance \(100 \Omega\). The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by \(5 \mathrm{Weber}\). What amount of charge will flow in the circuit as a result?

Two blocks of \(2 \mathrm{~kg}\) and \(1 \mathrm{~kg}\) are in contact on a frictionless table. If a force of \(3 \mathrm{~N}\) is applied on \(2 \mathrm{~kg}\) block, then the force of contact between the two blocks will be :

A straight conductor \(0.1 \mathrm{m}\) long moves in uniform magnetic field \(0.1 \mathrm{T}\). The velocity the conductor is \(15 \mathrm{m} / \mathrm{s}\) and is directer perpendicular to the field. The emf inducod between the two ends of the conductor is

A glass slab consists of thin uniform layers of progressively decreasing refractive indices RI (see figure) such that the RI of any layer is \(\mu-m \Delta \mu\). Here, \(\mu\) and \(\Delta \mu\) denote the \(\mathrm{RI}\) of 0 th layer and the difference in RI between any two consecutive layers, respectively. The integer \(m=0,1,2,3, \ldots\) denotes the numbers of the successive layers. A ray of light from the oth layer enters the 1st layer at an angle of incidence of \(30^{\circ}\). After undergoing the mth refraction, the ray emerges parallel to the interface. If \(\mu=1.5\) and \(\Delta \mu=0.015,\) the value of \(m\) is

An electron accelerated through a potential of \(10000 \mathrm{V}\) from rest has a de-Broglie wave length \(\lambda\). What should be the accelerating potential, so that the wavelength is doubled?

The smallest positive root of the equation \(\tan x-x=0\) lies in

The value of integral \(\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{(sinx-xcosx)}{x(x+sinx)}dx\) is

Let \(f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1\end{array}\right|\), then \(\lim _{x \rightarrow 0} \frac{f(x)}{x^2}=\)

The change of entropy \((d S)\) is defined as

Let \(P\) and \(T\) be the subsets of \(x\), \(y\) -plane defined by \(P=\left\{(x, y): x>0, y>0\right.\) and \(\left.x^{2}+y^{2}=1\right\}\), \(T=\left\{(x, y): x>0, y>0\right.\) and \(\left.x^{8}+y^{8} < 1\right\}\). Then, \(P \cap T\) is

In the electrical circuit shown in the figure, the current through the \(4 \Omega\) resistor is