Orange light of wavelength \(6000 \times 10^{-10}\, m\) in illuminates a single slit of width \(0.6 \times 10^{-4}\, m\) The maximum possible number of diffraction minima produced on both sides of the central maximum is\(........\)

Match the List-I with List-II

	List-I		List-II
A	Radio-wave	I	is produced by Magnetron value
B	Micro-wave	II	Due to change in the vibrational modes of atoms
C	Infrared-wave	II	Due to inner shell electrons moving from higher energy level to lower energy level
D	X-ray	IV	Due to rapid acceleration of electrons

Choose the correct answer from the options given below:

The position vectors of two 1 kg particles, (A) and (B), are given by
\(\overrightarrow{\mathrm{r}}_{\mathrm{A}}=\left(\alpha_1 \mathrm{t}^2 \hat{i}+\alpha_2 \mathrm{t} \hat{j}+\alpha_3 \mathrm{t} \hat{k}\right) \mathrm{m}\) and \(\overrightarrow{\mathrm{r}}_{\mathrm{B}}=(\beta_1 \mathrm{t} \hat{i}+\beta_2 \mathrm{t}^2 \hat{j}\) \(+\beta_3 \mathrm{t} \hat{k}) \mathrm{m}\), respectively; \((\alpha_1=1 \mathrm{~m} / \mathrm{s}^2, \alpha_2=3 \mathrm{n} \mathrm{m} / \mathrm{s},\) \(\alpha_3=2 \mathrm{~m} / \mathrm{s},\) \(\beta_1=2 \mathrm{~m} / \mathrm{s}, \beta_2=-1 \mathrm{~m} / \mathrm{s}^2, \beta_3=4 \mathrm{pm} / \mathrm{s})\), where t is time, n and p are constants. At \(t=1 \mathrm{~s},\left|\overrightarrow{V_A}\right|=\left|\vec{V}_B\right|\) and velocities \(\vec{V}_A\) and \(\vec{V}_B\) of the particles are orthogonal to each other. At \(t=1 \mathrm{~s}\), the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is \(\sqrt{\mathrm{L}} \mathrm{kgm}^2 \mathrm{~s}^{-1}\). The value of L is _______ .

Two long current carrying thin wires, both with current \(I\), are held by insulating threads oflength \(L\) and are in equilibrium as shown in the figure, with threads making an angle '\(\theta\)' with the vertical. If wires have mass \(\lambda\) per unit length then the value of \(l\) is 
(\(g =\) gravitational acceleration)

A concave mirror for face viewing has focal length of \(0.4\,m.\) The distance at which you hold the mirror from your face in order to see your image upright with a magnification of \(5\) is......\(m\)

For the photoelectric effect, the maximum kinetic energy \(\left(E_{\mathrm{k}}\right)\) of the photoelectrons is plotted against the frequency \((v)\) of the incident photons as shown in figure. The slope of the graph gives _______.

A charge of \(4\,\mu C\) is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be.

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in opposite directions with same speed of v and in the same plane as the bar. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency \( \omega \). The ratio of v and \( \omega \) is:

Let \(y^2=12 x\) be the parabola and \(S\) be its focus. Let PQ be a focal chord of the parabola such that \((\mathrm{SP})(\mathrm{SQ})=\frac{147}{4}\). Let C be the circle described taking PQ as a diameter. If the equation of a circle \(C\) is \(64 x^2+64 y^2-\alpha x-64 \sqrt{3} y=\beta\), then \(\beta-\alpha\) is equal to ________.

The radius of circle, having minimum area, which touches the cruve  \(y = 4 - {x^2}\) and the lines \(y = \left| x \right|\) is :

Let \(\mathrm{T}_{\mathrm{r}}\) be the \(\mathrm{r}^{\text {th }}\) term of an A.P. If for some \(\mathrm{m}, \mathrm{T}_{\mathrm{m}}=\frac{1}{25}, \mathrm{~T}_{25}=\frac{1}{20}\), and \(20 \sum_{\mathrm{r}=1}^{25} \mathrm{~T}_{\mathrm{r}}=13\), then \(5 \mathrm{~m} \sum_{\mathrm{r}=\mathrm{m}}^{2 \mathrm{~m}} \mathrm{~T}_{\mathrm{r}}\) is equal to

If \(\frac{1}{(20-a)(40-a)}+\frac{1}{(40-a)(60-a)}+\ldots \ldots+\) \(\frac{1}{(180-a)(200-a)}=\frac{1}{256}\), then the maximum value of \(a\) is.