Consider a Young’s double slit experiment as shown in figure. What should be the slit separation \(d\) in terms of wavelength \(\lambda \) such that the first minima occurs directly in front of the slit \((S_1)\)?

A charged particle going around in a circle can be considered to be a current loop. A particle of mass \(m\) carrying charge \(q\) is moving in a plane with speed \(v\) under the influence of magnetic field \(\overrightarrow{ B }\). The magnetic moment of this moving particle

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, \(\mathrm{y}_1(\mathrm{x}, \mathrm{t})=4 \sin (\mathrm{kx}-\omega \mathrm{t})\) and \(\mathrm{y}_2(\mathrm{x}, \mathrm{t})=2 \sin \left(\mathrm{kx}-\omega \mathrm{t}+\frac{2 \pi}{3}\right)\), are \(:\)
(Take the angular frequency of initial waves same as \(\omega\))

A person pushes a box on a rough horizontal platform surface. He applies a force of \(200\, N\) over a distance of \(15\, m .\) Thereafter, he gets progressively tired and his applied force reduces linearly with distance of \(100\, N\). The total distance through which the box has been moved is \(30\, m\). What is the work done by the person during the total movement of the box\(........J\)\(?\)

In the wave equation \(y =0.5 \sin \frac{2 \pi}{\lambda}(400 t - x )\,m\)  the velocity of the wave will be ......... \(m / s\)

A neutron moving with a speed \('v'\) makes a head on collision with a stationary hydrogen atom in ground state . The minimum kinetic energy of the neutron for which inelastic collision will take place is....\(eV\)

In the first configuration (1) as shown in the figure, four identical charges \(\left(q_0\right)\) are kept at the corners \(A, B, C\) and \(D\) of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points \(\mathrm{G}, \mathrm{E}, \mathrm{H}\) and F, of the square, If \(\mathrm{K}=\frac{1}{4 \pi \varepsilon_0}\), the difference between the potential energies of configuration (2) and (1) is given by :

Match List - I with List - II.

List - I	List - II
A. Boltzmann constant	I. \([M^{-1}L^3T^{-2}]\)
B. Stefan's constant	II. \([ML^2T^{-1}]\)
C. Planck's constant	III. \([ML^2T^{-2}K^{-1}]\)
D. Gravitational constant	IV. \([ML^0T^{-3}K^{-4}]\)

Choose the correct answer from the options given below :

Given below are two statements: One is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A:\) For measuring the potential difference across a resistance of \(600\,\Omega\), the voltmeter with resistance \(1000\,\Omega\) will be preferred over voltmeter with resistance \(4000\,\Omega\). Reason \(R:\) Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance. In the light of the above statements, choose the most appropriate answer from the options given below.

The Young's modulus of steel wire of radius \(r\) and length \(L\) is \(Y\). If the radius \(r\) and length \(L\) of the wire are doubled then the value of \(Y\)