A plane EM wave is propagating along $$x$$ direction. It has a wavelength of $$4 \mathrm{~mm}$$. If electric field is in $$y$$ direction with the maximum magnitude of $$60 \mathrm{~Vm}^{-1}$$, the equation for magnetic field is :

A galvanometer has a coil of resistance $$200 \Omega$$ with a full scale deflection at $$20 \mu \mathrm{A}$$. The value of resistance to be added to use it as an ammeter of range $$(0-20) \mathrm{mA}$$ is :

The dimensional formula of latent heat is :

A sphere of relative density $$\sigma$$ and diameter $$D$$ has concentric cavity of diameter $$d$$. The ratio of $$\frac{D}{d}$$, if it just floats on water in a tank is :

The volume of an ideal gas $$(\gamma=1.5)$$ is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :

A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is $$1.42 \mathrm{~eV}$$. The wavelength of light emitted from the LED is :

A particle of mass $$m$$ moves on a straight line with its velocity increasing with distance according to the equation $$v=\alpha \sqrt{x}$$, where $$\alpha$$ is a constant. The total work done by all the forces applied on the particle during its displacement from $$x=0$$ to $$x=\mathrm{d}$$, will be :

Given below are two statements :

Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account

Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law.

In the light of the above statements, choose the correct answer from the options given below :

A particle moving in a straight line covers half the distance with speed $$6 \mathrm{~m} / \mathrm{s}$$. The other half is covered in two equal time intervals with speeds $$9 \mathrm{~m} / \mathrm{s}$$ and $$15 \mathrm{~m} / \mathrm{s}$$ respectively. The average speed of the particle during the motion is :

Given below are two statements :

Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.

Statement (II) : Concave lens always forms a virtual and erect image.

In the light of the above statements, choose the correct answer from the options given below :

A sample of 1 mole gas at temperature $$T$$ is adiabatically expanded to double its volume. If adiab constant for the gas is $$\gamma=\frac{3}{2}$$, then the work done by the gas in the process is :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $$\frac{A}{3}$$ and the height is $$d$$, the capacitance of the arrangement is :

One main scale division of a vernier caliper is equal to $$\mathrm{m}$$ units. If $$\mathrm{n}^{\text {th }}$$ division of main scale coincides with $$(n+1)^{\text {th }}$$ division of vernier scale, the least count of the vernier caliper is :

A heavy iron bar, of weight $$W$$ is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $$\theta$$ with the horizontal. The weight experienced by the person is :

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of the masses $$\frac{m_2}{m_1}$$ is :

The energy equivalent of $$1 \mathrm{~g}$$ of substance is :

The equivalent resistance between A and B is :

An astronaut takes a ball of mass $$m$$ from earth to space. He throws the ball into a circular orbit about earth at an altitude of $$318.5 \mathrm{~km}$$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $$x \frac{\mathrm{GM}_{\mathrm{e}} \mathrm{m}}{21 \mathrm{R}_{\mathrm{e}}}$$. The value of $$x$$ is (take $$\mathrm{R}_{\mathrm{e}}=6370 \mathrm{~km})$$ :

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

A square loop of edge length $$2 \mathrm{~m}$$ carrying current of $$2 \mathrm{~A}$$ is placed with its edges parallel to the $$x$$-$$y$$ axis. A magnetic field is passing through the $$x$$-$$y$$ plane and expressed as $$\vec{B}=B_0(1+4 x) \hat{k}$$, where $$B_o=5 T$$. The net magnetic force experienced by the loop is _________ $$\mathrm{N}$$.

At the centre of a half ring of radius $$\mathrm{R}=10 \mathrm{~cm}$$ and linear charge density $$4 \mathrm{~nC} \mathrm{~m}^{-1}$$, the potential is $$x \pi \mathrm{V}$$. The value of $$x$$ is _________.

In a Young's double slit experiment, the intensity at a point is $$\left(\frac{1}{4}\right)^{\text {th }}$$ of the maximum intensity, the minimum distance of the point from the central maximum is _________ $$\mu \mathrm{m}$$. (Given : $$\lambda=600 \mathrm{~nm}, \mathrm{~d}=1.0 \mathrm{~mm}, \mathrm{D}=1.0 \mathrm{~m}$$)

If $$\vec{a}$$ and $$\vec{b}$$ makes an angle $$\cos ^{-1}\left(\frac{5}{9}\right)$$ with each other, then $$|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$$ for $$|\vec{a}|=n|\vec{b}|$$ The integer value of $$\mathrm{n}$$ is _________.

Two persons pull a wire towards themselves. Each person exerts a force of $$200 \mathrm{~N}$$ on the wire. Young's modulus of the material of wire is $$1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Original length of the wire is $$2 \mathrm{~m}$$ and the area of cross section is $$2 \mathrm{~cm}^2$$. The wire will extend in length by _________ $$\mu \mathrm{m}$$.

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $$4 \mathrm{~m}, 2 \mathrm{~ms}^{-1}$$ and $$16 \mathrm{~ms}^{-2}$$ at a certain instant. The amplitude of the motion is $$\sqrt{x}, \mathrm{~m}$$ where $$x$$ is _________.

A star has $$100 \%$$ helium composition. It starts to convert three $${ }^4 \mathrm{He}$$ into one $${ }^{12} \mathrm{C}$$ via triple alpha process as $${ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}$$. The mass of the star is $$2.0 \times 10^{32} \mathrm{~kg}$$ and it generates energy at the rate of $$5.808 \times 10^{30} \mathrm{~W}$$. The rate of converting these $${ }^4 \mathrm{He}$$ to $${ }^{12} \mathrm{C}$$ is $$\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}$$, where $$\mathrm{n}$$ is _________. [ Take, mass of $${ }^4 \mathrm{He}=4.0026 \mathrm{u}$$, mass of $${ }^{12} \mathrm{C}=12 \mathrm{u}$$]

A string is wrapped around the rim of a wheel of moment of inertia $$0.40 \mathrm{~kgm}^2$$ and radius $$10 \mathrm{~cm}$$. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $$40 \mathrm{~N}$$. The angular velocity of the wheel after $$10 \mathrm{~s}$$ is $$x \mathrm{~rad} / \mathrm{s}$$, where $$x$$ is __________.

When a coil is connected across a $$20 \mathrm{~V}$$ dc supply, it draws a current of $$5 \mathrm{~A}$$. When it is connected across $$20 \mathrm{~V}, 50 \mathrm{~Hz}$$ ac supply, it draws a current of $$4 \mathrm{~A}$$. The self inductance of the coil is __________ $$\mathrm{mH}$$. (Take $$\pi=3$$)

The current flowing through the $$1 \Omega$$ resistor is $$\frac{n}{10}$$ A. The value of $$n$$ is _______.