The current flowing through R$$_2$$ is :

A plane electromagnetic wave of frequency $$20 ~\mathrm{MHz}$$ propagates in free space along $$\mathrm{x}$$-direction. At a particular space and time, $$\overrightarrow{\mathrm{E}}=6.6 \hat{j} \mathrm{~V} / \mathrm{m}$$. What is $$\overrightarrow{\mathrm{B}}$$ at this point?

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.

A. The electron will experience magnetic force along the axis of the solenoid.

B. The electron will not experience magnetic force.

C. The electron will continue to move along the axis of the solenoid.

D. The electron will be accelerated along the axis of the solenoid.

E. The electron will follow parabolic path-inside the solenoid.

Choose the correct answer from the options given below:

The Thermodynamic process, in which internal energy of the system remains constant is

Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$

Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass.

Reason R: For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar.

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

The energy of $$\mathrm{He}^{+}$$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $$-13.6 ~\mathrm{eV})$$ :

When one light ray is reflected from a plane mirror with $$30^{\circ}$$ angle of reflection, the angle of deviation of the ray after reflection is :

A capacitor of capacitance $$\mathrm{C}$$ is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is :

The ratio of the de-Broglie wavelengths of proton and electron having same Kinetic energy :

(Assume $$m_{p}=m_{e} \times 1849$$ )

Eight equal drops of water are falling through air with a steady speed of $$10 \mathrm{~cm} / \mathrm{s}$$. If the drops coalesce, the new velocity is:-

The logic operations performed by the given digital circuit is equivalent to:

A projectile is projected at $$30^{\circ}$$ from horizontal with initial velocity $$40 \mathrm{~ms}^{-1}$$. The velocity of the projectile at $$\mathrm{t}=2 \mathrm{~s}$$ from the start will be : (Given $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ )

A body of mass $$500 \mathrm{~g}$$ moves along $$\mathrm{x}$$-axis such that it's velocity varies with displacement $$\mathrm{x}$$ according to the relation $$v=10 \sqrt{x} \mathrm{~m} / \mathrm{s}$$ the force acting on the body is:-

A space ship of mass $$2 \times 10^{4} \mathrm{~kg}$$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ and radius of earth $$=6400 \mathrm{~km}$$ ):

When vector $$\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$$ is subtracted from vector $$\overrightarrow{\mathrm{B}}$$, it gives a vector equal to $$2 \hat{j}$$. Then the magnitude of vector $$\overrightarrow{\mathrm{B}}$$ will be :

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

If $$\mathrm{V}$$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

The root mean square speed of molecules of nitrogen gas at $$27^{\circ} \mathrm{C}$$ is approximately : (Given mass of a nitrogen molecule $$=4.6 \times 10^{-26} \mathrm{~kg}$$ and take Boltzmann constant $$\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{JK}^{-1}$$ )

As shown in the figure, a plane mirror is fixed at a height of $$50 \mathrm{~cm}$$ from the bottom of tank containing water $$\left(\mu=\frac{4}{3}\right)$$. The height of water in the tank is $$8 \mathrm{~cm}$$. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ___________ $$\mathrm{cm}$$.

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $$\omega$$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be $$\frac{E}{x}$$. The value of $$x$$ is

The surface tension of soap solution is $$3.5 \times 10^{-2} \mathrm{~Nm}^{-1}$$. The amount of work done required to increase the radius of soap bubble from $$10 \mathrm{~cm}$$ to $$20 \mathrm{~cm}$$ is _________ $$\times ~10^{-4} \mathrm{~J}$$.

$$(\operatorname{take} \pi=22 / 7)$$

A wire of density $$8 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$$ is stretched between two clamps $$0.5 \mathrm{~m}$$ apart. The extension developed in the wire is $$3.2 \times 10^{-4} \mathrm{~m}$$. If $$Y=8 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$$, the fundamental frequency of vibration in the wire will be ___________ $$\mathrm{Hz}$$.

A metallic cube of side $$15 \mathrm{~cm}$$ moving along $$y$$-axis at a uniform velocity of $$2 \mathrm{~ms}^{-1}$$. In a region of uniform magnetic field of magnitude $$0.5 \mathrm{~T}$$ directed along $$z$$-axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be _________ mV.

A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $$1: 2^{1 / 3}$$. Their respective speed have a ratio of $$n: 1$$. The value of $n$ is __________.

A block of mass $$5 \mathrm{~kg}$$ starting from rest pulled up on a smooth incline plane making an angle of $$30^{\circ}$$ with horizontal with an affective acceleration of $$1 \mathrm{~ms}^{-2}$$. The power delivered by the pulling force at $$t=10 \mathrm{~s}$$ from the start is ___________ W.

[use $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$ ]

(calculate the nearest integer value)

In the given circuit, $$\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=0.2 \mu \mathrm{F}, \mathrm{C}_{3}=2 \mu \mathrm{F}, \mathrm{C}_{4}=4 \mu \mathrm{F}, \mathrm{C}_{5}=2 \mu \mathrm{F}, \mathrm{C}_{6}=2 \mu \mathrm{F}$$, The charge stored on capacitor $$\mathrm{C}_{4}$$ is ____________ $$\mu \mathrm{C}$$.

A coil has an inductance of $$2 \mathrm{H}$$ and resistance of $$4 ~\Omega$$. A $$10 \mathrm{~V}$$ is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be ___________ $$\times 10^{-2} \mathrm{~J}$$.

Two identical cells each of emf $$1.5 \mathrm{~V}$$ are connected in series across a $$10 ~\Omega$$ resistance. An ideal voltmeter connected across $$10 ~\Omega$$ resistance reads $$1.5 \mathrm{~V}$$. The internal resistance of each cell is __________ $$\Omega$$.