A particle starts with an initial velocity of $$10.0 \mathrm{~ms}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0 \mathrm{~ms}^{-2}$$. The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{-1}$$ is __________.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.

Reason R: The wavelengths of waves are different in different media.

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

The temperature of an ideal gas is increased from $$200 \mathrm{~K}$$ to $$800 \mathrm{~K}$$. If r.m.s. speed of gas at $$200 \mathrm{~K}$$ is $$v_{0}$$. Then, r.m.s. speed of the gas at $$800 \mathrm{~K}$$ will be:

The energy density associated with electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ of an electromagnetic wave in free space is given by $$\left(\epsilon_{0}-\right.$$ permittivity of free space, $$\mu_{0}-$$ permeability of free space)

A 2 meter long scale with least count of $$0.2 \mathrm{~cm}$$ is used to measure the locations of objects on an optical bench. While measuring the focal length of a convex lens, the object pin and the convex lens are placed at $$80 \mathrm{~cm}$$ mark and $$1 \mathrm{~m}$$ mark, respectively. The image of the object pin on the other side of lens coincides with image pin that is kept at $$180 \mathrm{~cm}$$ mark. The $$\%$$ error in the estimation of focal length is:

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

Assertion A: When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed.

Reason R: A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container.

In the light of the above statements, choose the most appropriate 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: Diffusion current in a p-n junction is greater than the drift current in magnitude if the junction is forward biased.

Reason R: Diffusion current in a p-n junction is from the $$\mathrm{n}$$-side to the p-side if the junction is forward biased.

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

A capacitor of capacitance $$150.0 ~\mu \mathrm{F}$$ is connected to an alternating source of emf given by $$\mathrm{E}=36 \sin (120 \pi \mathrm{t}) \mathrm{V}$$. The maximum value of current in the circuit is approximately equal to :

Figure shows a part of an electric circuit. The potentials at points $$a, b$$ and $$c$$ are $$30 \mathrm{~V}, 12 \mathrm{~V}$$ and $$2 \mathrm{~V}$$ respectively. The current through the $$20 ~\Omega$$ resistor will be,

As shown in the figure, a particle is moving with constant speed $$\pi ~\mathrm{m} / \mathrm{s}$$. Considering its motion from $$\mathrm{A}$$ to $$\mathrm{B}$$, the magnitude of the average velocity is :

The work functions of Aluminium and Gold are $$4.1 ~\mathrm{eV}$$ and and $$5.1 ~\mathrm{eV}$$ respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is

A body cools in 7 minutes from $$60^{\circ} \mathrm{C}$$ to $$40^{\circ} \mathrm{C}$$. The temperature of the surrounding is $$10^{\circ} \mathrm{C}$$. The temperature of the body after the next 7 minutes will be:

A dipole comprises of two charged particles of identical magnitude $$q$$ and opposite in nature. The mass 'm' of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance '$$l$$'. If the dipole is placed in a uniform electric field '$$\bar{E}$$'; in such a way that dipole axis makes a very small angle with the electric field, '$$\bar{E}$$'. The angular frequency of the oscillations of the dipole when released is given by:

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

A student is provided with a variable voltage source $$\mathrm{V}$$, a test resistor $$R_{T}=10 ~\Omega$$, two identical galvanometers $$G_{1}$$ and $$G_{2}$$ and two additional resistors, $$R_{1}=10 ~M \Omega$$ and $$R_{2}=0.001 ~\Omega$$. For conducting an experiment to verify ohm's law, the most suitable circuit is:

A small particle of mass $$m$$ moves in such a way that its potential energy $$U=\frac{1}{2} m ~\omega^{2} r^{2}$$ where $$\omega$$ is constant and $$r$$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $$n^{\text {th }}$$ orbit will be proportional to,

A child of mass $$5 \mathrm{~kg}$$ is going round a merry-go-round that makes 1 rotation in $$3.14 \mathrm{~s}$$. The radius of the merry-go-round is $$2 \mathrm{~m}$$. The centrifugal force on the child will be

The weight of a body on the surface of the earth is $$100 \mathrm{~N}$$. The gravitational force on it when taken at a height, from the surface of earth, equal to one-fourth the radius of the earth is:

Choose the incorrect statement from the following:

Experimentally it is found that $$12.8 ~\mathrm{eV}$$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $$\frac{9}{x} \times 10^{-10} \mathrm{~m}$$. The value of the $$x$$ is __________.

$$\left(1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \mathrm{Nm}^{2} / \mathrm{C}^{2}\right.$$ and electronic charge $$\left.=1.6 \times 10^{-19} \mathrm{C}\right)$$

Two concentric circular coils with radii $$1 \mathrm{~cm}$$ and $$1000 \mathrm{~cm}$$, and number of turns 10 and 200 respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be ___________ $$\times 10^{-8} \mathrm{H}$$. (Take, $$\pi^{2}=10$$ )

As shown in the figure, two parallel plate capacitors having equal plate area of $$200 \mathrm{~cm}^{2}$$ are joined in such a way that $$a \neq b$$. The equivalent capacitance of the combination is $$x \in_{0} \mathrm{~F}$$. The value of $$x$$ is ____________.

A body is dropped on ground from a height '$$h_{1}$$' and after hitting the ground, it rebounds to a height '$$h_{2}$$'. If the ratio of velocities of the body just before and after hitting ground is 4 , then percentage loss in kinetic energy of the body is $$\frac{x}{4}$$. The value of $$x$$ is ____________.

As shown in the figure, the voltmeter reads $$2 \mathrm{~V}$$ across $$5 ~\Omega$$ resistor. The resistance of the voltmeter is _________ $$\Omega$$.

A proton with a kinetic energy of $$2.0 ~\mathrm{eV}$$ moves into a region of uniform magnetic field of magnitude $$\frac{\pi}{2} \times 10^{-3} \mathrm{~T}$$. The angle between the direction of magnetic field and velocity of proton is $$60^{\circ}$$. The pitch of the helical path taken by the proton is __________ $$\mathrm{cm}$$. (Take, mass of proton $$=1.6 \times 10^{-27} \mathrm{~kg}$$ and Charge on proton $$=1.6 \times 10^{-19} \mathrm{C}$$ ).

A simple pendulum with length $$100 \mathrm{~cm}$$ and bob of mass $$250 \mathrm{~g}$$ is executing S.H.M. of amplitude $$10 \mathrm{~cm}$$. The maximum tension in the string is found to be $$\frac{x}{40} \mathrm{~N}$$. The value of $$x$$ is ___________.

A metal block of mass $$\mathrm{m}$$ is suspended from a rigid support through a metal wire of diameter $$14 \mathrm{~mm}$$. The tensile stress developed in the wire under equilibrium state is $$7 \times 10^{5} \mathrm{Nm}^{-2}$$. The value of mass $$\mathrm{m}$$ is _________ $$\mathrm{kg}$$. (Take, $$\mathrm{g}=9.8 \mathrm{~ms}^{-2}$$ and $$\pi=\frac{22}{7}$$ )

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $$\sqrt{\frac{2}{x}}$$. The value of $$x$$ is ___________.

A beam of light consisting of two wavelengths $$7000~\mathop A\limits^o $$ and $$5500~\mathop A\limits^o $$ is used to obtain interference pattern in Young's double slit experiment. The distance between the slits is $$2.5 \mathrm{~mm}$$ and the distance between the plane of slits and the screen is $$150 \mathrm{~cm}$$. The least distance from the central fringe, where the bright fringes due to both the wavelengths coincide, is $$n \times 10^{-5} \mathrm{~m}$$. The value of $$n$$ is __________.