The distance travelled by an object in time $$t$$ is given by $$s=(2.5) t^{2}$$. The instantaneous speed of the object at $$\mathrm{t}=5 \mathrm{~s}$$ will be:

Given below are two statements:

Statement I : For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.

Statement II : Escape velocity is independent of the radius of the planet.

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

In the equation $$\left[X+\frac{a}{Y^{2}}\right][Y-b]=\mathrm{R} T, X$$ is pressure, $$Y$$ is volume, $$\mathrm{R}$$ is universal gas constant and $$T$$ is temperature. The physical quantity equivalent to the ratio $$\frac{a}{b}$$ is:

The initial pressure and volume of an ideal gas are P$$_0$$ and V$$_0$$. The final pressure of the gas when the gas is suddenly compressed to volume $$\frac{V_0}{4}$$ will be :

(Given $$\gamma$$ = ratio of specific heats at constant pressure and at constant volume)

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

Assertion A : A spherical body of radius $$(5 \pm 0.1) \mathrm{mm}$$ having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is $$4 \%$$.

Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius.

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

A vehicle of mass $$200 \mathrm{~kg}$$ is moving along a levelled curved road of radius $$70 \mathrm{~m}$$ with angular velocity of $$0.2 ~\mathrm{rad} / \mathrm{s}$$. The centripetal force acting on the vehicle is:

Two planets A and B of radii $$\mathrm{R}$$ and 1.5 R have densities $$\rho$$ and $$\rho / 2$$ respectively. The ratio of acceleration due to gravity at the surface of $$\mathrm{B}$$ to $$\mathrm{A}$$ is:

In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $$z$$-axis and magnetic field is along the positive $$x$$-axis. Then the direction of propagation of electromagnetic wave is:

In the network shown below, the charge accumulated in the capacitor in steady state will be:

In a Young's double slits experiment, the ratio of amplitude of light coming from slits is $$2: 1$$. The ratio of the maximum to minimum intensity in the interference pattern is:

The mean free path of molecules of a certain gas at STP is $$1500 \mathrm{~d}$$, where $$\mathrm{d}$$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $$373 \mathrm{~K}$$ is approximately:

The output from NAND gate having inputs A and B given below will be,

A $$10 ~\mu \mathrm{C}$$ charge is divided into two parts and placed at $$1 \mathrm{~cm}$$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

Given below are two statements:

Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.

Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.

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

Given below are two statements:

Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.

Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.

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

An electron is moving along the positive $$\mathrm{x}$$-axis. If the uniform magnetic field is applied parallel to the negative z-axis, then

A. The electron will experience magnetic force along positive y-axis

B. The electron will experience magnetic force along negative y-axis

C. The electron will not experience any force in magnetic field

D. The electron will continue to move along the positive $$\mathrm{x}$$-axis

E. The electron will move along circular path in magnetic field

Choose the correct answer from the options given below:

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

A passenger sitting in a train A moving at $$90 \mathrm{~km} / \mathrm{h}$$ observes another train $$\mathrm{B}$$ moving in the opposite direction for $$8 \mathrm{~s}$$. If the velocity of the train B is $$54 \mathrm{~km} / \mathrm{h}$$, then length of train B is:

Three point charges $$\mathrm{q},-2 \mathrm{q}$$ and $$2 \mathrm{q}$$ are placed on $x$-axis at a distance $$x=0, x=\frac{3}{4} R$$ and $$x=R$$ respectively from origin as shown. If $$\mathrm{q}=2 \times 10^{-6} \mathrm{C}$$ and $$\mathrm{R}=2 \mathrm{~cm}$$, the magnitude of net force experienced by the charge $$-2 q$$ is ___________ N.

An atom absorbs a photon of wavelength $$500 \mathrm{~nm}$$ and emits another photon of wavelength $$600 \mathrm{~nm}$$. The net energy absorbed by the atom in this process is $$n \times 10^{-4} ~\mathrm{eV}$$. The value of n is __________. [Assume the atom to be stationary during the absorption and emission process] (Take $$\mathrm{h}=6.6 \times 10^{-34} ~\mathrm{Js}$$ and $$\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$$ )

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be _________ rad s$$^{-2}$$.

A straight wire $$\mathrm{AB}$$ of mass $$40 \mathrm{~g}$$ and length $$50 \mathrm{~cm}$$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $$0.40 \mathrm{~T}$$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ___________ A.

$$\left(\right.$$ Take $$g=10 \mathrm{~ms}^{-2}$$ ).

Two plates $$\mathrm{A}$$ and $$\mathrm{B}$$ have thermal conductivities $$84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ and $$126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces of $$\mathrm{A}$$ and $$\mathrm{B}$$ are kept at $$100^{\circ} \mathrm{C}$$ and $$0{ }^{\circ} \mathrm{C}$$ respectively, then the temperature of the surface of contact in steady state is _____________ $${ }^{\circ} \mathrm{C}$$.

In an experiment with sonometer when a mass of $$180 \mathrm{~g}$$ is attached to the string, it vibrates with fundamental frequency of $$30 \mathrm{~Hz}$$. When a mass $$\mathrm{m}$$ is attached, the string vibrates with fundamental frequency of $$50 \mathrm{~Hz}$$. The value of $$\mathrm{m}$$ is ___________ g.

An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $$24 \mathrm{~cm}^{2}$$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $$12 ~\Omega$$. If an externally applied uniform magnetic field in the core along its axis changes from $$1.5 \mathrm{~T}$$ in one direction to $$1.5 ~\mathrm{T}$$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be ___________ $$\mathrm{mC}$$.

In the circuit shown, the energy stored in the capacitor is $$n ~\mu \mathrm{J}$$. The value of $$n$$ is __________

A bi convex lens of focal length $$10 \mathrm{~cm}$$ is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ____________ D.

A car accelerates from rest to $$u \mathrm{~m} / \mathrm{s}$$. The energy spent in this process is E J. The energy required to accelerate the car from $$u \mathrm{~m} / \mathrm{s}$$ to $$2 \mathrm{u} \mathrm{m} / \mathrm{s}$$ is $$\mathrm{nE~J}$$. The value of $$\mathrm{n}$$ is ____________.