A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be

Given below are two statements:

Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance.

Statement II : A car moving towards east takes a turn and moves towards north, the speed remains unchanged. The acceleration of the car is zero.

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

Match List I with List II

	LIST I		LIST II
A.	Spring constant	I.	$$\mathrm{[T^{-1}]}$$
B.	Angular speed	II.	$$\mathrm{[MT^{-2}]}$$
C.	Angular momentum	III.	$$\mathrm{[ML^2]}$$
D.	Moment of inertia	IV.	$$\mathrm{[ML^2T^{-1}]}$$

Choose the correct answer from the options given below:

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

Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology.

Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar)

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

The ratio of escape velocity of a planet to the escape velocity of earth will be:-

Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$ move round the earth in the same orbit. The mass of $$\mathrm{A}$$ is twice the mass of $$\mathrm{B}$$. The quantity which is same for the two satellites will be

Three forces $$F_{1}=10 \mathrm{~N}, F_{2}=8 \mathrm{~N}, \mathrm{~F}_{3}=6 \mathrm{~N}$$ are acting on a particle of mass $$5 \mathrm{~kg}$$. The forces $$\mathrm{F}_{2}$$ and $$\mathrm{F}_{3}$$ are applied perpendicularly so that particle remains at rest. If the force $$F_{1}$$ is removed, then the acceleration of the particle is:

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is $$12 \mathrm{~cm}$$. When viewed from the opposite side, the apparent distance of the bubble is observed as $$4 \mathrm{~cm}$$. If the side of the ice cube is $$24 \mathrm{~cm}$$, the refractive index of the ice cube is

A proton and an $$\alpha$$-particle are accelerated from rest by $$2 \mathrm{~V}$$ and $$4 \mathrm{~V}$$ potentials, respectively. The ratio of their de-Broglie wavelength is :

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

Assertion A : If an electric dipole of dipole moment $$30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}$$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.

Reason R : Electric dipole consists of two equal and opposite charges.

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

Given below are two statements:

Statement I : The diamagnetic property depends on temperature.

Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetizing field.

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

A wire of resistance $$160 ~\Omega$$ is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be

A ball is thrown vertically upward with an initial velocity of $$150 \mathrm{~m} / \mathrm{s}$$. The ratio of velocity after $$3 \mathrm{~s}$$ and $$5 \mathrm{~s}$$ is $$\frac{x+1}{x}$$. The value of $$x$$ is ___________.

$$\left\{\right.$$ take, $$\left.g=10 \mathrm{~m} / \mathrm{s}^{2}\right\}$$

If the r. m.s speed of chlorine molecule is $$490 \mathrm{~m} / \mathrm{s}$$ at $$27^{\circ} \mathrm{C}$$, the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon $$=39.9 \mathrm{u}$$, molecular mass of chlorine $$=70.9 \mathrm{u}$$ )

A $$12.5 \mathrm{~eV}$$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

Given below are two statements:

Statement I : When the frequency of an a.c source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.

Statement II : In a series LCR circuit, the value of power factor at resonance is one.

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

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ KJ. [The coefficient of friction between tyre of bus and road is 0.04.]

64 identical drops each charged upto potential of $$10 ~\mathrm{mV}$$ are combined to form a bigger drop. The potential of the bigger drop will be __________ $$\mathrm{mV}$$.

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $$\frac{x}{5}$$. The value of $$x$$ is ___________.

The current flowing through a conductor connected across a source is $$2 \mathrm{~A}$$ and 1.2 $$\mathrm{A}$$ at $$0^{\circ} \mathrm{C}$$ and $$100^{\circ} \mathrm{C}$$ respectively. The current flowing through the conductor at $$50^{\circ} \mathrm{C}$$ will be ___________ $$\times 10^{2} \mathrm{~mA}$$.

Glycerin of density $$1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$$ is flowing through the conical section of pipe The area of cross-section of the pipe at its ends are $$10 \mathrm{~cm}^{2}$$ and $$5 \mathrm{~cm}^{2}$$ and pressure drop across its length is $$3 ~\mathrm{Nm}^{-2}$$. The rate of flow of glycerin through the pipe is $$x \times 10^{-5} \mathrm{~m}^{3} \mathrm{~s}^{-1}$$. The value of $$x$$ is ___________.

Two convex lenses of focal length $$20 \mathrm{~cm}$$ each are placed coaxially with a separation of $$60 \mathrm{~cm}$$ between them. The image of the distant object formed by the combination is at _____________ $$\mathrm{cm}$$ from the first lens.

For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1:3:5$$ respectively. If the frequency of fifth harmonic is $$405 \mathrm{~Hz}$$ and the speed of sound in air is $$324 \mathrm{~ms}^{-1}$$ the length of the organ pipe is _________ $$\mathrm{m}$$.

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm{He}^{4}+\mathrm{Q}$$

Given :

$${ }_{92}^{238} \mathrm{U}=238.05060 ~\mathrm{u}$$,

$${ }_{90}^{234} \mathrm{Th}=234.04360 ~\mathrm{u}$$,

$${ }_{2}^{4} \mathrm{He}=4.00260 ~\mathrm{u}$$ and

$$1 \mathrm{u}=931.5 \frac{\mathrm{MeV}}{c^{2}}$$

The energy released $$(Q)$$ during the alpha decay of $${ }_{92}^{238} \mathrm{U}$$ is __________ MeV

A conducting circular loop is placed in a uniform magnetic field of $$0.4 \mathrm{~T}$$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $$1 \mathrm{~mm} / \mathrm{s}$$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $$2 \mathrm{~cm}$$ will be ___________ $$\mu \mathrm{V}$$.