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Arrange the four graphs in descending order of total work done; where \( W_1 \), \( W_2 \), \( W_3 \) and \( W_4 \) are the work done corresponding to figure a, b, c and d respectively.

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below.

If \( \rho \) is the density and \( \eta \) is coefficient of viscosity of fluid which flows with a speed \( v \) in the pipe of diameter \( d \), the correct formula for Reynolds number \( R_{e} \) is:

A flask contains argon and oxygen in the ratio of \( 3 : 2 \) in mass and the mixture is kept at \( 27^\circ \text{C} \). The ratio of their average kinetic energy per molecule respectively will be:

The charge on capacitor of capacitance \( 15\,\mu\text{F} \) in the figure given below is:

A parallel plate capacitor with plate area \( A \) and plate separation \( d = 2\,\text{m} \) has a capacitance of \( 4\,\mu\text{F} \). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \( K = 3 \) (as show in figure) will be:

Sixty four conducting drops each of radius \( 0.02\,\text{m} \) and each carrying a charge of \( 5\,\mu\text{C} \) are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be:

The equivalent resistance between points \( A \) and \( B \) in the given network is:

A bar magnet having a magnetic moment of \( 2.0 \times 10^{5} \, \text{J}\,\text{T}^{-1} \), is placed along the direction of uniform magnetic field of magnitude \( B = 14 \times 10^{-5} \, \text{T} \). The work done in rotating the magnet slowly through \( 60^\circ \) from the direction of field is:

Two coils of self inductance \( L_1 \) and \( L_2 \) are connected in series combination having mutual inductance of the coils as \( M \). The equivalent self inductance of the combination will be:

A metallic conductor of length \( 1 \, \text{m} \) rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity \( 5 \, \text{rad s}^{-1} \). If the horizontal component of earth's magnetic field is \( 0.2 \times 10^{-4} \, \text{T} \), then emf induced between the two ends of the conductor is:

Which is the correct ascending order of wavelengths?

For a specific wavelength \( 670 \, \text{nm} \) of light coming from a galaxy moving with velocity \( v \), the observed wavelength is \( 670.7 \, \text{nm} \). The value of \( v \) is:

A metal surface is illuminated by a radiation of wavelength 4500 Å  The ejected photo-electron enters a constant magnetic field of \( 2 \, \text{mT} \) making an angle of \( 90^{\circ} \) with the magnetic field. If it starts revolving in a circular path of radius \( 2 \, \text{mm} \), the work function of the metal is approximately:

A radioactive nucleus can decay by two different processes. Half-life for the first process is \( 3.0 \) hours while it is \( 4.5 \) hours for the second process. The effective half-life of the nucleus will be:

The positive feedback is required by an amplifier to act an oscillator. The feedback here means:

A sinusoidal wave \( y(t) = 40 \sin(10 \times 10^{6} \pi t) \) is amplitude modulated by another sinusoidal wave \( x(t) = 20 \sin(1000 \pi t) \). The amplitude of minimum frequency component of modulated signal is:

A ball is projected vertically upward with an initial velocity of \( 50 \, \text{m s}^{-1} \) at \( t = 0 \, \text{s} \). At \( t = 2 \, \text{s} \), another ball is projected vertically with same velocity. At \( t = \_\_\_\_ \, \text{s} \), second ball will meet the first ball \( (g = 10 \, \text{m s}^{-2}) \).

A batsmen hits back a ball of mass \( 0.4 \, \text{kg} \) straight in the direction of the bowler without changing its initial speed of \( 15 \, \text{m s}^{-1} \). The impulse imparted to the ball is \( \_\_\_\_\_ \, \text{N s} \).

A system to \( 10 \) balls each of mass \( 2 \, \text{kg} \) are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between \( 7^{\text{th}} \) and \( 8^{\text{th}} \) ball is \( \_\_\_\_ \, \text{N} \) when \( 6^{\text{th}} \) ball just leaves the table.

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$^\circ$C to 70$^\circ$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min$^{-1}$.

[Heat of combustion = 8 $\times$ 10$^3$ J g$^{-1}$, Specific heat of water = 4.2 J g$^{-1}$ $^\circ$C$^{-1}$]

A heat engine operates with the cold reservoir at temperature \( 324 \, \text{K} \). The minimum temperature of the hot reservoir, if the heat engine takes \( 300 \, \text{J} \) heat from the hot reservoir and delivers \( 180 \, \text{J} \) heat to the cold reservoir per cycle, is _______ \( \text{K} \).

A set of \( 20 \) tuning forks is arranged in a series of increasing frequencies. If each fork gives \( 4 \) beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _______ \( \text{Hz} \).

Two \( 10 \, \text{cm} \) long, straight wires, each carrying a current of \( 5 \, \text{A} \) are kept parallel to each other. If each wire experienced a force of \( 10^{-5} \, \text{N} \), then separation between the wires is _______ \( \text{cm} \).

A small bulb is placed at the bottom of a tank containing water to a depth of \( \sqrt{7} \, \text{m} \). The refractive index of water is \( \frac{4}{3} \). The area of the surface of water through which light from the bulb can emerge out is \( x \pi \, \text{m}^2 \). The value of \( x \) is ________.

A travelling microscope is used to determine the refractive index of a glass slab. If \( 40 \) divisions are there in \( 1 \, \text{cm} \) on main scale and \( 50 \) Vernier scale divisions are equal to \( 49 \) main scale divisions, then least count of the travelling microscope is _______ \( \times 10^{-6} \, \text{m} \).

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength  6630 Å  is \( 0.42 \, \text{V} \). If the threshold frequency is \( x \times 10^{13} \,/ \text{s}^{} \), where \( x \) is _______ (nearest integer).
(Given, speed light \( 3 \times 10^{8} \, \text{m} \, /\text{s}^{} \), Planck’s constant \( = 6.63 \times 10^{-34} \, \text{J} \, \text{s} \))