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Thermodynamic processes are indicated in the following diagram. Match the following: **Column-I** (P) Process I (Q) Process II (R) Process III (S) Process IV **Column-II** (a) Adiabatic (b) Isobaric (c) Isochoric (d) Isothermal

If a cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then coefficient of friction between the cycle tyres and road is:

For a parallel beam of monochromatic light of wavelength $\lambda$, diffraction is produced by a single slit whose width '$a$' is of the order of the wavelength of the light. If '$D$' is the distance of the screen from the slit, the width of the central maxima will be

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block will be:

A certain quantity of water cools from $70^{\circ}\text{C}$ to $60^{\circ}\text{C}$ in the first $5\text{ minutes}$ and to $54^{\circ}\text{C}$ in the next $5\text{ minutes}$. The temperature of the surroundings will be:

Assume that light of wavelength $600 nm$ is coming from a star. The limit of resolution of telescope whose objective has a diameter of $2 m$ is :

A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position? (Take $g = 10 \text{ m/s}^2$)

In thermodynamic processes, which of the following statements is not true?

A body of mass 0.4 kg is whirled in a vertical circle making 2 rev/sec. If the radius of the circle is 2 m, then tension in the string when the body is at the top of the circle is:

Steam at $100^{\circ}\text{C}$ is passed into $20\text{ g}$ of water at $10^{\circ}\text{C}$. When water acquires a temperature of $80^{\circ}\text{C}$, the mass of water present will be (Take specific heat of water $= 1\text{ cal g}^{-1\circ}\text{C}^{-1}$ and latent heat of steam $= 540\text{ cal g}^{-1}$)

One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3 = \text{constant}$. The heat capacity of the gas during this process is:

A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface. At some instant, the gun fires bullets of mass 10 g with a velocity of 500 m/s with respect to the car. The number of bullets fired per second is ten. The average thrust on the system is:

The compound which shows metamerism is :

The product formed from the following reaction sequence is:

In the diagram shown, the normal reaction force between $2 \text{ kg}$ and $1 \text{ kg}$ blocks is: (Consider the surface to be smooth and $g=10 \text{ m/s}^2$)

A slab of stone of area of $0.36\text{ m}^2$ and thickness $0.1\text{ m}$ is exposed on the lower surface to steam at $100^{\circ}\text{C}$. A block of ice at $0^{\circ}\text{C}$ rests on the upper surface of the slab. In one hour $4.8\text{ kg}$ of ice is melted. The thermal conductivity of slab is : (Given latent heat of fusion of ice $=3.36 \times 10^5\text{ J kg}^{-1}$)

A Carnot engine has an efficiency of $50\%$ when its source is at a temperature $327^\circ \mathrm{C}$. The temperature of the sink is:

A point mass $m$ is moved in a vertical circle of radius $r$ with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is:

A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is ($g=10 \text{ m/s}^2$) nearly:

Liquid oxygen at $50\text{ K}$ is heated to $300\text{ K}$ at constant pressure of $1\text{ atm}$. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?