JEE Main 2021 PYQ

The angle between vector A and (A - B) is

Match List I with List II. Choose the correct answer from the options given below :

In an octagon of equal side, what is the sum of

The resultant of these forces OP, OQ, OR, OS and OT is approximately ...... N. [Take, and given and unit vectors along X, Y axis

If , the angle between and is . The value of will be ........... .

What will be the projection of vector on vector ?

Two vectors and have equal magnitude. The magnitude of is times the magnitude of . The angle between and is :

Statement I Two forces and where , when act at an angle to each other, the magnitude of their resultant is , when they act at an angle , the magnitude of their resultant becomes . This is possible onl

Three particles and are moving along thevectors and respectively. They strike on a point and start tomove in different directions. Now particle ismoving normal to the plane which contains vector and .

Assertion If are four points on a semi-circular arc with centre at 'O' such that , then Reason R : Polygon law of vector addition yields In the light of the above statements, choose the most appropria

Two vectors and have equal magnitudes. If the magnitude of is times the magnitude of , then angle between and is :

If and are two vectors satisfying the relation Then the value of will be

The magnitude of vectors OA, OB, and OC in the given figure are equal. The direction of OA + OB - OC with X - axis will be

Match List-I with List-II. List-I List-II A. Torque 1. B.Impulse 2. C. Tension 3. D. Surface tension 4. Choose the most appropriate answer from the options given below. [31 Aug 2021 Shift 1]

The value of tension in a long thin metal wire has been changed from to . The lengths of the metal wire at two different values of tension and are and respectively. The actual length of the metal wire

A solid cylinder of mass is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined

A steel block of rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration . The normal reaction by the floor, if

An electron with kinetic energy enters between parallel plates of a capacitor at an angle with the plates. It leaves the plates at angle with kinetic energy . Then, the ratio of kinetic energies will

Find the gravitational force of attraction between the ring and sphere as shown in the figure, where the plane of the ring is perpendicular to the line joining the centres. If is the distance between

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter.

A boy pushes a box of mass with a force on a frictionless surface. If the box was initially at rest, then ________ m is the displacement along the -axis after .

A body of mass rests on a horizontal floor with which it has a coefficient of static friction . It is desired to make the body move by applying the minimum possible force newton. The value of will be

A monoatomic gas of mass is kept in an insulated container. Container is moving with velocity . If container is suddenly stopped, then change in temperature of the gas gas constant is Value of is ....

Water drops are falling from a nozzle of a shower onto the floor, from a height of . The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third dro

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ratio of velocity of the centre of mass at the botto

Given below are two statements: Statement I An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anyw

In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released.

The average translational kinetic energy of gas molecules at .......... °C becomes equal to the KE of an electron accelerated from rest through a potential difference of . [Given, ]

The total charge enclosed in an incremental volume of located at the origin is , if electric flux density of its field is found as .

In thermodynamics, heat and work are

A uniform heavy rod of weight , cross-sectional area and length is hanging from a fixed support. Young's modulus of the material of the rod is . Neglecting the lateral contraction, find the elongation

A uniform chain of length and mass overhangs a smooth table with laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is ....

A bob of mass m suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density times that of the bob and the length of

The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is . The value of x is

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a [26 Aug 2021 Shift 2]

A closed organ pipe of length and an open organ pipe contain gases of densities and respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first

The mass per unit length of a uniform wire is . A transverse wave of the form is produced in it, where is in metre and is in second. Then, the expected value of tension in the wire is . Value of is ..

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where, is the ratio of specific heats)

The electric field in a region is given by with . The flux of this field through a rectangular surface area parallel to the -plane is .......... .

A physical quantity 'y' is represented by the formula If the percentage errors found in and are and respectively, then find the value of and .[27 Jul 2021 Shift 2]

The pitch of the screw gauge is and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies 8 divisions below the reference line. Wh

A current through a wire depends on time as , where and . Find the charge crossed through a section of the wire in . 24 Feb 2021 Shift1

Wires and are made of same material having the breaking stress of . and have cross-sectional area of and , respectively. Masses of and hang from them as shown in the figure. The maximum mass that can

The solid cylinder of length and mass M has a radius of . Calculate the density of the material used, if the moment of inertia of the cylinder about an axis CD parallel to AB as shown in figure is .

If the velocity-time graph has the shape , what would be the shape of the corresponding acceleration-time graph ? 24 Feb 2021 Shift1

The work done by a gas molecule in an isolated system is given by, , where is the displacement, is the Boltzmann constant and is the temperature, and are constants. Then, the dimensions of will be 24

If you are provided a set of resistances and . Connect these resistances, so as to obtain an equivalent resistance of .

If the time period of a long simple pendulum is , the acceleration due to gravity at the place, where pendulum is executing SHM is

The value of current in the 6Ω resistance is :

A solid disc of radius and mass is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bri

The period of oscillation of a simple pendulum is Measured value of is from metre scale having a minimum division of and time of one complete oscillation is measured from stopwatch of resolution. The

Given below is the plot of a potential energy function for a system, in which a particle is in one dimensional motion, while a conservative force acts on it. Suppose that , the incorrect statement for

The volume of a given mass of monoatomic gas changes with temperature according to the relation . The work done when temperature changes by will be . The value of is.......... universal gas constant

A certain charge is divided into two parts and How should the charges and be divided so that and placed at a certain distance apart experience maximum electrostatic repulsion?

Consider a long wire as shown in the figure. The galvanometer jockey is placed at on at a distance from . The galvanometer shows zero deflection.The value of , to the nearest integer, is__________.

An ideal gas is expanding such that . The coefficient of volume expansion of the gas is

A car is moving on a plane inclined at to the horizontal with an acceleration of parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the s

Match List-I with List-II. List - I List - II A. Magnetic induction B. Magnetic flux C. Magnetic permeability D. Magnetisation Choose the most appropriate answer from the options given below. [26 Aug

A capacitor of capacitance is suddenly connected to a battery of 100 volt through a resistance The time taken for the capacitor to be charged to get is : Take

The resistance of a conductor at is and at is . What will be the temperature coefficient of resistance of the conductor?

A scooter accelerates from rest for time at constant rate and then retards at constant rate for time and comes to rest. The correct value of will be [26 Feb 2021 Shift 2]

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is , the weight of the same obje

A particle executes SHM, the graph of velocity as a function of displacement is

Two identical tennis balls each having mass 'm' and charge ' ' are suspended from a fixed point by threads of length . What is the equilibrium separation when each thread makes a small angle with the

Two small spheres each of mass are suspended from a point by threads long. They are equally charged and repel each other to a distance of . The charge on each of the sphere is . The value of will be .

Two cars X and Y are approaching each other with velocities and respectively. The frequency of a whistle sound as emitted by a passenger in car X, heard by the passenger in car Y is . If the velocity

A current of enters one corner of an equilateral triangle having three wires of resistance each and leaves by the corner . The currents , in ampere is ............ .

Two electrons each are fixed at a distance . A third charge proton placed at the mid-point is displaced slightly by a distance perpendicular to the line joining the two fixed charges. Proton will exec

A particle of mass originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation Where and are constants. The force acts only for the

Two identical particles of mass each go round a circle of radius , under the action of their mutual gravitational attraction. The angular speed of each particle is :

Angular momentum of a single particle moving with constant speed along circular path

A porter lifts a heavy suitcase of mass and at the destination lowers it down by a distance of with a constant velocity. Calculate the workdone by the porter in lowering the suitcase. take

The boxes of masses and are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass to strike the ground starting from rest. (Use, )

An engine is attached to a wagon through a shock absorber of length . The system with a total mass of is moving with a speed of , when the brakes are applied to bring it to rest. In the process of the

In 5 minutes, a body cools from 75°C to 65°C at room temperature of 25°C. The temperature of body at the end of next 5 minutes is _______°C

For an ideal gas the instantaneous change in pressure p with volume V is given by the equation . If at V = 0 is the given boundary condition, then the maximum temperature one mole of gas can attain is

A bullet of , moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity . The length of the pendulum is and mass of the bob is . The minimum value of v .

Two particles having masses and respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is . The value of will be ............ .

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon fr

A solid disc of radius and mass rolls down without slipping on an inclined plane making an angle with the horizontal. The acceleration of the disc will be , where is (Round off to the nearest integer)

A mosquito is moving with a velocity and accelerating in uniform conditions. What will be the direction of mosquito after 2s? [16 Mar 2021 Shift 2]

Four equal masses, each are placed at the corners of a square of length as shown in the figure

A rod CD of thermal resistance is joined at the middle of an identical rod AB as shown in figure. The end A,B and D are maintained at and respectively. The heat current in CD is P watt. The value ofP

The equivalent resistance of the given circuit between the terminals A and B is

The voltage drop across resistance in the given figure will be ........ V.

A parallel plate capacitor has plate area and plate separation of . The space between the plates is filled upto a thickness with a material of dielectric constant of 10 . The resultant capacitance of

If is the electronic charge, is the speed of light in free space and is Planck's constant, the quantity has dimensions of [25 Feb 2021 Shift 2]

A current of exists in a wire of cross sectional area of with a drift velocity of . The number of free electrons in each cubic metre of the wire is

If and represent capacity and voltage respectively, then what are the dimensions of , where [26 Feb 2021 Shift 2]

A wire having a linear mass density is stretched between two rigid supports with a tension of . The wire resonates at a frequency of . The next higher frequency at which the same wire resonates is . T

Two blocks and are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is . Then, the maximum horizontal force that can be applied

For the circuit shown, the value of current at time t = 3.2 s will be ______ A. [Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)]

An object of mass is being moved with a constant velocity under the action of an applied force of along a frictionless surface with following surface profile. The correct applied force versus distance

The rms speeds of the molecules of hydrogen, oxygen and carbondioxide at the same temperature are and respectively, then

A ball of mass moving with a velocity along the -axis, hits another ball of mass which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal piec

In order to determine the Young's modulus of a wire of radius (measured using a scale of least count ) and length (measured using a scale of least count ), a weight of mass (measured using a scale of

A satellite is launched into a circular orbit of radius R around earth, while a second satellite is launched into a circular orbit of radius 1.02 R. The percentage difference in the time periods of th

27 similar drops of mercury are maintained at each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ........... that of a smaller drop.

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time ' ' is proportional to:

A resistor dissipates 192 J of energy in 1 s when a current of is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5 s is ........ J.

In a spring gun having spring constant a small ball 'B' of mass is put in its barrel (as shown in figure) by compressing the spring through . There should be a box placed at a distance 'd' on the grou

A ball with a speed of collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of with the original direction. The ratio of velocities of the balls

A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is___.

The temperature of equal masses of three different liquids and z are and , respectively. The temperature of mixture when x is mixed with y is and that when y is mixed with z is . The temperatureof mix

The frequency of a car horn encountered a change from 400 Hz to 500 Hz. When the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ______ km/h.

A mass of is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figur. A simple pendulum of length has the same period of oscillatio

The pressure acting on a submarine is at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be (Assume that atmospheric pressure is , densi

If two similar springs each of spring constant are joined in series, the new spring constant and time period would be changed by a factor

If the rms speed of oxygen molecules at is , find the rms speed of hydrogen molecules at .

In the given figure, two wheels and are connected by a belt . The radius of is three times as that of In case of same rotational kinetic energy, the ratio of rotational inertias will be . The value of

In an electric circuit, a call of certain emf provides a potential difference of across a load resistance of . However, it provides a potential difference of across a load resistance of .The emf of th

Five equal resistances are connected in a network as shown in figure. The net resistance between the points and is

Two masses and , each of mass are fixed together by a massless spring. A force acts on the mass as shown in figure. If the mass starts moving away from mass with acceleration , then the acceleration o

Two spherical balls having equal masses with radius of each are thrown upwards along the same vertical direction at an interval of with the same initial velocity of , then these balls collide at a hei

A soap bubble of radius is formed inside the another soap bubble of radius . The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the

Section B : Numerical Type Questions A body of mass 2M splits into four masses , which are rearranged to form a square as shown in the figure. The ratio of for which, the gravitational potential energ

The position of the centre of mass of a uniform semi-circular wire of radius 'R' placed in plane with its centre at the origin and the line joining its ends as -axis is given by . Then, the value of i

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules

In the given figure, a body of mass is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant , t

Two identical metal wires of thermal conductivities and respectively are connected in series. The effective thermal conductivity of the combination is

If is the free charge on the capacitor plates and is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge can be expressed as :

In the given figure, there is a circuit of potentiometer of length The resistance per unit length is per . Across , a battery of emf and internal resistance ' is connected. The maximum value of emf me

A sphere of mass and radius is rolling with an initial speed of goes up an inclined plane which makes an angle of with the horizontal plane, without slipping. How long will the sphere take to return t

Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude

A hydraulic press can lift when a mass is placed on the smaller piston. It can lift ............ when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decrea

A raindrop with radius falls from a cloud at a height above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attain

A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that . The speed of particle will be

Statement I If three forces and are represented by three sides of a triangle and , then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement II A triangle made

The point moves with a uniform speed along the circumference of a circle of radius and covers in . The perpendicular projection from on the diameter represents the simple harmonic motion of . The rest

Three capacitors and are connected as shown in figure. Find the ratio of the charges on capacitors and , respectively.

Two spherical soap bubbles of radii and in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

An electric dipole is placed on -axis in proximity to a line charge of linear charge density . Line charge is placed on z-axis and positive and negative charge of dipole is at a distance of and from t

The trajectory of a projectile in a vertical plane is , where and are constants and and are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle

For full scale deflection of total 50 divisions, voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is will be

A resistor develops of thermal energy in , when a current of is passed through it. If the current is increased from to , what will be the energy developed in 20 s?

The internal energy , pressure and volume of an ideal gas are related as . The gas is

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius and density ? Take viscosity of liquid . (Neglect buoyancy due to air).

In the reported figure of Earth, the value of acceleration due to gravity is same at point and but it is smaller than that of its value at point (surface of the Earth). The value of will be . The valu

Match List-I with List-II List-I List-II A. (Planck's constant) 1. B. (kinetic energy) 2 C. (electric potential) 3. D. (linear momentum) 4. Choose the correct answer from the options given below.[25 F

The given potentiometer has its wire of resistance 10Ω. When the sliding contact is in the middle of the potentiometer wire, the potential drop across 2Ω resistor is :

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45° and 60° with the direction of displacement respectively. Th

A circular hole of radius is cut out of a circular disc of radius as shown in figure The centroid of the remaining circular portion with respect to point will be

The initial mass of a rocket is . Calculate at what rate the fuel should be burnt, so that the rocket is given an acceleration of . The gases come out at a relative speed of with respect to the rocket

What equal length of an iron wire and a copper-nickel alloy wire, each of diameter connected parallel to give an equivalent resistance of ? (Given, resistivities of iron and copper-nickel alloy wire a

If the length of the pendulum in pendulum clock increases by , then the error in time per day is [26 Aug 2021 Shift 2]

A block of mass attached to a spring is made to oscillate with an initial amplitude of . After , the amplitude decreases to . Determine the value of the damping constant for this motion. (Take, In )

An engine of a train moving with uniform acceleration, passes the signal-post with velocity and the last compartment with velocity . The velocity with which middle point of the train passes the signal

The masses and radii of the Earth and Moon are and , respectively. Their centres are at a distance r apart. Find the minimum escape velocity for a particle of mass m to be projected from the middle of

Two discs have moments of inertia and about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, and respectively and are brought int

For a gas in a state and in a state and are the temperatures in two different states and respectively. Then

In the given figure, a mass is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is . The mass oscillates on a frictionless surface with

If and are the values of Young's modulus, bulk modulus and modulus of rigidity of any material, respectively. Choose the correct relation for these parameters. 24 Feb 2021 Shift1

Consider a badminton racket with length scales as shown in the figure. If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible,

Four identical rectangular plates with length, and breadth, are arranged as shown in figure. The equivalent capacitance between and is . The value of is ......... (Round off to the nearest integer)

Which of the following is not a dimensionless quantity? [27 Aug 2021 Shift 1]

Four identical solid spheres each of mass and radius are placed with their centres on the four corners of a square of side . The moment of inertia of the system about one side of square, where the axi

Find out the surface charge density at the intersection of point plane and -axis, in the region of uniform line charge of lying along the -axis in free space

Two identical conducting spheres with negligible volume have and charges, respectively. They are brought into contact and then separated by a distance of . The electrostatic force acting between the s

The angular speed of truck wheel is increased from 900 rpm to in . The number of revolutions by the truck engine during this time is ......... (Assuming the acceleration to be uniform).

Match List-I with List-II. List-I List-II A. Isothermal 1. Pressure constant B. Isochoric 2. Temperature constant C. Adiabatic C. Adiabatic D. Isobaric 4. Heat content is constantChoose the correct an

The length of metallic wire is when tension in it is . It is when the tension is . The original length of the wire will be

The angular momentum of a planet of mass moving around the Sun in an elliptical orbit is . The magnitude of the areal velocity of the planet is

Three students and perform an experiment for determining the acceleration due to gravity (g) using a simple pendulum. They use different lengths of pendulum and record time for different number of osc

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass , decay constant , then how much time is required for the amplitude of the system to drop to h

A pendulum bob has a speed of 3 m/s at its lowest position. The pendulum is 50 cm long. The speed of bob, when the length makes an angle of 60° to the vertical will be (g = 10 m/s ) ______ m/s.

Which of the following equations represents a travelling wave?

The time period of a simple pendulum is given by . The measured value of the length of pendulum is known to a accuracy. The time for 200 oscillations of the pendulum is found to be 100 s using a clock

A mass of is placed at the centre of a uniform spherical shell of mass and radius . If the gravitational potential at a point, from the centre is . The value of V is

A particle of mass is hanging from a spring of force constant . The mass is pulled slightly downward and released, so that it executes free simple harmonic motion with time period T. The time when the

Two stars of masses and at a distance rotate about their common centre of mass in free space. The period of revolution is 24 Feb 2021 Shift1

The vernier scale used for measurement has a positive zero error of . If while taking a measurement, it was noted that ' 0 ' on the vernier scale lies between and , vernier coincidence is 6 , then the

A body of mass M moving at speed collides elastically with a mass m at rest. After the collision, the two masses move at angles and with respect to the initial direction of motion of the body of mass

Two particles A and B having charges and respectively are held fixed with a separation of . At what position a third charged particle should be placed, so that it does not experience a net electric fo

A body having specific charge is resting on a frictionless plane at a distance from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of is applied hor

A cord is wound round the circumference of wheel of radius . The axis of the wheel is horizontal and the moment of inertia about it is . A weight is attached to the cord at the end. The weight falls f

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance from the earth's centre, where is the radius of the earth. The wall of the tunnel is frictionless. If a particle is

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field as

The projectile motion of a particle of mass is shown in the figure.The initial velocity of the particle is and the air resistance is assumed to be negligible. The magnitude of the change in momentum b

Two wires of same length and thickness having specific resistances and respectively are connected in parallel. The effective resistivity is . The value of to the nearest integer, is

In a certain thermodynamical process, the pressure of a gas depends on its volume as . The work done when the temperature changes from to will be ........... , where denotes number of moles of a gas.

The two thin co-axial rings, each of radius a and having charges +Q and -Q respectively, are separated by a distance of s. The potential difference between the centres of the two rings is

As shown in the figure, a block of mass is kept on a horizontal rough surface of coefficient of friction . The critical force to be applied on the vertical surface as shown at an angle with horizontal

If the angular velocity of Earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately (Take , the radius of Earth, , take

A cube of side has point charges located at each of its vertices except at the origin, where the charge is . The electric field at the centre of cube is 24 Feb 2021 Shift1

The amplitude of wave disturbance propagating in the positive -direction is given by at time and at , where and are in meres. The shape of wave does not change during the propagation. The velocity of

A block of mass slides along a floor, while a force of magnitude is applied to it at an angle as shown in figure. The coefficient of kinetic friction is . Then, the block's acceleration is given by (

A boy of mass is standing on a piece of wood having mass . If the coefficient of friction between the wood and the floor is , the maximum force that the boy can exert on the rope, so that the piece of

One mole of an ideal gas at is taken from to as shown in the given indicator diagram. The work done by the system will be ______ . [Given: (Round off to the nearest integer)

Calculate the value of mean free path for oxygen molecules at temperature and pressure . Assume the molecular diameter and the gas is ideal.

A particle is moving with uniform speed along the circumference of a circle of radius under the action of a central fictitious force which is inversely proportional to . Its time period of revolution

When two soap bubbles of radii and coalesce, the radius of curvature of common surface is

A bullet of ' ' mass is fired from a gun of mass . If the bullet moves with the muzzle speed of , the impulse imparted to the gun and velocity of recoil of gun are:

A Carnot's engine working between and has a work output of per cycle. The amount of heat energy supplied to the engine from the source in each cycle is

Two satellites revolve around a planet in coplanar circular orbits in anti-clockwise direction. Their period of revolutions are and , respectively. The radius of the orbit of nearer satellite is . The

A capacitor is first charged to a potential difference of using a battery. Then, the battery is removed and the capacitor is connected to an uncharged capacitor of . The charge in on equilibrium condi

A point charge of is at a distance vertically above the centre of a square of side as shown in figure. The magnitude of the electric flux through the square will be ..........

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at second after its fall to the next droplet is . At what rate the droplets are coming from the

The entropy of any system is given by where and are the constants. and are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. Choose the incorrect option fr

The normal reaction 'N' for a vehicle of mass, negotiating a turn on a banked road at maximum possible speed without skidding is _______

The maximum and minimum distance of a comet from the Sun are and , respectively. If the speed of the comet at the nearest point is , then the speed at the farthest point is

A conducting wire of length , area of cross-section and electric resistivity is connected between the terminals of a battery. A potential difference is developed between its ends, causing an electric

A large number of water drops, each of radius , combine to have a drop of radius . If the surface tension is and mechanical equivalent of heat is J, the rise in heat energy per unit volume will be

The number of molecules in one litre of an ideal gas at and 2 atmospheric pressure with mean kinetic energy per molecules is :

If the velocity of a body related to displacement x is given by , then the acceleration of the body is .[27 Aug 2021 Shift 1]

A person is swimming with a speed of at an angle of with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is . The value of to the nearest intege

The motion of a mass on a spring, with spring constant K is as shown in figure. The equation of motion is given by Asin\ω t+ Bcos\ωtwith Suppose that at time , the position of mass is and velocity , t

A current of is passing through a non-linear magnesium wire of cross-section . At every point the direction of current density is at an angle of with the unit vector of area of cross-section. The magn

A block moving horizontally on a smooth surface with a speed of splits into two equal parts. If one of the parts moves at in the same direction, then the fractional change in the kinetic energy will b

What will be the nature of flow of water from a circular tap, when its flow rate increased from to ? The radius of the tap and viscosity of water are and , respectively. (Density of water )

A block of mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius . If the block takes 40 s to complete one round, the normal force by the side walls of th

A uniform heating wire of resistance is connected across a potential difference of . The wire is then cut into half and potential difference of is applied across each half separately. The ratio of pow

The coefficient of static friction between a wooden block of mass and a vertical rough wall is . The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall wil

A ball is thrown up with a certain velocity so that it reaches a height ' '. Find the ratio of the two different times of the ball reaching in both the directions.[27 Jul 2021 Shift 1]

In an electrical circuit, a battery is connected to pass of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at . The work done by th

A particle performs simple harmonic motion with a period of . The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is . The value of to the near

The radius in kilometre to which the present radius of Earth to be compressed so that the escape velocity is increased 10 times is

A polyatomic ideal gas has 24 vibrational modes. What is the value of ?

In the given figure, a battery of emf is connected across a conductor of length and different area of cross-sections having radii and .Choose the correct option as one moves from P to Q :

A wire is bend to form a square loop. A supply having internal resistance of is connected across one of its sides. The potential drop across the diagonals of the square loop is _________

A sample of gas with is taken through an adiabatic process in which the volume is compressed from to . If the initial pressure is . The absolute value of the work done by the gas in the process is ...

A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant and of same area and thickness are inserted in the space between the plate

A car accelerates from rest at a constant rate for some time after which it decelerates at a constant rate to come to rest. If the total time elapsed is seconds, the total distance travelled is [17 Ma

A circular disc reaches from top to bottom of an inclined plane of length ' When it slips down the plane, it takes time ' . When it rolls down the plane, it takes time . The value of is The value of x

A student determined Young's modulus of elasticity using the formula . The value of g is taken to be , without any significant error, his observations are as following. Physical quantity Least count o

A monoatomic ideal gas, initially at temperature is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature by releasing the piston sudden

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given ar

A body takes 4 min. to cool from 61° C to 59°C. If the temperature of the surroundings is 30°C, the time taken by the body to cool from 51°C to 49° C is :

In the reported figure, heat energy absorbed by a system in going through a cyclic process is ______ πJ.

Which of the following graphs represent the behavior of an ideal gas ? Symbols have their usual meaning.

Two particles and of equal masses are suspended from two massless springs of spring constants and , respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time . If he remains stationary on a moving escalator then the escalator takes him up in

In the figure given, the electric current flowing through the resistor is . The value of to the nearest Integer is ...3...

A square shaped wire with resistance of each side is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in unit of Ω will be

Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolut

A body weights on a spring balance at the North pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator ? (Use, and radius of earth, )

Two thin metallic spherical shells of radii and are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained

A force of acts on a particle. The workdone by this force when the particle is moved from to is ______ J.

Two separate wires and are stretched by and respectively, when they are subjected to a force of . Assume that both the wires are made up of same material and the radius of wire is 4 times that of the

A cube is placed inside an electric field, . The side of the cube is and is placed in the field as shown in the given figur. The charge inside the cube is

A sphere of radius and mass rolls along a horizontal plane with constant speed . It encounters an inclined plane at angle and climbs upwards. Assuming that it rolls without slipping, how far up the sp

The radius of a sphere is measured to be . Suppose the percentage error in its volume is . The value of to the nearest , is ............. .[18 Mar 2021 Shift 2]

In the given figure switches and are in open condition. The resistance across ab when the switches and are closed is_______ .

A Copper (Cu) rod of length and crosssectional area is joined with a similar Aluminium (Al) rod as shown in figure. Find the resistance of the combination between the ends A and B. (Take Resistivity o

A particle of mass moves in a circular orbit under the central potential field, , where is a positive constant. The correct radius-velocity graph of the particle's motion is

Which of the following equations is dimensionally incorrect? Where, t = time, h = height, s = surface tension, θ = angle, ρ = density, a, r = radius, g = acceleration due to gravity, V = volume, p = p

A system consists of two identical spheres each of mass and radius at the end of light rod. The distance between the centres of the two spheres is . What will be the moment of inertia of the system ab

In the given circuit of potentiometer, the potential difference across (10 m length) is larger than and as well. For key (closed), the jockey is adjusted to touch the wire at point , so that there is

Consider a binary star system of star A and star B with masses and revolving in a circular orbit of radii and , respectively. If and are the time period of star and star , respectively, then:

Two narrow bores of diameter and are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of two limbs of the tube. [Take surfa

A particle of mass 'm' is moving in time 't' on a trajectory given by Where α and β are dimensional constants. The angular momentum of the particle becomes the same as it was for t = 0 at time t = ___

Consider a sample of oxygen behaving like an ideal gas. At , the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be (Molecular weight of oxygen is ; )

The percentage increase in the speed of transverse waves produced in a stretched string, if the tension is increased by , will be ............ %.

A student is performing the experiment of resonance column. The diameter of the column tube is . The frequency of the tuning fork is . Speed of the sound at the given temperature is . The zero of the

The resistance , where and A. The percentage error in is . The value of to the nearest integer is..........[16 Mar 2021 Shift 1]

The potential energy (U) of a diatomic molecule is a function dependent on (interatomic distance) as where, and are positive constants. The equilibrium distance between two atoms will be , where

Moment of inertia of a square plate of side / about the axis passing through one of the corner and perpendicular to the plane of square plate is given by

Two waves are simultaneously passing through a string and their equations are [Given, amplitudes and and wave number ]. The amplitude of resulting wave will be .......... .

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (Which is ⊥ to the plane of the disc an

Find the electric field at point (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length carrying a charge . The distance of the point from the centre of the rod

A uniformly charged disc of radius R having surface charge density σ is placed in the xy-plane with its centre at the origin. Find the electric field intensity along the Z - axis at a distance Z from

Two satellites and of masses and are revolving around the Earth at height of and , respectively. If and are the time periods of and respectively, then the value of is(Given, radius of Earth , mass of

The acceleration due to gravity is found upto an accuracy of on a planet. The energy supplied to a simple pendulum to known mass m to undertake oscillations of time period T is being estimated. If tim

If be the radius of Earth, then the ratio between the acceleration due to gravity at a depth r below and a height r above the Earth surface is (Given, )

Match List-I with List-II. List-I List-II (Rydberg constant) B. h (Planck's constant) (Magnetic field energy density) D. η (Coefficient of viscosity) Choose the most appropriate answer from the option

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30° with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ with the

If one mole of an ideal gas at is allowed to expand reversibly and isothermally ( to ), its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume

A block moving horizontally on a smooth surface with a speed of splits into two parts with masses in the ratio of . If the smaller part moves at in the same direction, then the fractional change in ki

The following bodies, 1. a ring 2. a disc 3. a solid cylinder 4. a solid sphere of same mass and radius are allowed t roll down without slipping simultaneously from the top of the inclined plane. The

The coefficient of static friction between two blocks is and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is ...... N. (Take, )

Four particles each of mass M, move along a circle of radius R under the action of their mutual gravitational attraction as shown in figur. The speed of each particle is

An electric bulb of at is used in a circuit having a supply. Calculate the resistance R to be connected in series with the bulb, so that the power delivered by the bulb is .

A particle is moving with constant acceleration a. Following graph shows versus x (displacement) plot. The acceleration of the particle is ........ [31 Aug 2021 Shift 2]

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of . Find the mass of Mars.

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging stream of

A uniform metallic wire is elongated by when subjected to a linear force . The elongation, if its length and diameter is doubled and subjected to the same force will be ........... cm

If time , velocity , and angular momentum are taken as the fundamental units. Then thedimension of mass in terms of and is : [20 Jul 2021 Shift 2]

Two cells of emf and with internal resistance and respectively are connected in series to an external resistor (see figure). The value of , at which the potential difference across the terminals of th

A particle is making simple harmonic motion along the X-axis. If at a distances and from the mean position the velocities of the particle are and respectively. The time period of its oscillation is gi

A cell of emf and internal resistance is connected with another cell of emf and internal resistance (as shown in the figure). The potential difference across points and is 24 Feb 2021 Shift1

The energy dissipated by a resistor is in when an electric current of flows through it. The resistance is ........ . (Round off to the nearest integer)

The normal density of a material is and its bulk modulus of elasticity is . The magnitude of increase in density of material, when a pressure is applied uniformly on all sides, will be

A large block of wood of mass is hanging from two long massless cords. bullet of mass is fired into the block and gets embedded in it. The system (block + bullet) then swing upwards, their centre of m

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of crosssectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to preve

If and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimension of P in the formula is[26 Aug 2021 Shift 1]

Two blocks of masses and are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is . What is the minimum radius of the wire? (Take, )

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is ____m. (Assume ther

A ball of mass moving with a velocity along -axis, hits another ball of mass , which is at rest. After collision, the first ball comes to rest and the second one disintegrates into two equal pieces. O

The area of cross-section of a railway track is . The temperature variation is . Coefficient of linear expansion of material of track is . The energy stored per meter in the track is _______ . (Young'

Inside a uniform spherical shell I. the gravitational field is zero. II. the gravitational potential is zero. III. the gravitational field is same everywher IV. the gravitation potential is same every

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ______ S.

Which one is the correct option for the two different thermodynamic processes?

A parallel plate capacitor whose capacitance is is charged by a battery to a potential difference between its plates. The charging battery is now disconnected and a porcelain plate with is inserted be

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy . At any instant, its kinetic energy is then its displacement 'y' is given by:

Figure shows a rod AB, which is bent in a 120° circular arc of radius R. A charge (-Q) is uniformly distributed over rod AB. What is the electric field E at the centre of curvature O ?

Two cars are approaching each other at an equal speed of . When they see each other, both blow horns having frequency of . The beat frequency heard by each driver will be ........ . [Velocity of sound

The material filled between the plates of a parallel plate capacitor has resistivity . The value of capacitance of the capacitor is . If a potential difference of is applied across the plates of the c

A balloon carries a total load of at normal pressure and temperature of . What load will the balloon carry on rising to a height at which the barometric pressure is of Hg and the temperature is ? [Ass

Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the

A butterfly is flying with a velocity in North-East direction. Wind is slowly blowing at from North to South. The resultant displacement of the butterfly in 3 seconds is :[20 Jul 2021 Shift 1]

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : , for ,

The correct relation between the degrees offreedom and the ratio of specific heat is :

A uniform thin bar of mass and length is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is .

In the given figure, the emf of the cell is and if internal resistance is . Calculate the power dissipated in the whole circuit

512 identical drops of mercury are charged to a potential of each. The drops are joined to form a single drop. The potential of this drop is.

A source and a detector move away from each other in absence of wind with a speed of with respect to the ground. If the detector detects a frequency of of the sound coming from the source, then the or

An inclined plane is bent in such a way that the vertical cross-section is given by where, is in vertical and in horizontal direction. If the upper surface of this curved plane is rough with coefficie

is the time-displacement equation of SHM. At , the displacement of the particle is and it is moving along negative -direction. Then, the initial phase angle will be

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0°C to 50°C when no work is done is _______. (R is the universal gas constant)

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 m and 2 m respectively. A moves towards B with a speed of 9 m/s and makes a

The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are and , respectively. Choose the correct option.[1 Sep 2021 Shift 2]

The diameter of a spherical bob is measured using a Vernier callipers. 9 divisions of the main scale, in the vernier calipers, are equal to 10 divisions of vernier scale. One main scale division is .

Consider a uniform circular disc of radius . It is pin supported at its centre and is at rest initially. The disc is acted upon by a constant force through a massless string wrapped around its periphe

A heat engine operates between a cold reservoir at temperature and a hot reservoir at temperature . It takes 300 f of heat from the hot reservoir and delivers of heat to the cold reservoir in a cycle.

A diatomic gas having and , is heated at constant pressure. The ratio is

Consider two identical springs each of spring constant and negligible mass compared to the mass as shown. Fig.1 shows one of them and Fig.2 shows their series combination. The ratios of time period of

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power . The position is given as a function of time by:

The function of time representing a simple harmonic motion with a period of is

The volume of an enclosure contains a mixture of three gases, of oxygen, of nitrogen and of carbon dioxide at absolute temperature . Consider as universal gas constant. The pressure of the mixture of

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by[18 Mar 2021 Shift 1]

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from to . If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the foll

An object of mass is executing simple harmonic motion. It amplitude is and time period (T) is . What will be the potential energy of the object at an instant starting from mean position. Assume that t

A mixture of hydrogen and oxygen has volume , temperature , pressure and mass . The ratio of masses of oxygen to hydrogen will be

If velocity [v], time [T] and force [F] are choosen as the base quantities, the dimensions of the mass will be [31 Aug 2021 Shift 2]

A capacitor is connected to a battery through a resistance of . It is found that the potential difference across the capacitor rises to in . The capacitance of the capacitor in ........... . [Given, ]

A particle is projected with velocity along -axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin, i.e. . The distance at which the parti

A wire of has a length of . It is stretched till its length increases by . The percentage change in resistance to the nearest integer is

Moment of inertia (MI) of four bodies, having same mass and radius, are reported as Ml of thin circular ring about its diameter, MI of circular disk about an axis perpendicular to the disk and going t

A bimetallic strip consists of metals and . It is mounted rigidly as shown. The metal has higher coefficient of expansion compared to that of metal . When the bimetallic strip is placed in a cold bath

A huge circular arc of length ly subtends an angle at the centre of the circle. How long it would take for a body to complete 4 rev if its speed is per sec?

Two identical springs of spring constant are attached to a block of mass and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harm

Two simple harmonic motion, are represented by the equations and Ratio of amplitude of to . The value of x is ............ .

The disc of mass with uniform surface mass density is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position , where is ............ (Round off to the nearest

The force is given in terms of time and displacement by the equation The dimensional formula of is :[25 Jul 2021 Shift 2]

A tuning fork of unknown frequency produces 5 beats/s with a fork of known frequency . When fork is filled, the beat frequency decreases to 2 beats\/s. What is the frequency of fork ?

For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant is used, which has the same area as the plates of the capacitor. The thickness of the die

A tuning fork is vibrating at . The length of the shortest closed organ pipe that will resonate with the tuning fork will be ........ cm. (Take, speed of sound in air as )

- A boy is rolling a ball on the frictionless floor with the speed of . The ball gets deflected by an obstacle on the way. After deflection it moves with of its initial kinetic energy. What is the spe

A force acts on a body of mass . If the body starts from rest, its position vector at time , will be :

In a screw gauge, 5th division of the circular scale coincides with the reference line when the ratchet is closed. There are 50 divisions on the circular scale, and the main scale moves by on a comple

The temperature at the junction of two insulating sheets, having thermal resistances and as well as top and bottom temperatures and (as shown in figure) is given by

The equivalent resistance of series combination of two resistors is . When they are connected in parallel, the equivalent resistance is . If , then the minimum value for is .......... (Round off to th

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion (A) When a rod lying freely is heated, no thermal stress is developed in it. Reason (R)

A rod of mass and length is lying on a horizontal frictionless surface. A particle of mass 'm' travelling along the surface hits at one end of the rod with a velocity 'u' in a direction perpendicular

A stone of mass is projected from a rubber catapult of length and area of cross section stretched by an amount . The velocity of the projected stone is __________ (Young's modulus of rubber )

A player kicks a football with an initial speed of at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Tak

The electric field in a region is given . The ratio of flux of reported field through the rectangular surface of area (parallel to YZ-plane) to that of the surface of area (parallel to - plane) is , w

Two wires of same length and radius are joined end to end and loaded. The Young's modulii of the materials of the two wires are and . The combination behaves as a single wire then its Young's modulus

An electric bulb rated as 200 W at 100 V is used in a circuit having 200 V supply. The resistance 'R' that must be put in series with the bulb so that the bulb delivers the same power is _____ Ω

A charge is placed at one corner of a cube as shown in figure. The flux of electrostatic field through the shaded area is

A sound wave of frequency travels with the speed of along the positive -axis. Each point of the wave moves to and fro through a total distance of . What will be the mathematical expression of this tra

Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be 24 Feb 2021 Shift1

The temperature of of an ideal diatomic gas is increased by without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of

A bullet of mass is fired on a wooden block to pierce through it, but it stops after moving a distance of into it. If the velocity of bullet before hitting the wood is and it slows down with uniform d

Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count

Consider a mixture of gas molecule of types A, B and having masses . The ratio of their root mean square speeds at normal temperature and pressure is :

A triangular plate is shown below. A force is applied at point . The torque at point with respect to point and are

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature ( is Boltzmann constant)

Two simple harmonic motions are represented by the equations and The amplitude of second motion is ..............times the amplitude in first motion.

A particle of mass and charge is lying at the mid-point of two stationary particles kept at a distance '2 ' when each is carrying same charge 'q'. If the free charged particle is displaced from its eq

A geostationary satellite is orbiting around an arbitrary planet at a height of above the surface of being the radius of . The time period of another satellite in hours at a height of from the surface

The velocity of a particle is . Its position is at , then its displacement after time is [17 Mar 2021 Shift 2]

An object is located at beneath the surface of the water. If the fractional compression is , the ratio of hydraulic stress to the corresponding hydraulic strain will be ............... (Take, density

Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric cons

A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium positi

Two resistors and are connected in parallel. The equivalent resistance of their parallel combination will be

The minimum and maximum distances of a planet revolving around the Sun are and . If the minimum speed of the planet on its trajectory is then its maximum speed will be :

Due to cold weather a water pipe of cross-sectional area is filled with ice at . Resistive heating is used to melt the ice. Current of is passed through resistance. Assuming that, all the heat produce

A person standing on a spring balance inside a stationary lift measures . The weight of that person, if the lift descends with uniform downward acceleration of will be ........... N.

Four identical particles of equal masses made to move along the circumference of a circle of radius under the action of their own mutual gravitational attraction. The speed of each particle will be 24

Two identical blocks and each of mass resting on the smooth horizontal floor are connected by a light spring of natural length and spring constant . A third block of mass moving with a speed along the

Section B : Numerical Type Questions When a rubber ball is taken to a depth of ....... m in deep sea, its volume decreases by . (The bulk modulus of rubber . Density of sea water )

A solid sphere of radius gravitationally attracts a particle placed at from its centre with a force . Now, a spherical cavity of radius is made in the sphere (as shown in figure) and the force becomes

A reversible engine has an efficiency of . If the temperature of the sink is reduced by , its efficiency becomes double. Calculate the temperature of the sink.

Two ideal electric dipoles and , having their dipole moment and respectively are placed on a plane with their centres at as shown in the figure. At point on the axis of dipole , the resultant electric

Thermodynamic process is shown below on a -V diagram for one mole of an ideal gas. If , then the ratio of temperature is

The height of victoria falls is . What is the difference in temperature of water at the top and at the bottom of fall ? [Given, and specific heat of water ]

One main scale division of a vernier callipers is and th division of the vernier scale coincide with ( th division of the main scal[16 Mar 2021 Shift 1]

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time is proportional to

The instantaneous velocity of a particle moving in a straight line is given as , where and are constants. The distance travelled by the particle between and is :[25 Jul 2021 Shift 2]

Consider a galvanometer shunted with resistance and of current passes through it. What is the resistance of the given galvanometer ?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion The escape velocities of planet and are same. But and are of unequal mass. Reason The pr

Consider a water tank as shown in the figure. It's cross-sectional area is . The tank has an opening near the bottom whose cross-section area is . A load of is applied on the water at the top when the

A particle executes SHM with amplitude a and time period . The displacement of the particle when its speed is half of maximum speed is . The value of is ........... .

Two ideal polyatomic gases at temperatures and are mixed so that there is no loss of energy. If and and and be the degrees of freedom, masses, number of molecules of the first and second gas respectiv

A swimmer can swim with velocity of in still water. Water flowing in a river has velocity . The direction with respect to the direction of flow of river water he should swim in order to reach the poin

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes of oleic acid per of the solution. Then, you make a thin film of this solution (monomolecular thickn

If the Kinetic energy of a moving body becomes four times its initial Kinetic energy, then the percentage change in its momentum will be :

The initial velocity required to project a body vertically upward from the surface of the Earth to reach a height of , where is the radius of the Earth, may be described in terms of escape velocity su

What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is l and perpendicular to each other?

In a parallel plate capacitor set up, the plate area of capacitor is and the plates are separated by . If the space between the plates are filled with a dielectric material of thickness and area (see

List-I List-II (a) Moment of Inertia(MI) of the rod (length L, Mass M, about an axis ⊥ to the rod passing through the midpoint) (i) (b) Moment of Inertia(MI) of the rod (length L, Mass 2M, about an ax

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is and that of the other part is . Given that . If the piston is removed, then the total entropy of the s

The velocity-displacement graph describing the motion of a bicycle is shown in the following figure.The acceleration-displacement graph of the bicycle's motion is best described by[16 Mar 2021 Shift 1

For a body executing SHM A. potential energy is always equal to its kinetic energy. B. average potential and kinetic energy over any given time interval are always equal. C. sum of the kinetic and pot

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature ?

A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m/s and 4 m/s

The diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process is (use, )

A thin circular ring of mass and radius is rotating about its axis with an angular speed ๗. Two particles having mass each are now attached at diametrically opposite points. The angular speed of the r

When a body slides down from rest along a smooth inclined plane making an angle of with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane makin

A parallel plate capacitor of capacitance is connected to a battery of . A dielectric slab of dielectric constant 2 is now inserted into the space between plates of capacitor while the battery remain

The circuit shown in the figure consists of a charged capacitor of capacity and a charge of . At time , when the key is closed, the value of current flowing through the resistor is . The value of to t

A body of mass moves under a force of . It starts from rest and was at the origin initially. After , its new coordinates are . The value of is (Round off to the nearest integer)

mole of a perfect gas undergoes a cyclic process (see figure) consisting of the following processes. : Isothermal expansion at temperature , so that the volume is doubled from to and pressure changes

Given below are two statements: Statement I A second's pendulum has a time period of . Statement II It takes precisely one second to move between the two extreme positions. In the light of the above s

Choose the incorrect statement. A. The electric lines of force entering into a Gaussian surface provide negative flux. B. A charge q is placed at the centre of a cube. The flux through all the faces w

The relation between time and distance for a moving body is given as , where and are constants. The retardation of the motion is: (When v stands for velocity)[25 Jul 2021 Shift 2]

The velocity-displacement graph of a particle is shown in the figure. The acceleration-displacement graph of the same particle is represented by [18 Mar 2021 Shift 2]

Calculate the amount of charge on capacitor of . The internal resistance of battery is .

A small bob tied at one end of a thin string of length is describing a vertical circle, so that the maximum and minimum tension in the string are in the ratio . The velocity of the bob at the highest

Given below are two statements: one is labelled as Assertion and the other is labelled as Reason . Assertion A: Moment of inertia of a circular disc of mass ' ' and radius 'R' about axes (passing thro

As shown in the figure, a particle of mass is placed at a point . When the particle is slightly displaced to its right, it starts moving and reaches the point . The speed of the particle at is . (Take

An oil drop of radius with a density is held stationary under a constant electric field in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (T

A force is applied on an intersection point of plane and -axis. The magnitude of torque of this force about a point is ....... (Round off to the nearest integer)

In a typical combustion engine, the work done by a gas molecule is given , where is the displacement, is the Boltzmann constant and is the temperature. If and are constants, dimensions of will be [26

In the given potentiometer circuit arrangement, the balancing length is measured to be . When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing len

The voltage across the resistor in the given circuit is volt.The value of to the nearest integer is

A helicopter is flying horizontally with a speed v at an altitude h has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped?[

An inclined plane making an angle of with the horizontal is placed in a uniform horizontal electric field as shown in the figure. A body of mass and charge is allowed to slide down from rest at a heig

Match List I with List II. List-I List-II (a) Capacitance, C (i) (b) Permittivity of free space, (ii) (c) Permeability of free space, (iii) (d) Electric field, E (iv) Choose the correct answer from th

The time period of a satellite in a circular orbit of radius is . The period of another satellite in a circular orbit of radius is

A modern grand-prix racing car of mass is travelling on a flat track in a circular arc of radius with a speed . If the coefficient of static friction between the tyres and the track is , then the magn

1 mole of rigid diatomic gas performs a work of when heat is supplied to it. The molar heat capacity of the gas during this transformation is , The value of is .......... . universal gas constant

If one mole of the polyatomic gas is having two vibrational modes and is the ratio of molar specific heats for polyatomic gas , then the value of is

Consider the combination of two capacitors and , with , when connected in parallel, the equivalent capacitance is time the equivalent capacitance of the same connected in series. Calculate the ratio o

A container is divided into two chambers by a partition. The volume of first chamber is and second chamber is . The first chamber contain of gas at pressure and second chamber contain of gas at pressu

If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be , where is (Round off to the nearest integer) (

Two Carnot engines and B operate in series such that engine A absorbs heat at and rejects heat to a sink at temperature . Engine absorbs half of the heat rejected by Engine and rejects heat to the sin

An infinite number of point charges, each carrying charge, are placed along the -axis at . The total force on a point charge, placed at the origin, is . The value of to the nearest integer, is .......

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process and are and respectively. Choose the correct option out of

A capacitor of is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is........... .

A rubber ball is released from a height of above the floor. It bounces back repeatedly, always rising to of the height through which it falls. Find the average speed of the ball. (Take, ) [17 Mar 2021

A heat engine has an efficiency of . When the temperature of sink is reduced by , its efficiency get doubled. The temperature of the source is :

An object of mass collides with another object of mass , which is at rest. After the collision, the objects move with equal speeds in opposite direction. The ratio of the masses is

A refrigerator consumes an average power to operate between temperature to . If there is no loss of energy,then how much average heat per seconddoes it transfer?

A body of mass 2 kg moving with a speed of 4 m/s. makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The spe

Consider two satellites and with periods of revolution and respectively, revolving around a planet in circular orbits. The ratio of angular velocity of satellite to the angular velocity of satellite i

The centre of a wheel rolling on a plane surface moves with a speed . A particle on the rim of the wheel at the same level as the centre will be moving at a speed . Then the value of is _______.

The length of a metal wire is , when the tension in it is and is when the tension is . The natural length of the wire is :

A ball of mass , moving with a velocity of , collides with a spring of length and force constant . The length of the compressed spring is . The value of to the nearest integer, is

is the time period of a simple pendulum at aplace. If the length of the pendulum is reduced to times of its initial value, the modified timeperiod is :

A steel rod of length is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so that the rod falls under gravity. Ignoring the friction due

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A Body having mass moving with speed has head-on collision elastically with another bod

Two solids and of mass and respectively are moving with equal linear momentum. The ratio of their kinetic energies will be , so the value of A will be .......... .

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surfac. The acceleration of the block with respect to the wedge is [Given, ] Assume all the surfaces shown

In the experiment of Ohm's law, a potential difference of is applied across the end of a conductor of length and diameter of . The measured current in the conductor is . The maximum permissible percen

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. Th

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density: [27 Aug 2021 Shift 2]

A planet revolving in elliptical orbit has I. a constant velocity of revolution II. has the least velocity when it is nearest to the Sun III. its areal velocity is directly proportional to its velocit

When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is

Consider a uniform wire of mass and length . It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of resistance is connected across . Calculate the current through the galvanometer when a potential differe

A cylindrical container of volume contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is . The pressure of the mixture of gases is [Take, gas constant

Time period of a simple pendulum is . The time taken to complete oscillations starting from mean position is . The value of is ......... .

A steel rod with and of length and area of cross-section is heated from to without being allowed to extend. The tension produced in the rod is , where the value of x is .......... .

A reversible heat engine converts one-fourth of the heat input into work. When the temperature of the sink is reduced by , its efficiency is doubled. The temperature in kelvin of the source will be ..

The root mean square speed of molecules of a given mass of a gas at and 1 atmosphere pressure is . The root mean square speed of molecules of the gas at and 2 atmosphere pressure is . The value of wil

A body of mass m dropped from a height h reaches the ground with a speed of . The value of workdone by the air-friction is

For an ideal heat engine, the temperature of the source is . In order to have efficiency the temperature of the sink should be ...... . (Round off to the nearest integer)

Time period of a simple pendulum is inside a lift, when the lift is stationary. If the lift moves upwards with an acceleration , then the time period of pendulum will be

An electric appliance supplies heat to the system. If the system delivers a power of . How long it would take to increase the internal energy by ?

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is

First, a set of n equal resistors of each are connected in series to a battery of emf and internal resistance . A current / is observed to flow. Then, the n resistors are connected in parallel to the

Statement I A cyclist is moving on an unbanked road with a speed of and takes a sharp circular turn along a path of radius of without reducing the speed. The static friction coefficient is . The cycli

A stone is dropped from the top of a building. When it crosses a point below the top, another stone starts to fall from a point below the top. Both stones reach the bottom of building simultaneously.

Consider a frame that is made up of two thin massless rods and as shown in the figure. vertical force of magnitude is applied at point of the frame.

A system consists of two types of gas molecules and having same number density . The diameter of and are and respectively. They suffer collision at room temperature. The ratio of average distance cove

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure. The potential energy U(x) versus time (t) plot of the particle is correctly shown in

A cylindrical wire of radius and conductivity is subjected to an electric field of . The expected value of current in the wire will be . The value of is .......... .

If E and H represent the intensity of electric field and magnetising field respectively, then the unit of E / H will be [27 Aug 2021 Shift 1]

A body of mass ' ' is launched up on a rough inclined plane making an angle of with the horizontal. The coefficient of friction between the body and plane is if the time of ascent is half of the time

Two travelling waves produces a standing wave represented by equation. The node closest to the origin in the region will be at x is ......... .

A mass hangs on a massless rod of length which rotates at a constant angular frequency. The mass moves with steady speed in a circular path of constant radius. Assume that the system is in steady circ

A particle executes simple harmonic motion represented by displacement function as If the position and velocity of the particle at are and respectively, then its amplitude is where the value of is ___

Given below are two statements: Statement I In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II In a diatomic molecule, the rotational energ

Five identical cells each of internal resistance and emf are connected in series and in parallel with an external resistance R. For what value of R, current in series and parallel combination will rem

Each side of a box made of metal sheet in cubic shape is at room temperature , the coefficient of linear expansion of the metal sheet is . The metal sheet is heated uniformly, by a small temperature ,

Four identical hollow cylindrical columns of mild steel support a big structure of mass . The inner and outer radii of each column are and , respectively. Assuming, uniform local distribution, calcula

Two small drops of mercury each of radius coalesce to form a single large drop. The ratio of total surface energy before and after the change is :