Previous Year Questions
309 questions — organised by subject with solutions and explanations.
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Two vectors and have equal magnitudes.The magnitude of 'n' times themagnitude of . The angle between and is :
Let and The value of is:
In the cube of side 'a' shown in the figure, thevector from the central point of the face ABODto the central point of the face BEFO will be:
Two masses m and are connected at the two ends of a massless rigid rod of length . The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system(see figure).
The elastic limit of brass is .what should be the minimum diameter of a brass rod if it is to support a 400 N Load without exceeding its elastic limit?
Water from a tap emerges vertically downwards with an initial speed of .the cross-sectional area of the tap is .Assume that the pressure is constant throughout the stream of water and that the flow is
A 200Ω resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be :
A smooth wire of the length is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB ,
A stationary source emits sound waves of frequency 500Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz ad 530Hz. Their respective speeds are,in
Four point charges –q, +q, +q and –q are placed on y-axis at y = 2d, y = -d, y = +d and y = +2d, respectively. The magnitude of the electric field E at a point on the x –axis at x = D, with D>>d, will
The specific heats, and of a gas of diatomic molecules, A, are given (in units of ) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21 If they are
In the figure shown, after the switch 'S' is turnedfrom position 'A' to position 'B', the energydissipated in the circuit in terms of capacitance'C' and total charge 'Q' is:
The gas mixture constists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total inernal energy of the system is:
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as then the radius of gyration of the disc about its axis passing through th
A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change is velocity of the particle, when it moves through an angle of 60° around the centre of
The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane : (i) a ring of radius R, (ii) a solid cylinder of radius and (iii) a solid sphere of radius
A particle of mass ‘m’ is moving with speed ‘ ’and collides with a mass ‘2m’ moving with speed ‘ ’ in the same direction. After collision, the first mass is stopped completely while the second one spl
Two sources of sound and produce sound waves of same frequency 660 Hz. A listener is moving from source towards v with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s.
In the circuit , the potential difference betweenA and B is :
A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is and that of the outer cylinder is .
The ratio of the weight of a body on the Earth’s surface to that on the surface of a planet is 9 : 4 , the mass of the planet is th of that of the Earth. If ‘R’ is the radius of the Earth, what is the
Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers and respectively, then:
A mixture of 2 moles of helium gas (atomic mass= 4 u), and 1 mole of argon gas (atomic mass= 40 u) is kept at 300 K in a container. The ratio of their rms speeds , is close to [9-Jan-2019 Shift 1]
A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf ε and internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length AJ at
When the switch S, in the circuit shown, isclosed, then the value of current i will be : [9-Jan-2019 Shift 1]
Determine the electric dipole moment of thesystem of three charges, placed on the verticesof an equilateral triangle, as shown in thefigure:
A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD)
Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularl
Water flows into a large tank with flat bottom at the rate of . Water is also leaking out of a hole of area 1 at its bottom. If the height of the water in the tank remains steady, then this height is:
Figure shows charge (q) versus voltage (v) graph for series and parallel combination of two given capacitors . The capacitances are :
The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river s
To mop-clean a floor, a cleaning machinepresses a circular mop of radius R verticallydown with a total force F and rotates it with aconstant angular speed about its axis. If theforce F is distributed
Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of
Ship A is sailing towards north-east with velocity km/hr where points east and north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will b
A parallel plate capacitor is of area 6 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants , = 10, = 12 and = 14. The di
The force of interaction between two atoms is given by F = αβ exp ; where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is :[11
A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it h
A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The siring is set into vibration using an external vibrator of frequency 100 Hz. The separation between s
Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, and which of the following is correct?[12 Apr 2019 Shift 2]
If the angular momentum of a planet of massm, moving around the Sun in a circular orbitis L, about the center of the Sun, its arealvelocity is : [9-Jan-2019 Shift 1]
Two equal resistance when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consu
A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120dB in intensity sound? [Given reference intensity of sound as ]
In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation of its resistance R with length l is α . Two equal resistances are connected as shown in the figure.
Seven capacitors, each of capacitance 2 µF, areto be connected in a configuration to obtain aneffective capacitance of µF. Which ofthe combinations, shown in figures below, willachieve the desired val
A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A,as shown in the figure. The point A is at height h from point B. The particle slides along the frict
Two stars of masses 3 × kg each, and at distance 2 × m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order t
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :
Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R = 8.3 J/mol K)
A rod of length 50cm is pivoted at one end. It is raised such that if makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal
A person standing on an open ground hears thesound of a jet aeroplane, coming from north atan angle 60° with ground level. But he findsthe aeroplane right vertically above his position.If υ is the spe
Two materials having coefficients of thermal conductivity ‘3K’ and ‘K’ and thickness ‘d’ and ‘3d’, respectively, are joined to forma slab as shown in the figure. The temperatures of the outer surfaces
A satellite of mass M is in a circular orbit ofradius R about the centre of the earth. Ameteorite of the same mass, falling towards theearth, collides with the satellite completelyinelastically. The s
A galvanometer of resistance 100 has 50 divisions on its scale and has sensitivity of 20 / division. It is to be converted to a voltmeter with three ranges, of 0-2V, 0- 10 V and 0-20V. The appropriate
A particle starts from the origin at time t = 0 andmoves along the positive x-axis. The graph ofvelocity with respect to time is shown in figure. Whatis the position of the particle at time t = 5s ? [
A particle undergoing simple harmonic motionhas time dependent displacement given by x (t) = A sin . The ratio of kinetic to potential energy of this particle at t = 210 s will be :
Charges –q and +q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP
Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of and specific heat of while liquid in B has density of and sp
A block of mass m, lying on a smoothhorizontal surface, is attached to a spring (ofnegligible mass) of spring constant k. The otherend of the spring is fixed, as shown in thefigure. The block is inita
An ideal gas occupies a volume of 2m3 at a pressure of 3 × 106 Pa. The energy of the gas is:
The mass and the diameter of a planet are threetimes the respective values for the Earth. Theperiod of oscillation of a simple pendulum onthe Earth is 2s. The period of oscillation of thesame pendulum
A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled
Three Carnot engines operate in series between a heat source at a temperature and a heat sink at temperature (see figure). There are two other reservoirs at temperature , and , as shown, with > > > .
There is a uniform spherically symmetricsurface charge density at a distance R0 from theorigin. The charge distribution is initially at restand starts expanding because of mutualrepulsion. The figure
An alpha-particle of mass m suffers 1-dimensional elastic coolision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of th
A wooden block floating in a bucket of water has of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of
Four particles A, B, C and D with masses are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is
When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by .The heat required to produce the same change in temperature, at a constant pressure is:
A thin smooth rod of length L and mass M is rotating freely with angular speed about an axis perpendicular to the rod and passing through its centre. Two beads of mass m and negligible size are at the
A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the oute
A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x
A plane is inclined at an angle with respect to the horizontal. A particle is projected with a speed u=2m/s from the base of the plane, making an angle with respect to the plane as shown in the figure
The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?[10 Ja
The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5µm diameter of wire is :[12 Jan 2019 Shift 1]
A force acts on a 2 kg object so that its position is given as a function of time as x = + 5. What is the work done by this force in first 5 seconds ?
The bob of a simple pendulum has mass 2 g and a charge of . It is at rest in a uniform horizontal electric field of intensity 2000 V/ m. At equilibrium, the angle that the pendulum makes with the vert
A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude .If the person stands up when the swing passes through its lowest point, the work done by him, assuming tha
The electric field in a region is given by , where E is in and x is in metres. The values of constants are A=20 SI unit and B=10 SI unit. If the potential at is and that at is , then is:
A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/ K mole]
A soap bubble, blown by a mechanical pump at themough of a tube, increases in volume, with time,at a constant rate. The graph that correctly depictsthe time dependence of pressure inside the bubbleis
Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water =1000 kg/ , coefficient of vi
Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others’ gravitational field in a circu
In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start from rest and travel with co
Space between two concentric conducting spheres of radii a and b (b>a) is filled with a medium of resistivity .The resistance between the two spheres will be:
Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of V/ m. The plate area is . What is the dielectric constant if the capacitance is 15 pF ?
The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as has the colour code ( Orange, Red, Brown). The resistors and are 80 Ω and 40 Ω respectively. Assuming that the
a moving Coil galvanometer allows a full scale current A.A series resistance of 2 MΩ is required to convert the above galvanometer into a voltmeter of range 0-5V. Therefore the value of shunt resistan
A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person
Charge is distributed within a sphere of radius Rwith a volume charge density ρ (r) = , where A and a are constants. If Q is the total chargeof this charge distribution, the radius R is :
A solid sphere, of radius R acquires a terminal velocity when falling (due t gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres.
A ball is thrown upward with an initial velocity from the surface of the earth. the motion of the ball is affected by a drag force equal to ( where m is mass of the ball V is its instaneous velocity a
A body is projected at t = 0 with a velocity 10 at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1s is R. Neglecting air resistance and taking acceleration due
A simple harmonic motion is represented by: y = 5(sin3πt+ cos3πt) cm The amplitude and time period of the motion are:
A current of 5A passes through a copper conductor (resistivity= Ωm) radius of cross section 5mm.Find the mobility of the charges if their drift velocity
The time dependence of the position of a particle of mass m=2 is given by . Its angular momentum, with respect to the origin, at time t=2 is:
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational sp
A particle executes simple harmonic motion withan amplitude of 5 cm. When the particle is at 4 cmfrom the mean position, the magnitude of itsvelocity in SI units is equal to that of its acceleration.T
A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and when in contact with ice. What is the temperature of an object in 0 °C, if this thermometer
In the circuit shown, find C if the effectivecapacitance of the whole circuit is to be 0.5 µF.All values in the circuit are in µF.
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it r
An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the t
Let a total charges 2 Q be distributed in a sphere of radius R, with the charge density given by , where r is the distance from the centre. Two charges A and B, of each are placed on diametrically opp
An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is C.m. What is the potential energy of the electric dipole ?
The magnitude of torque on a particle of mass1kg is 2.5 Nm about the origin. If the force actingon it is 1 N, and the distance of the particle fromthe origin is 5m, the angle between the force andthe
In the given circuit the internal resistance of the18 V cell is negligible. If = 400 Ω, = 100 Ωand = 500 Ω and the reading of an ideal voltmeteracross is 5V, then the value will be :
A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound in air by resonance tube method. Resonance is observed to occur at two successive length of the air column, and
Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the
Young’s moduli of two wires A and B are in the ratio 7:4. Wire A is 2m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, th
A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights and on the
When M1 gram of ice at (specific heat = 0.5 cal is added to is added to of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in is:
An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5Ω. The value of R, to give a potential difference of 5 mV acros
Three particles of masses and are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The co-ordinates of the centre of mass will be:
In the circuit shown, a four–wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r= 0.01 Ω/cm If an ideal voltm
A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle . It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, el
Half mole of an ideal monoatomic gas is heated at constant pressure of 1atm from 20 °C to 90°C. Work done by gas is close to : ( Gas constant R = 8.31 J /mol.K)
A rigid massless rod of length 3l has twomasses attached at each end as shown in thefigure. The rod is pivoted at point P on thehorizontal axis (see figure). When released frominitial horizontal posit
A parallel plate capacitor has 1µF capacitance. One of its two plates is given +2µC charge and the other plate, +4µC charge. The potential difference developed across the capacitor is:
Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured is SI units. The tension in the string is :
A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling with out slipping, angular acceleration of the cylinder is:
The displacement of a damped harmonic oscillator is given by Here t it is in seconds.The time taken for its amplitude of vibration to drop to half of its initial value is close to:
One mole of an ideal gas passes through a process where pressure and volume obey the relation / .here and are constants, calculate the change in the temperature of the gas if its volume changes from t
One kg of water at , is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of . The rms voltage in the mains is . Ignoring heat loss from the kettle, time
In SI units, the dimensions of is[8 Apr 2019 Shift 1]
A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and change q, The time period of the pendulum i
A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended
The trajectory of a projectile near the surface of the earth is given as . If it were launched at an angle with speed then .[12 Apr 2019 Shift 1]
Determine the charge on the capacitor in the following circuit:
A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5 m. When released, it slips off the table in a very short time s, remaining ess
A system of three charges are placed as shown in the figure: If D > > d, the potential energy of the system is best given by:
A test particle is moving in a circular orbit in the gravitational field produced by a mass density . Identify the correct relation between the radius R of the particle’s orbit and its period T:
In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is incresed b
Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bu
For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127ºC. At 2 atm pressure and at 227ºC, the rms speed of the molecules will be:
A thin disc of mass M and radius R has mass per unit area where r is the distance from its center . Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane
The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circu
A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut–off, the coordinates of the centre of mass of the remaining portio
A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11V is connected across it is :
A particle starts from origin O from rest and moves with a uniform acceleration along the positive x– axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v
A carbon resistance has a following colourcode. What is the value of the resistance ?
The density of a material in SI units is 128 kg . In certain units in which the unit of length is 25 cm and the unit of mass is 50 g, the numerical value of density of the material is :[10 Jan 2019 Sh
The charges Q + q and +q are placed at thevertices of a right-angle isosceles triangle asshown below. The net electrostatic energy ofthe configuration is zero, if the value of Q is :
Two point charges and are placed on the x-axis at x = l m and x = 4 mrespectively. The electric field (in V/m) at apoint y = 3 m on y-axis is,
A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of θ , where θ is the angle by which it has rotated, is given as 2 . If
The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0
Two particles A, B are moving on two concentric circles of radii and with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure : The relative velocity at t
For a uniformly charged ring of radius R, theelectric field on its axis has the largestmagnitude at a distance h from its centre. Thenvalue of h is : [9-Jan-2019 Shift 1]
A cubic block of side 0.5m floats on water with 30% of its volume under water. what is the maximum weight that can be put on the block without fully submerging it under water?{Take, density of water=
A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move th
In an experiment , the resistance of a material is plotted as a function of temperature ( in some range) .As shown in the figure , It is a straight lineone may conclude that:
A capacitor with capacitance is charged to . If the plates are pulled apart to reduce the capacitance to , how much work is done?
The position of a particle as a function of time t, is given by where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be:[9 Apr 2019 Shift 2]
A body of mass 2 kg makes an elastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body
A particle is moving with a velocity = K , where K is a constant. Thegeneral equation for its path is: [9-Jan-2019 Shift 1]
A liquid of density ρ is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh. 50% of the liquid passes through the mesh unaffected. 25% looses all of its momentum and 25% com
Following figure shows two process A and B for a gas. If and are the amount of heat absorbed by the system in two cases, and and are changes in internal energies, respectively, then:
A body of mass 1 kg falls freely from a height of 100 m on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × N/m. The body sticks to the platform and the spring's
In the figure shown, what is the current (in Ampere) drawn from the battery? You are given:
A travelling harmonic wave is represented by the equation y (x, t) = sin (50 t + 2x), where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave? The
Two Coaxial discs, having moments of inertia and are rotating with respective angular velocity and , about their common axis.They are brought in contact with each other and thereafter they rotate with
A submarine experience a pressure of at a depth of in a sea. When it goes further to a depth of .it experiences a pressure of .then is approximately(density of water and acceleration due to gravity ):
A moving coil galvanometer has resistance 50Ω and it indicates full deflection at 4 mA current. A voltmeter is made using this galvanometer and a 5 kΩ resistance. The maximum voltage, that can be meas
A satellite is moving with a constant speed vin circular orbit around the earth. An object ofmass 'm' is ejected from the satellite such thatit just escapes from the gravitational pull of theearth. At
If Surface tension (S), Moment of Inertia (I) and Planck's constant (h), were to be taken as the fundamental units, the dimensional formula for Linear momentum would be:[8 Apr 2019 Shift 2]
The position vector of the centre of mass cm of an symmetric uniform bar of negligible area of cross-section as shown in figure is :
If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be :-[11 Jan 2019 Shift 2]
Expression for time in terms of G (universalgravitational constant), h (Planck constant) andc (speed of light) is proportional to :[9 Jan 2019 Shift 2]
A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle's apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immers
A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of diele
A copper wire is stretched to make it 0.5%longer. The percentage change in its electricalresistance if its volume remains unchanged is : [9-Jan-2019 Shift 1]
In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured by using a watch of 1 second least count. The mean value of time taken
A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by
A spaceship orbits around a planet at a height of 20km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions mad
A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the mjnimum energy that the launcher should have
Two satellites, A and B, have masses m and 2mrespectively. A is in a circular orbit of radius R, andB is in a circular orbit of radius 2R around the earth.The ratio of their kinetic energies, , is:
An L-shaped object, made of thin rods ofuniform mass density, is suspended with astring as shown in figure. If AB = BC, and theangle made by AB with downward vertical isθ, then : [9-Jan-2019 Shift 1]
Two Particles , of masses M and 2M moving , as shown,with speeds of 10m/s and 5m/s , collied elastically at the origin. After the collision , they move along the indicated directions with speeds and ,
A moving coil galvanometer, having a resistance G, produces full scale deflection when a current flows through it. This galvanometer can be converted into (i) an anometer of range 0 to by connecting a
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre 'O' and can rotate fr
In an experiment, brass and steal wires of length 1 m each with areas of cross section are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and
The position co-ordinates of a particle movingin a 3-D coordinate system is given by x = a cosωt y = a sinωt and z = aωt The speed of the particle is :[9 Jan 2019 Shift 2]
A particle which is experiencing a force, given by = - 12 , undergoes a displacement of = . If the particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy
A particle is moving with speed along positive . Calculate the speed of the particle at time (assume that the particle is origin at )[12 Apr 2019 Shift 2]
A thermally insulated vessel contains 150 g of water at 0°C. Then the air from the vessel is pumped out adiabatically. A fraction of water turns into ice and the rest evaporates at 0°C itself. The mas
Two blocks A and B of mass and are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also . The maximum force F tha
A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine (B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a refle
In the given circuit,an ideal voltmeter connected across the 10Ω resistance reads 2V. The internal resistance r, of each cell is
Two kg of a monoatomic gas is at a pressure of 4 × N/ . The density of the gas is 8 kg / . What is the order of energy of the gas due to its thermal motion ?
For the given cyclic process CAB as shown fora gas, the work is :
Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dielectrics,
A particle moves from the point (2.0 + 4.0 ) m , at t = 0 , with an initial velocity (5.0 + 4.0 ) . It is acted upon by a constant force whichproduces a constant acceleration (4.0 + 4.0 ) . What is th
The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0° respectively. it is observe
An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature, 300 K. The mean time between two successive collisions is 6 × s. If the pressure is doubled and temperature is increased to
A metal of mass 5 g and radius 1 cm is fixed to a thin stick AB if negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about
A charge Q is distributed over three concentricspherical shells of radii a, b, c (a < b < c ) suchthat their surface charge densities are equal toone another. The total potential at a point atdistance
Three blocks A, B and C are lying on a smoothhorizontal surface, as shown in the figure. A andB have equal masses, m while C has mass M.Block A is given an brutal speed v towards Bdue to which it coll
A pendulum is executing simple harmonic motion and its maximum kinetic energy is . If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the fir
In the figure shown below, the charge on the leftplate of the 10 µF capacitor is –30 µC. ?The chargeon the right plate of the 6 µF capacitor is :
The resistive network shown below is connected to a D. C. source of 16 V. The power consumed by the network is 4 Watt. The value of R is.
A metal wire of resistance 3Ω is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an an
Temperature difference of 120°C is maintained between two ends of a uniform rod AB of length 2L. Another bent rod PQ, of same crosssection as AB and length , is connected across AB (See figure). In st
In a conductor, if the number of conduction electrons per unit volume is and mean free time is 25 fs (femto second), it’s approximate resistivity is:
To verify Ohm’slaw, a student connects the voltmeter across the battery as, shown in the figure. The measured voltage is plotted as a function of the current, and the following graph is obtained. If i
For the circuit shown, with and the potential difference between the points ’a' and ‘b’ is approximately (in V) :
A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The man pushes his son so that he starts moving at a speed of 0.70 with respect to the man. Th
A volume cylinder is field with 1 mol gas room temperature (300k) The molicular diameter of ,and its root mean square speed , are found to be 0.3 nm and 200m/s, respectively.what is the average collis
In the given circuit, the charge on 4µF capacitor will be:
In the given circuit the cells have zero internalresistance. The currents (in Amperes) passingthrough resistance , and respectively, are:
The area of a square is The area of 7 such squares taking into account the significant figures is:[9 Apr 2019 Shift 2]
The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to: [Boltzmann Constant J/K Avogadro Number /kg Radius of Earth :
A parallel plate capacitor with plates of area 1m2each, area t a separation of 0.1 m. If the electricfield between the plates is 100 N/C, the magnitudeof charge each plate is :- (Take = 8.85 × )
In the density measurement of a cube, the mass and edge length are measured as and , respectively. The error in the measurement of density is:[9 Apr 2019 Shift 1]
A 2 W carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is :
A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α/ °C. It is observed that an external compressive force F, is app
A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equal Y. When this rod is heated by temperature T and simultaneously subjected to a net
In a meter bridge experiment the circuit diagram and the corresponding observation table are shown in figure . Which of the readings is inconsistent ?
n moles of an ideal gas with constant volume heat capacity Cv undergo an isobraric expansion by certain volume . The ratio of the work done in the process, to the heat supplied is :
The charge on a capacitor plate in a circuit, as afunction of time, is shown in the figure:What is the value of current at t = 4 s ?
A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of and is converted into a uniform disc of radius 2R. The second part is converted into a uniform sol
A heat source at T= K is connected to another heat reservoir at T = K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 , the energy flux through it in the stea
A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d ≪ a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in t
A passenger train of length 60m travels at aspeed of 80 km/hr. Another freight train oflength 120 m travels at a speed of 30 km/hr.The ratio of times taken by the passenger trainto completely cross th
A musician using an open flute of length 50 cm produces second harmonic sound waves. A person runs towards the musician from another end of a hall at a speed of 10 km/h. If the wave speed is 330 m/s,
The number density of molecules of a gas depends on their distance r from the origin as, . Then the total number of molecules is proportional to
At ,a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from to it regains its original length of 0.2 m. The value
A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harm
A progressive wave travelling along the positive x – direction is represented by . Its snapshot at t = 0 is given in the figure. For this wave, the phase ϕ is
A rigid diatomic ideal gas undergoes anadiabatic process at room temperature,. Therelation between temperature and volume ofthis process is = constant, then x is :
A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximat
The actual value of resistance R, shown in the figure is 30Ω. This is measured in an experiment as shown using the standard formula R = , where V and I are the readingsof the voltmeter and ammeter, re
A parallel plate capacitor with square plates is filled with four dielectrics of dielectric constants arranged as shown in the figure. The effective dielectric constant K will be :
A Carnot engine has an efficiency of . When by , its efficiency is doubled. The temperature of the source and the sink are, respectively,
A spring whose unstretched length is has a force constant The spring is cut into two pieces of unstretched lengths and where, and is an integer. The ratio of the corresponding force constants, and wil
A particle of mass m is moving in a straight linewith momentum p. Starting at time t = 0, a forceF = kt acts in the same direction on the movingparticle during time interval T so that itsmomentum chan
In free space, a particle A of charge is held fixed at a point P. Another particle B of the same charge and mass is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance
The galvanometer deflection, when key is closed but is open, equals (see figure). On closing also and adjusting to 5W, the deflection in galvanometer becomes . The resistance of the galvanometer is, t
Ice at –20° C os added tp 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Spe
If gas molecules each of mass kg collide with a surface (perpendicular to it) elastically per second over an area 1 with a speed m/s, the pressure exerted by the gas molecules will be of the order of
A body of mass m1 moving with an unknown velocity of , undergoes a collinear collision with a body of mass moving with a velocity . After collision, and move with velocities of and , respectively. If
The top of a water tank is open to air and its water level is maintained. It is giving out 0.74 water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the o
An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibri
A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If and are the values of the time taken by it to hit the target
A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J. The gas absorbs 250 J of heat along
A heavy ball of mass M is suspended from the ceiling of a car by a light string of mass m (m ≪ M). When the car is at rest, the speed of transverse waves in the string is 60 . When the car has acceler
A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is of the material of the bob. If the bob is inside
An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is , m is its mass and is Boltzman constant, then its temperature will
In a Wheatstone bridge (see fig.), Resistances P and Q are approximately equal. When R = 400 Ω, the bridge is equal. When R = 400 Ω, the bridge is balanced. On inter-changing P and Q, the value of R,
Moment of inertia of a body about a given axis is . Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of must be applied about the axis
If ‘M’ is the mass of water that rises in a capillary tube of radius ‘r’, then mass of water which will rise in a capillary tube of radius ‘2r’ is:
The moment of inertia of a solid sphere, about anaxis parallel to its diameter and at a distance of xfrom it, is I(x)'. Which one of the graphs representsthe variation of I(x) with x correctly ?
The resistance of the meter bridge AB is given figure is 4Ω. With a cell of emf ε = 0.5 V and rheostat resistance = 2 Ω the null point is obtained at some point J. When the cell is replaced by another
A satellite is revolving in a circular orbit at aheight h from the earth surface, such that h << Rwhere R is the radius of the earth. Assumingthat the effect of earth's atmosphere can beneglected the
A straight rod of length L extends from x = a to x = L + a. The gravitational force is exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + , is given by:
A wire of length 2L, is made by joining two wires A and B of same length but different radii r and 2r and made of the same material. It is vibrating at a frequency such that the joint of the two wires
A positive point charge is released from rest at a distance from a positive line charge with uniform density. The speed ( v) of the point charge, as a function of instantaneous distance r from line ch
A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 , from the ground. The bu
An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water a temperature of 8.4°C Calculate the specific heat of the
A point dipole is kept at the origin. The potential and electric field due to this dipole on the y – axis at a distance d are, respectively. (Take V = 0 at indignity)
A slob is subjected to two forces and of same magnitude F as shown in the figure. Force is in XY-plane while force acts along z-axis at the point . The moment of these forces about point O will be :
Two forces P and Q of magnitude 2F and 3F, respectively, are at an angle θ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle is :
A particle is executing simple harmonic motion(SHM) of amplitude A, along the x-axis, aboutx = 0. When its potential Energy (PE) equalskinetic energy (KE), the position of the particlewill be :
The pressure wave, , corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is On some other day when temperature is T, the speed of sound produced by the same bl
A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000Hz.what will be the apparent frequency of the source whe
In the formula and , have dimensions of capacitance and magnetic field, respectively. what are the dimensions of Y in SI units?[10 Apr 2019 Shift 2]
A wedge of mass M = 4m lies on a frictionless plane. A particle of mass mapproaches the wedge with speed . There is no friction between the particle andthe plane or between the particle and the wedge.
A string is wound around a hollow cylinder of mass 5 kg and radius 0.5 m. If the string is now pulled with a horizontal force of 40 N, and the cylinder is rolling without slipping on a horizontal surf
A particle of mass m is moving along a trajectory given by The torque,acting on the particle about the origin, at t=0 is :
A cylinder with fixed capacity of 67.2lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : [Given that R=8.31J ]
The value of acceleration due to gravity at Earth‘s surface is . The altitude above its surface at which the acceleration due to gravity decreases to , is close to (Radius of earth m )
A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in fig. Work done bv normal reaction on block in time t is :
A bullet of mass 20g has an initial speed of ,just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of , the speed of the bullet after emerging from the
A circular disc of mass M and radius R has two identical discs and of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axi
A simple pendulum of length 1 m is oscillating with an angular frequency 10 rad/s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1 rad/s and an amplitude
A string is clamped at both the ends and it is vibrating in its harmonic. The equation of the stationary wave is .The length of the string is: (All quantities are in SI units.)
A solid sphere of mass ‘M’ and radius ‘a’ is surrounded by a uniform concentric spherical shell of thickness 2a and mass 2M. The gravitational field at distance ‘3a’ from the centre will be:
A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that , what will be the tensile stress that would be developed in the wire?
A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What
The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11Hz is
Two electric dipoles, A, B with respectivedipole moments = - 4 and = - placed on the x - axis with a separation R , as shown in the figure The distance from A at which both of themproduce the same pot
The position vector of a particle changes with time according to the relation . What is the magnitude of the acceleration at t = 1?[9 Apr 2019 Shift 2]
A massless spring(k = 800 N/m), attached with a mass (500g) is completely immersed in 1 kg of water. The spring is stretched by 2cm and released so that it starts vibrating. What would be the order of
A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. When would be the heat energy absorbed by the gas, in this process?
The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4 × km) is and kinetic energy required for the satellite to be in a circular orbit at this height is .
Which of the following combination has the dimension of electrical resistance ( is the permittivity of vacuum and is the permeability of vacuum)?[12 Apr 2019 Shift 1]
A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum – height (p-h) diagram is:
Four equal point charges Q each are placed inthe xy plane at (0, 2), (4, 2), (4, –2) and (0, –2).The work required to put a fifth charge Q at theorigin of the coordinate system will be :
Three charges +Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, Ls zero, then value of q is : [9-Jan-2
In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 Ω resistor is connected in series with , the null point shifts by 10 c
A galvanometer having a resistance of 20 Ω and 30 divisions on both sides has figure of merit 0.005 ampere/division. The resistance that should be connected in series such that it can be used as a vol
The given graph shows variation (with distancer from centre) of :
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to dropto of the original amplitude is
A resistance is shown in the figure. Its valueand tolerance are given respectively by: [9-Jan-2019 Shift 1]
A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centred at orign. A point charge q is moving towards the ring along the z-axis and has speed The minimum value of v such
A block of mass is pushed in case and pulled in case , by a force , making an angle of with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is . The di
The parallel combination of two air filled parallel plate capacitors of capacitance C and nC is connected to a battery of voltage, V. When the capacitors are fully charged, the battery is removed and
In the given circuit diagram, the currents, = –0.3A, = 0.8 A and = 0.4 A, are flowing as shown. The currents and ,respectively, are :
When 100 g of a liquid A at 100°C is added to 50 g of a liquid B at temperature 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100 g of liquid A at 100°C is adde
A uniform metallic wire has a resistance of 18 Ω and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is :
A gas can be taken from A to B via two differentprocesses ACB and ADB When path ACB is used 60 J of heat flows into thesystem and 30 J of work is done by the system. Ifpath ADB is used work done by th
A thin circular plate of mass M and radius R has its density varying as with as constant and r is the distance from its center. The moment of Inertia of the circular plate about an axis perpendicular
Two Carrnot engines A and B are operated in series. The first one, A, receives heat at (= 600 K) and rejects to a reservoir at temperature . The second engine B receives heat rejected by the first eng
Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole as shown. In this case:
Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 ,is v. If the electron density in copper is 9 × / the value of v in mm/s is close to (Take charge of electron
A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is . If the speed of the train is reduced to 17 m/s, the frequenc
Two rods A and B of identical dimensions areat temperature 30°C. If A is heated upto 180°Cand B upto T°C, then the new lengths are thesame. If the ratio of the coefficients of linearexpansion of A and
The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:
Let l, r, c and v represent inductance, resistance,capacitance and voltage, respectively. Thedimension of in SI units will be:[12 Jan 2019 Shift 2]
A cell of internal resistance r drives current through an external resistance R. The power delivered by the cell to the external resistance will be maximum when:
A uniform cable of mass ‘M’ and length ‘L’ is placed on a horizontal surface such that its part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the wo
A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cy