Previous Year Questions
74 questions — organised by subject with solutions and explanations.
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Take the mean distance of the moon and the sun from the earth to be km and respectively. Their masses are and kg respectively. The radius of the earth is 6400 km. Let be the difference in the forces e
A thin , free to rotate in the vertical plane about the fixed end N , is held horizontal. When the end is released the speed of this end, when the rod makes an angle a with the horizontal, will be pro
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up[Main 8 April 2018]
A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20V. If a dielectric material of dielectric constant is inserted between the plates, the magnitude of the included char
A thin uniform bar of length and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2 v and respe
A given object takes n times more time to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the
A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is , how long will the charges take to travel a distance d ?
The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii)the time at which the car will cat
What an air bubble of radius rises from the bottom to the surface of a lake, its radius becomes . Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake woul
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of . There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading
Two moles of an ideal monoatomic gas occupies a volume V at 27°C . The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b)change in its internal energy.[Ma
The relative error in the determination of the surface area of a sphere isα. Then the relative error in the determination of its volume is :[Main 15 April 2018 S1]
A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants and c . Which
A capacitor is charged up to a voltage by connecting it to battery B through switch ( 1). Now is disconnected from battery and connected to a circuit consisting of two uncharged capacitors and through
In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and B is :[Main 15 April 2018 S1]
A proton of mass collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of with respect to each other. The m
A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are and fill half the circle. The angle θ between the radius vecto
A particle executes simple harmonic motion and is located at x=a, b and c at times and respectively. The frequency of the oscillation is :[Main 16 April 2018 S1]
The equivalent capacitance between A and B in the circuit given below, is[Main 15 April 2018 S1]
From a uniform circular disc of radius R and mass , a small disc of radius is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of th
Two cornot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature . Engine receives heat rejected by engine and in turn
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the power of R. If the period of rotation of the particles is T, then :[Main 8 Ap
The end correction of a resonance column is 1 cm. If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be :[Main 16 April 2018 S1]
A tuning fork vibrates with frequency 256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is )[Main 15
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :[Main 16 April 2018 S1]
Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :[Main 16 April 2018 S1]
A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius , and the othe
A body of mass 2 kg slides down with an acceleration of on a rough inclined plane having a slope of . The external force required to take the same body up the plane with the same acceleration will be
In the following circuit, the switch S is closed at . The charge on the capacitor as a function of time will be given by [Main 16 April 2018 S1]
An oscillator of mass M is at rest in its equilibrium position in a potential A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This pro
A solid ball of radius has a charge density given by for . The electric field outside the ball is :
A galvanometer with its coil resistance 25 Ω requires a current of 1 mA for its full deflection. In order to construct an ammeter to read up to a current of 2 A, the approximate value of the shunt res
Three concentric metal shells A,B and C of respective radii a,b and c have surface charge densities and respectively. The potential of shell B is :[Main 8 April 2018]
One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :[Main 16 April 2018 S1]
In a meter bridge, as shown in the figure, it is given that resistance and that the balance is obtained at a distance 39.5 cm from end A (by Jockey J). After interchanging the resistances X and Y, a n
The percentage errors in quantities P, Q,R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity The maximum percentage error in the value of A will be :[Main 16 April
The mass of a hydrogen molecule is kg.If hydrogen molecules strike, per second, a fixed wall of area at an angle of 45° to the normal, and rebound elastically with a speed of m/s, then the pressure on
A man in a car at location Q on a straight highway is moving with speed v. He decides to reach a point in qa field at a distance from the highway (point m ) as shown in the figure. Speed of the car in
A small soap bubble of radius 4 cm is trapped inside another bubble of radius6 cm without any contact. Let be the pressure inside the inner bubble and the pressure outside the outer bubble. Radius of
A body takes 10 minutes to cool from to . The temperature of surroundings is constant at . Then, the temperature of the body after next 10 minutes will be approximately :
As shown in the figure, forces of each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm , shifting the upper face parallel to itself by 0.5 cm . If the side of
An automobile, travelling at , can be stopped at a distance of by applying brakes. If the same automobile is travelling at , the minimum stopping distance, in metres, is (assume no skidding)[Main 15 A
One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature,27°C. The work done on the gas will be :[Main 15 April 2018 S1]
A uniform rod AB is suspended from a point X, at a variable distance x from A,as shown. To make the rod horizontal, a mass m is suspended from its end A. Aset of (m,x) values is recorded. The appropri
A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area of floats on the surface of the liquid, covering en
In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52cm of the potentiometer wire. If the cell is shunted by
A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220V, a steady current of 2 A passes in it and temperature is 500°C more than room temperature.What
Two simple harmonic motions, as shown below, are at right angles. They are combined to form lissajous figures. Identify the correct match below :ParametersCurve(1) Line(2) Parabola(3) Circle(4) Ellips
A charge Q is placed at a distance a/2 above the centre of the square surface of edge a as shown in the figureThe electric flux through the square surface is :[Main 15 April 2018 S1]
The value closest to the thermal velocity of a Helium atom at room temperature ( 300 K ) in is :
The density of a material in the shape of a cube is determined by measuring three sides ofthe cube and its mass. If the relative errors in measuring the mass and length arerespectively 1.5% and 1%, th
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting sphere, C
A Carnot’s engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerat
A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is and its Young’s modulus is Pa.What will be the fundamental frequency of
On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10cm. The resistance of their series combination is 1kΩ. How much was the resistance on the left slot before
Two sitar strings, A and B, playing the note‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to dec
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of What is the force constant of the bonds connecting one atom with the order ? (Mole wt. of silver = 1
Two particles of the same mass m are moving in circular orbits because of force,given by The first particle is at a distance , and the second, at . The best estimate for the ratio of kinetic energies
In a collinear collision, a particle with an initial speed strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnit
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through th
A parallel plate capacitor with area and separation between the plates 1.5 cm , is connected across a battery of emf V . If the force of attraction between the plates is , the value of V is approximat
Two masses and , connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that
A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by :[Main 15 April 2018 S1]
A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at , with an amplitude A. An electric field
In a circuit for finding the resistance of agalvanometer by half deflection method,a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60µA/division. In t
The relative uncertainty in the period of a satellite orbiting around the earth is . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the e
A body of mass m starts moving from rest along x-axis so that its velocity varies as where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on th
A particle is moving in a circular path of radius a under the action of an attractive potential . Its total energy is :[Main 8 April 2018]
5 beats/second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m . The frequency of the fork will be
Two batteries with e.m.f. 12V and 13V are connected in parallel across a load resistor of 10Ω . The internal resistances of the two batteries are 1Ω and 2Ω respectively. The voltage across the load li
Two moles of helium are mixed with n moles of hydrogen. If for the mixture, then the value of n is :[Main 16 April 2018 S1]