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Home » IIT-JEE MAIN:PHYSICS FULL SYLLABUS TEST

01/06/2020 / Leave a comment

Important Instructions:

(1) There is only one correct option.

(2) Duration of Test is 1 Hour and Questions Paper Contains 30 Questions. The Max. Marks are 120.

(3) Each correct answer carries 4 marks, while 1 mark will be deducted for every wrong answer. Guessing of answer reduces your effort.

1 / 30

What should be the maximum acceptance angle at the air core interface of an optical fibre if n_{1} and n_{1} are the refractive indices of the core and the cladding, respectively

2 / 30

A system of four gates is set up as shown. The ‘truth table’ corresponding to this system is :

3 / 30

The rectangular surface of area 8 cm × 4 cm of a black body at temperature 127°C emits energy E per second. If the length and breadth are reduced to half of the initial value and the temperature is raised to 327°C, the rate of emission of energy becomes

4 / 30

The transverse displacement y (x, t) of a wave is given by e^{-(ax2 + bt2 + 2√(ab)xt) }

This represents a:

5 / 30

How many degree of freedom the gas molecules have if under STP the gas density ρ=1.3 kg/m^{2} and the velocity of sound propagation in it is 330 m/sec

6 / 30

A stuntman plans to run across a roof top and horizontally jumps on to another roof 4.9 m below the first one and at a distance of 6.2 m away. What is the minimum velocity, he must have before the jump ?

7 / 30

A ball projected from ground at an angle of 45° just clears a wall in front. If point of projection is 4 m from the foot of wall and ball strikes the ground at a distance of 6 m on the other side of the wall, the height of the wall is :

8 / 30

The potential energy of a 1 kg particle free to move along the x-axis is given by V(x) = (x^{4}/4 - x^{2}/2) J. The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is

9 / 30

The radiation corresponding to 3→2 transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of 3 × 10^{-4} T. If the radius of thelargest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to:

10 / 30

A coil having n turns and resistance RΩ is connected with a galvanometer of resistance 4RΩ. This combination is moved in time t seconds from a magnetic field W_{1} weber to W_{2} weber. The induced current in the circuit is

11 / 30

A particle of mass m is under a potential v(x) = (1/2) k_{1}x^{2} for x > 0 and v(x) = k_{1}x^{2} for x < 0. When disturbed a little from the position x = 0, it will

12 / 30

Three charges of (+ 2q), (– q) and (– q) are placed at the corners A, B and C of the equilateral triangle of side a as shown in the given figure. Then the dipole moment of this combination is

13 / 30

A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is

14 / 30

If a tiny test charge, is placed in a cavity, a region in between the molecules of a dielectric, will experience a force equal to its charge times

15 / 30

Two batteries, two resistors and two condensers are connected as shown. The charge on 2μF capacitor is

16 / 30

In an A.C. circuit with voltage V and current I the power dissipated

17 / 30

A Carnot freezer takes heat from water at 0°C inside it and rejects it to the room at a temperature of 27°C. The latent heat of ice is 336 × 103 J kg^{-1}. If 5 kg of water at 0°C is converted into ice at 0°C by the freezer, then the energy consumed by the freezer is close to :

18 / 30

A hydrogen atom emits green light when it changes from n = 4 energy level to the n = 2 level. Which colour of light would the atom emit when it changes from n = 5 level to the n=2 level?

19 / 30

Torques τ_{1} and τ_{2} are required for a magnetic needle to remain perpendicular to the magnetic fields at two different places. The magnetic fields at the those places are B_{1} and B_{2} respectively; then ratio B_{1}/B_{2}

20 / 30

Radioactive material 'A' has decay constant '8 λ' and material 'B' has decay constant 'λ'. Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 1/e

21 / 30

The earth’s magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to 8 × 10^{22} Am^{2}, the value of earth’s magnetic field near the equator is close to (radius of the earth = 6.4 × 10^{6} m)

22 / 30

A satellite is revolving round the earth with velocity v. The minimum percentage increase in its velocity necessary for the escape of satellite will be

23 / 30

Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

24 / 30

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as :_{92}U^{235} + _{0}n^{1} → _{56}Ba^{141} + _{36}Kr^{92} + 3x +Q(energy), where three particles named x are produced and energy Q is released. What is the name of the particle x ?

25 / 30

Two fixed frictionless inclined planes making an angle 30° and 60° with the vertical are shown in the figure. Two blocks A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ?

26 / 30

The work function of a metallic surface is 5.01 eV, photoelectrons are emitted when light of wavelength 2000Å falls on it. The minimum potential difference required to stop the fastest photoelectrons (h = 4.14 × 10^{-15} eV–s)

27 / 30

A thin sheet of glass (μ = 1.5) of thickness 6 microns introduced in the path of one of interfering beams in a double slit experiment shifts the central fringe to a position previously occupied by fifth bright fringe. Then the wave length of the light used is

28 / 30

A particle of charge 16 × 10^{-16} C moving with velocity 10 ms^{-1} along x-axis enters a region where magnetic field of induction B is along the y-axis and an electric field of magnitude 10^{4} Vm^{-1} is along the negative z-axis. If the charged particle continues moving along x-axis, the magnitude of B is :

29 / 30

Inside a cylinder closed at both ends is a movable piston. On one side of the piston is a mass m of a gas, and on the other side a mass 2m of the same gas. What fraction of volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? The temperature is the same throughout.

30 / 30

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

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15/04/2020 / Leave a comment

At a specific temperature, the energy densities for a black body for three different wavelengths are 10, 19 and 7 units. For these wavelengths if the absorption coefficient of a body is respectively 0.8, 0.3 and 0.9 then the emissive powers of this body for these wavelengths are in the ratio

Two straight long conductors AOB and COD are perpendicular to each other and carry currents I_{1} and I_{2} respectively. The magnitude of the magnetic induction at a point P at a distance ‘a’ from the point O in a direction perpendicular to the plane ABCD is

56 tuning forks are so arranged in series that each fork gives 4 beats per sec with the previous one. The frequency of the last fork is 3 times that of the first. The frequency of the first fork is

For sky wave propagation of a 10 MHz signal, what should be the minimum electron density in ionosphere

In the Bohr model an electron moves in a circular orbit around the proton. Considering the orbiting electron to be a circular current loop, the magnetic moment of the hydrogen atom, when the electron is in n^{th} excited state, is :

The time taken by a body in sliding down a rough inclined plane of angle of inclination 45° is n times the time taken by the same body in slipping down a similar frictionless plane. The coefficient of dynamic friction between the body and the plane will be

Two slits separated by a distance of 1 mm are illuminated with red light of wavelength 6.5 ×10^{-7} m. The interference fringes are observed on a screen placed 1 m from the slits. The distance between third dark fringe & the fifth bright fringe is equal to

In a npn transistor 1010 electrons enter the emitter in 10^{-6} s. 4% of the electrons are lost in the base. The current transfer ratio will be

In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half- a degree (= 0.5°), then the least count of the instrument is:

A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A_{1}. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A_{2}. The ratio of A_{1}/A_{2} is

The mutual inductance of a pair of coils, each of N turns, is M henry. If a current of I ampere in one of the coils is brought to zero in t second, the emf induced per turn in the other coil, in volt, will be

From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path. The relation between H, u and n is:

The counting rate observed from a radioactive source at t = 0 second was 1600 counts per second and at t = 8 seconds it was 100 counts per second. The counting rate observed, as counts per second at t = 6 seconds will be

A charge Q is distributed over two concentric hollow spheres of radii r and R (>r) such that the surface densities are equal and placed on the same axial points. Then the potential at the common centre is

A wheel is rolling straight on ground without slipping. If the axis of the wheel has speed v, the instantenous velocity of a point P on the rim, defined by angle q, relative to the ground will be

The co-ordinates of a moving particle at any time ‘t’are given by x = αt^{3} and y = βt^{3} . The speed of the particle at time ‘t’ is given by

A Carnot’s engine works as a refrigerator between 250 K and 300 K. If it receives 750 calories of heat from the reservoir at the lower temperature, the amount of heat rejected at the higher temperature is

A gas molecule of mass M at the surface of the Earth has kinetic energy equivalent to 0°C. If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (k_{B} is Boltzmann constant).

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays.If λ_{min} is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ_{min} with log V is correctly represented in :

In a series resonant circuit, having L, C and R as its elements, the resonant current is i. The power dissipated in the circuit at resonance is

Hysteresis loops for two magnetic materials A and B are given below :

These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use :

A lens is placed between a source of light and a wall. It forms images of area A_{1} and A_{2} on the wall, for its two different positions. The area of the source of light is

A cylindrical vessel of cross-section A contains water to a height h. There is a hole in the bottom of radius ‘a’. The time in which it will be emptied is:

A cell of e.m.f. E is connected across a reistance R. The potential difference between the terminals of the cell is found to be V. The internal resistance of the cell must be

If a battery is connected across series combination of a capacitor and a resistor, at t = 0. If at an instant t potential difference across the capacitor be ‘V’ and energy stored in it be U. Then which of the following graph is correct.

A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which inelastic collision will take place is :

A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal :

The electric field in a region of space is given by, E = E iˆ + 2E ˆj where E_{0} = 100 N/C. The flux of the field through a circular surface of radius 0.02 m parallel to the Y-Z plane is nearly:

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:

Three particles of equal mass m are situated at the vertices of an equilateral triangle of side L. What should be the velocity of each particle so that they move on a circular path without changing L?

The average score is 20%

In the arrangement shown in the Fig, the ends P and Q of an unstretchable string move downwards with uniform speed U. Pulleys A and B are fixed. Mass M moves upwards with a speed

y = 2(cm)sin[πt/2+Φ] What is the maximum acceleration of the particle doing the SHM

Using mass(M), length(L), time(T) and electric current (A) as fundamental quantities the dimensions of permittivity will be

There are two wires of the same length. The diameter of second wire is twice that of the first. On applying the same load to both the wires, the extension produced in them will be in ratio of

A sphere is placed in front of a convex lens of focal length f. The radius of the sphere is much smaller compared to f. The image of the sphere would look spherical if the object distance is

A Hydrogen atom and a Li^{++ }ion are both in the second excited state. If l_{H} and l_{Li} are their respective electronic angular momenta, and E_{H} and E_{Li} their respective energies, then

A rectangular block of mass m and area of crosssection A floats in a liquid of density r. If it is given a small vertical displacemnet from equilibrium it undergoes oscillation with a time period T. Then

While determining the specific resistance of a wire using a metre bridge the formula used is (where X, D, L and ρ denote unknown resistance, diameter of the wire, the length of the wire and the specific resistance of the wire)

What is the electric potential at the centre of the square?

A radar has a power of 1kW and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = 6.4 × 10^{6}m) is :

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year = 9.46 × 1015 m) of the order of :

An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20m. If the car is going twice as fast i.e., 120 km/h, the stopping distance will be

An ideal coil of 10H is connected in series with a resistance of 5W and a battery of 5V. 2second after the connection is made, the current flowing in ampere in the circuit is

A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of 25.5 kVm^{-1}. The density of liquid is 1.26 × 10^{3} kg m^{-3}. The radius of the drop is (neglect buoyancy).

A space craft of mass ‘M’, moving with velocity ‘v’ suddenly breaks into two pieces. After the explosion mass ‘m’ becomes stationary. What is the velocity of the other part of the craft ?

The circuit shown here has two batteries of 8.0 V and 16.0 V and three resistors 3 Ω, 9 Ω and 9 Ω and a capacitor of 5.0 μF. How much is the current (I) in the circuit in steady state?

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is:

Two waves of wavelengths 99 cm and 100 cm both travelling with velocity 396 m/s are made to interfere. The number of beats produced per second are

A block is placed on a frictionless horizontal table. The mass of the block is m and springs are attached on either side with force constants K_{1} and K_{2}. If the block is displaced a little and left to oscillate, then the angular frequency of oscillation will be

A bullet looses (1/n)^{th} of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be:

In a series LCR circuit R = 200Ω and the voltage and the frequency of the main supply is 220V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30°. On taking out the inductor from the circuit the current leads the voltage by 30°. The power dissipated in the LCR circuit is

In the isothermal expansion of 10g of gas from volume V to 2V the work done by the gas is 575J. What is the root mean square speed of the molecules of the gas at that temperature?

A parallel plate capacitor of area 60 cm^{2} and separation 3 mm is charged initially to 90 μC. If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of 2.5 × 10^{-8} C/s, then what is the magnetic field between the plates ?

The temperature of reservoir of Carnot’s engine operating with an efficency of 70% is 1000 kelvin. The temperature of its sink is

A beam of light of intensity 12 watt/cm^{2} is incident on a totally reflecting plane mirror of area 1.5 cm^{2}, then the force (in newton) acting on the mirror will be

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the center is

The escape velocity for a body of mass 1 kg from the earth surface is 11.2 kms^{-1}. The escape velocity for a body of mass 100 kg would be

An air bubble of radius 0.1 cm is in a liquid having surface tension 0.06 N/m and density 10^{3} kg/m^{3}. The pressure inside the bubble is 1100 Nm^{-2} greater than the atmospheric pressure. At what depth is the bubble below the surface of the liquid? (g = 9.8 ms^{-2})

At the centre of a circular coil of radius 5 cm carrying current, magnetic field due to earth is 0.5 × 10^{-5} W/m^{2}. What should be the current flowing through the coil so that it annuls the earth’s magnetic field

An ideal gas is initially at temperature T and volume V. Its volume is increased by ΔV due to an increase in temperature ΔT, pressure remaining constant. The quantity δ = ΔV/VΔT varies with temperature as

The average score is 31%

A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged conducting sheet P, as shown in the figure. The surface charge density σ of the sheet is proportional to

An aluminium foil of relative emittance of 0.1 is placed in between two concentric spheres at temperature 300 K and 200 K respectively. What is the temperature of this foil when steady state is reached? Assume the spheres to be black bodies. (σ = 5.672 × 10^{-8})

A given ideal gas with γ = C_{p}/C_{v} at a temperature T. If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

While measuring the length of the rod by vernier callipers the reading on main scale is 6.4 cm and the eight division on vernier is in line with marking on main scale division. If the least count of callipers is 0.01 and zero error –0.04 cm, the length of the rod is

The activity of a radioactive element decreases to one-third of the original activity I_{0} in a period of nine years. After a further lapse of nine years its activity will be

The effective resistance between points A and B of infinite network is

An unstable nucleus decays in three different modes, each mode having a different half-life T1, T2, T3 (T1 >> T2 >> T3). The overall half-life of the sample would be

500 g of water and 100 g of ice at 0°C are in a calorimeter whose water equivalent is 40 g. 10 g of steam at 100°C is added to it. Then water in the calorimeter is : (Latent heat of ice = 80 cal/g, Latent heat of steam = 540 cal/ g)

From a sphere of mass M and radius R, a smaller sphere of radius R/2 is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure). For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is 3R, the gravitational force between the two sphere is:

The velocity of a particle is v = v_{0} + gt + ft^{2}. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the n^{th} orbital will therefore be proportional to :

An object is moving towards a concave mirror of focal length 24 cm. When it is at a distance of 60 cm from the mirror its speed is 9 cm/s. The speed of its image at the instant is

In the X-rays tube before striking the target we accelerate the electrons through a potential difference of U volt. For which of the following value of U, we will have X-rays of largest wavelength?

A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to

Which of the following graph represents the input characteristics of a common emmiter transistor correctly ?

The efficiency of an ideal gas with adiabatic exponent ‘γ’ for the shown cyclic process would be

A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of 30° with the horizontal. The ball strikes the ground at B. What is the value of the distance AB ? (Moment of inertia of a spherical shell of mass m and radius R about its diameter = 2/3 mR^{2}

Given that radius of earth is 6.4 × 10^{6} m and a transmitting antenna at the top of a tower has a height 40 m and the height of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in los mode?

The space between the parallel plates of a capacitor is tightly filled with three dielectric slabs A,B, C of thickness 5 mm, 3 mm and 2 mm with dielectric constants 2, 3 and 5 respectively. If a potential difference of 351 volts is applied to plates then electric field intensity in slab A is

There is a spherical cavity of radius R/2 in uniformly charged spherical region having charge density r and radius R. A small charged particle having q_{0} charge is released at point O. It will collide withthe wall of cavity with kinetic energy

A structural steel rod has a radius of 10 mm and length of 1.0 m. A 100 kN force stretches it along its length. Young’s modulus of structural steel is 2 × 10^{11} Nm^{2}. The percentage strain is about

A small bar magnet is being slowly inserted with constant velocity inside a solenoid as shown in figure. Which graph best represents the relationship between emf induced with time

In young’s double slit experiment, if intensity of maxima on screen is I_{1} (assume equal intensity of the source). If the sources become incoherent, average intensity on the screen is I_{2}, then the ratio of I_{1}/I_{2 }is

In an organ pipe, three successive resonance frequencies are observed at 425, 595 and 765Hz. The length of organ pipe is (Velocity of sound in air = 340 m/s).

A photoelectric surface is illuminated successively by monochromatic light of wavelengths λ and λ/2. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface is :

A ball is thrown from a point with a speed 'v_{0} ' at an elevation angle of θ. From the same point and at the same instant, a person starts running with a constant speed v_{0}/2 to catch the ball.Will the person be able to catch the ball? If yes, what should be the angle of projection q ?

Consider two npn transistors as shown in figure. If 0 Volts corresponds to false and 5 Volts correspond to true then the output at C corresponds to :

The figure of merit of a galvanometer is defined as

Two bodies of mass m and 2m connected by an unextended spring of spring constant ‘k’ are allowed to fall simultaneously in a uniform gravitational field g. The extension ‘x’ in the spring when the bodies A and B are falling

Two bodies A and B of masses 10 kg and 5 kg are placed very slightly separated as shown in figure.

The coefficients of friction between the floor and the blocks are as μ_{s} = μ_{k} = 0.4, g between block A and ground breaks, block A will start pressing block B and when welding of B also breaks, blockB will start pressing the vertical wall. If F = 20 N, with how much force does block A presses the block B

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT. What will be its value at the centre of loop?

An engine approaches a hill with a constant speed. When it is at a distance of 0.9 km, it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is 330 m/ s, then the speed of the engine is :

The amplitude of velocityof a particle acted on by a force F cos w t along the x direction, is given by x=1/√(aω^{2}-bω+c) where a, b, c, are constants and b^{2} < 4 ac. For what value of ω does the resonance occur ?

An electric charge 10^{-3} μ C is placed at the origin (0, 0) of X – Y co-ordinate system. Two points A and B are situated at ( √2, √2) and (2, 0) respectively. The potential difference between the points A and B will be

One end of a massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in ms^{-2}) can a man of 60 kg climb on the rope?

A mass of 50g of water in a closed vessel, with surroundings at a constant temperature takes 2 minutes to cool from 30°C to 25°C. A mass of 100g of another liquid in an identical vessel with identical surroundings takes the same time to cool from 30° C to 25° C. The specific heat of the liquid is : (The water equivalent of the vessel is 30g.)

A particle of mass m moves with a constant velocity. Which of the following statements is not correct about its angular momentum ?

A satellite of mass m revolves around the earth of radius R at a height x from its surface. If g is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is

In a uniform magnetic field of induction B a wire in the form of a semicircle of radius r rotates about the diameter of the circle with an angular frequency w. The axis of rotation is perpendicular to the field. If the total resistance of the circuit is R, the mean power generated per period of rotation is

A compound microscope has an objective and eye-piece as thin lenses of focal lengths 1 cm and 5 cm respectively. The distance between the objective and the eye-piece is 20 cm. The distance at which the object must be placed in front of the objective if the final image is located at 25 cm from the eye - piece, is numerically

The insulation property of air breaks down at E = 3 × 10^{6} volts/ metre. The maximum charge that can be given to a sphere of diameter 5 m is approximately

At ground level, there is a downard vertical electric field of about 100 V/m. From this data calculate order of surface charge density on earth by assuming that earth is a conductor.

The velocity of projection of a body is increased by 2%, other factors remaining unchanged, what will be the percentage change in the maximum height attained

If a bar magnet of magnetic moment 80 units be cut into two halves of equal lengths, the magnetic moment of each half will be

Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is Io as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

A Zener diode is connected to a battery and a load as show below:

The currents, I, I_{Z} and I_{L} are respectively

In diagrams (1 to 4), variation of volume with changing pressure is shown. A gas is taken along the path ABCD. The change in internal energy of the gas will be

Hydrogen (_{1}H1 ) , Deuterium ( _{1}H^{2} ) , singly ionised Helium (_{2}He^{4})^{+} and doubly ionised lithium ( _{3}Li^{6} )^{++} all have one electron around the nucleus. Consider an electron transition from n = 2 to n = 1. If the wavelengths of emitted radiation are λ_{1}, λ_{2} , λ_{3} and λ_{4} respectively then approximately which one of the following is correct?

In the following diagram the reading of the ammeter is (when the internal resistance of the battery is zero)

An electromagnetic wave of frequency 1 × 10^{14} hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ε_{0} = 8.8 × 10^{-12} C2/Nm^{2}, then average energy density of electric field will be:

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. The frequency of vibration of the 8 kg block is :

In a Young’s double slit experiment with light of wavelength l the separation of slits is d and distance of screen is D such that D >> d >>λ. If the fringe width is β, the distance from point of maximum intensity to the point where intensity falls to half of maximum intensity on either side is:

When light of 3000 Å is incident on sodium chloride, the stopping potential is 1.85 volt and when light of 4000 Å is incident, then the stopping potential becomes 0.82 volt. The threshold wavelength for sodium is: (h = 6.6 × 10^{-34} J-sec.)

In four complete revolution of the cap, the distance travelled on the pitch scale is 2 mm. If there are 50 divisions on the circular scale, then the least count of the screw gauge is

A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it extends by l_{a} and when the weight is immersed completely in water, the extension is reduced to l_{w}. Then the relatively density of material of the weight is

The Thallium-201 half-life is 74 hours. If the sample has an activity of 80 millicuries initially, what will be the activity after 9.25 days ?

Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be:

Three bars each of area of cross - section A and length L are connected in series. The thermal conductivities of their materials are K, 2K, 1.5K. If the temperatures of the external ends of the first and last bar are 200 & 18ºC, then the temperatures of both the junctions are

A 2V battery is connected across AB as shown in the figure. The value of the current supplied by the battery when in one case battery’s positive terminal is connected to A and in other case when positive terminal of battery is connected to B will respectively be:

A pendulum with time period of 1s is losing energy. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s^{-1}) is :

14/04/2020 / Leave a comment

Relative permittivity and permeability of a material ε_{r} and μ_{r} , respectively. Which of the following values of these quantities are allowed for a diamagnetic material?

In a cubical vessel are enclosed n molecules of a gas each having a mass m and an average speed v. If l is the length of each edge of the cube, the pressure exerted by the gas will be

Wires 1 and 2 carrying currents i_{1} and i_{2} respectively are inclined at an angle θ to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire 1?

A wooden block of volume 1000 cc is suspended from a spring balance. It weighs 12 N in air. It is then held suspended in water with half of it inside water. What would be the reading in spring balance now?

An electromagnetic wave in vacuum has the electric and magnetic field E and B, which are always perpendicular to each other. The direction of polarization is given by X and that of wave propagation by k . Then

A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. If the Young’s modulii of copper and steel are respectively 1.0 × 1011 Nm^{-2} and 2.0 × 1011 Nm^{-2} , the total extension of the composite wire is :

A sphere, a cube and a thin circular plate all made of the same material and having the same mass, are initially heated to a temperature of 200oC. Which of these objects will cool slowest when left in air at room temperature?

A boy playing on the roof of a 10 m high building throws a ball with a speed of 10m/s at an angle of 30º with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground ? [g = 10 m/s^{2}, sin30^{o }= 1/2, cos30^{o} =√3/2 ]

The current gain of a common emitter amplifier is 69. If the emitter current is 7.0 mA, collector current is :

A pendulum consists of a wooden bob of mass m and length ‘l’. A bullet of mass m_{1} is fired towards the pendulum with a speed v_{1}. The bullet emerges out of the bob with a speed v_{1}/3, and the bob just completes motion along a vertical circle. Then v_{1} is

A person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator?

A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane at the loop exists everywhere with half the loop outside the field, as shown in figure. The induced emf is

In the circuit shown, the total current supplied by the battery is

A proton, a deutron and an a particle accelerated through the same potential difference enter a region of uniform magnetic field, moving at right angles to B. What is the ratio of their K.E.?

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that other slit. If I_{m} be the maximum intensity, the resultant intensity I when they interfere at phase difference Φ is given by :

The instantaneous values of current and voltage in an A.C. circuit are I = 4 sin ωt and E = 100 cos(ωt+π/3) respectively. The phase difference between voltage and current is

The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows :

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is : (Take C_{v} =1.5 R, where R is gas constant)

The correct graph between the gravitational potential (V_{g}) due to a hollow sphere and distance from its centre will be

Let there be a spherically symmetric charge distribution with charge density varying as ρ(r) = ρ_{0 }(5/4-r/R) upto r = R , and ρ(r) = 0 for r > R , where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by

The half life of a radioactive substance is 20 minutes. The approximate time interval (t_{2} – t_{1}) between the time t_{2} when 2/3 of it had decayed and time t_{1} when 1/3 of it had decayed is :

In the figure battery B supplies 12 V. Take C_{1} = 1 μF, C_{2} = 2 μF, C_{3} = 3 μF, C_{4} = 4 μF. Charge on capacitor C_{1} when only1 S_{1} is closed is

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V_{0} and its pressure is P_{0}. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency

A ray of light is incident at an angle of 60° on one face of a prism of angle 30°. The ray emerging out of the prism makes an angle of 30° with the incident ray. The emergent ray is

Three identical spheres, each of mass 1 kg are kept as shown in figure, touching each other, with their centres on a straight line. If their centres are marked P, Q, R respectively, the distance of centre of mass of the system from P is

Range of frequencies alloted for commercial FM radio broadcast is

Two periodic waves of intensities I_{1} and I_{2} pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Which of the following units denotes the dimension ML^{2}/Q^{2}, where Q denotes the electric charge?

A particle of mass m_{1} collides head-on with another stationary particle of mass m_{2} (m_{2} > m_{1}). The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

A hydrogen-like atom has one electron revolving around a stationary nucleus. The energy required to excite the electron from the second orbit to the third orbit is 47.2 eV. The atomic number of the atom is

The average score is 13%

In the arrangement shown L_{1}, L_{2} are slits and S_{1}, S_{2} two independent sources on the screen, interference fringes

The surface charge density of a thin charged disc of radius R is s. The value of the electric field at the centre of the disc is σ/2ε_{0}. With respect to the field at the centre, the electric field along the axis at a distance R from the centre of the disc :

The load versus elongation graphs for four wires of same length and made of the same material are shown in the figure. The thinnest wire is represented by the line

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations.The bus has acceleration 2 m/s^{2} and the car has acceleration 4 m/s^{2}. The car will catch up the bus after a time of :

Which logic gate with inputs A and B performs the same operation as that performed by the following circuit?

A straight section PO of a circuit lies along the x-axis from x = –a/2 to x = +a/2, and carries a steady current ‘I’. The magnitude of magnetic field due to the section PO at a point to y = + a will be

Electrons are accelerated through a potential difference V and protons are accelerated through a potential difference 4 V. The de-Broglie wavelengths are λ_{e} and λ_{p} for electrons and protons respectively. The ratio of λ_{e}/λ_{p }is given by : (given me is mass of electron and mp is mass of proton).

A projectile can have the same range ‘R’ for two angles of projection. If ‘T_{1}’ and ‘T_{2}’ to be time of flights in the two cases, then the product of the two time of flights is directly proportional to

A flat plate P of mass ‘M’ executes SHM in a horizontal plane by sliding over a frictionless surface with a frequency V. A block ‘B’ of mass ‘m’ rests on the plate as shown in figure. Coefficient of friction between the surface of B and P is m. What is the maximum amplitude of oscillation that the plate block system can have if the block B is not to slip on the plate :

A non-conducting partition divides a container into two equal compartments. One is filled with helium gas at 200 K and the other is filled with oxygen gas at 400 K. The number of molecules in each gas isthe same. If the partition is removed to allow the gases to mix, the final temperature will be

In frequency modulation

Six equal resistances are connected between points P, Q and R as shown in figure. Then net resistance will be maximum between :

A bucket full of hot water is kept in a room and it cools from 75^{0}C to 70^{0}C in T_{1} minutes, from 70^{0}C to 65^{0}C in T_{2} minutes and from 65^{0}C to 60^{0}C in T_{3} minutes. Then

P–V plots for two gases during adiabatic processes are shown in the figure. Plots 1 and 2 should correspond respectively to

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM. If the Young's modulus of the material of the wire is Y then 1/Y is equal to: (g = gravitational acceleration)

A body is thrown vertically upwards from the surface of earth in such a way that it reaches upto a height equal to 10Re. The velocity imparted to the body will be

The equivalent capacity of the network, (with all capacitors having the same capacitance C)

A metallic wire of density d is lying horizontal on the surface of water. The maximum length of wire so that it may not sink will be

Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle q from the vertical. If the mass of each charge is m, then the electrostatic potential at the centre of line joining them will be (k=1/4πε_{0})

Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction, separated by a distance r. Then the angular velocity of the rod is

The length of an elastic string is x when the tension is 5N. Its length is y when the tension is 7N. What will be its length, when the tension is 9N?

What is the ratio of the circumference of the first Bohr orbit for the electron in the hydrogen atom to the de Brogile wavelength of electrons having the same velocity as the electron in the first Bohr orbit of the hydrogen atom?

A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz. A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6. When A moves away from C with speed 4 m/s, the number of beats heard at C is 18. The speed of sound is 340 m/s. The frequency of the source at B is :

A glass slab has the left half of refractive index n_{1}, and the right half of n_{2}=3n_{1}. The effective refractive index of the whole slab is

A rod of length L is placed on x – axis between x = 0 and x = L. The linear density i.e., mass per unit length denoted by r, of this rod, varies as, r= a + bx. What should be the dimensions of b?

A magnetic needle lying parallel to a magnetic field requiers W units of work to turn it through 600 . The torque needed to maintain the needle in this position will be

The radioactivity of a sample is R_{1} at a time T_{1} and R_{2} at a time T_{2}. If the half life of the specimen is T, the number of atoms that have disintegrated in the time (T_{2}–T_{1}) is proportional to

The electric field associated with an e.m. wave in vacuum is given by E = 40 cos (kz – 6 ×10^{8}t)iˆ, where E, z and t are in volt/m, meter and seconds respectively. The value of wave vector k is

A transformer is used to light a 140 W, 24 V bulb from a 240 V a.c. mains. The current in the main cable is 0.7 A. The efficiency of the transformer is

In the given circuit, the current drawn from the source is

The average score is 15%

Two particles A and B of equal mass M are moving with the same speed v as shown in the figure. They collide completely inelastically and move as a single particle C. The angle q that the path of C makes with the X-axis is given by:

Hot water cools from 60°C to 50°C in the first 10 minutes and to 42°C in the next 10 minutes. The temperature of the surroundings is:

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u =U/V∝ T^{4 } and pressure p=1/3(U/V). If the shell now undergoes an adiabatic expansion the relation between T and R is :

A point particle of mass 0.1 kg is executing SHM of amplitude of 0.1m. When the particle passes through the mean position, its kinetic energy is 18 × 10^{-3} J. The equation of motion of this particle when the initial phase of oscillation is 45° can be given by –

Two spherical bubbles are in contact with each other internally as shown. The radius of curvature of the common surface is R, then –

Currents of a 10 ampere and 2 ampere are passed through two parallel thin wires A and B respectively in opposite directions. Wire A is infinitely long and the length of the wire B is 2 m. The force acting on the conductor B, which is situated at 10 cm distance from A will be

Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in volume of contained air and S change in total surface area, T is the surface tension and P atmospheric pressure, then which of the following relation is correct?

In Young's double slit experiment shown in figure S_{1} and S_{1} are coherent sources and S is the screen having a hole at a point 1.0 mm away from the central line. White light (400 to 700 nm) is sentthrough the slits. Which wavelength passing through the hole has strong intensity?

A monoatomic ideal gas is filled in a nonconducting container. The gas can be compressed by a movable nonconducting piston. The gas is compressed slowly to 12.5% of its initial volume. Find final temperature of the gas if it is T_{0} initially –

The position of a projectile launched from the origin at t = 0 is given by r = (40iˆ + 50 ˆj)m at t =2s. If the projectile was launched at an angle q from the horizontal, then q is (take g = 10 ms^{2})

In the LC circuit, the current in the direction shown and the charges on the capacitor plates have the signs shown. At this time

A glass prism of refractive index 1.5 is immersed in water (refractive index 4/3 ) as shown in figure. A light beam incident normally on the face AB is totally reflected to reach the face BC, if

What happens when the applied load increases and upto breaking stress in the experiment to determine the Young's modulus of elasticity ?

A particle falls freely near the surface of the earth. Consider a fixed point O (not vertically below the particle) on the ground. Then pickup the incorrect alternative or alternatives.

What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

A piece of wood from a recently cut tree shows 20 decays per minute. A wooden piece of same size placed in a museum (obtained from a tree cut many years back) shows 2 decays per minute. If half life of C^{14} is 5730 years, then age of the wooden piece placed in the museum is approximately

A point charge +Q is positioned at the center of the base of a square pyramid as shown. The flux through one of the four identical upper faces of the pyramid is –

When the specific heat of a solid is measured by the method of mixture, the heat is lost to surroundings from the calorimeter by the process of

The length of a magnet is large compared to its width and breadth. The time period of its oscillation in a vibration magnetometer is 2s. The magnet is cut along its length into three equal parts and these parts are then placed on each other with their like poles together. The time period of this combination will be

Two blocks of mass M_{1} = 20 kg and M_{2} = 12 kg are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is :

A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius r/2. The resistance of new wire will be :

An ideal ammeter (zero resistance) and an ideal voltmeter (infinite resistance) are connected as shown. The ammeter and voltmeter reading for R1 = 5 Ω, R2 = 15 Ω, R3 = 1.25 Ω and E = 20 V are given as

The current voltage relation of a diode is given by I = (e^{1000V/T} -1) mA, where the applied voltage V is in volts and the temperature T is in degree kelvin. If a student makes an error measuring ±0.01V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA?

Consider an optical communication system operating at a wavelength of 800 nm. Suppose, only 1% of the optical source frequency is the available channel bandwidth for optical communication. How many channels can be accommodated for transmitting audio signals requiring a bandwidth of 8 kHz ?

If the ratio of the concentration of electrons to that of holes in a semiconductor is 7/5 and the ratio of currents is 7/4, then what is the ratio of their drift velocities?

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance C if the equivalent capacitance between point A and B is to be 1 mFis :

A diatomic molecule is made of two masses m_{1} and m_{2} which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by : (n is an integer)

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is 1/3. If the line joining the centre of the hemispherical surface to the insectmakes an angle a with the vertical, the maximum possible value of a so that the insect does not slip is given by

A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S , then

The fundamental frequency of a sonometer wire of length l is n_{0}. A bridge is now introduced at a distance of Δl (<< l) from the centre of the wire.The lengths of wire on the two sides of the bridge are now vibrated in their fundamental modes.Then, the beat frequency nearly is –

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