Physics

Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the \(z\) direction. When filled with a liquid of surface tension \(S\) and density \(\rho\), the liquid surface makes angle \(\theta_0(\theta_0 \ll 1)\) with the \(x\)-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is :

(take \(\theta(x) = \sin\theta(x) = \tan\theta(x) = \frac{dy}{dx}\), \(g\) is the acceleration due to gravity)

A microscope has an objective of focal length 2 cm, eyepiece of focal length 4 cm and the tube length of 40 cm. If the distance of distinct vision of eye is 25 cm, the magnification in the microscope is

An electron (mass \(9\times10^{-31}\) kg and charge \(1.6\times10^{-19}\)C) moving with speed \(c/100\) (\(c\) = speed of light) is injected into a magnetic field \(\vec B\) of magnitude \(9\times10^{-4}\) T perpendicular to its direction of motion. We wish to apply an uniform electric field \(\vec E\) together with the magnetic field so that the electron does not deflect from its path. Then (speed of light \(c = 3\times10^{8}\) ms\(^{-1}\))

There are two inclined surfaces of equal length (\(L\)) and same angle of inclination \(45^\circ\) with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction (\(\mu_k\)) between the object and the rough surface is close to

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m. If \(F_A\) and \(F_B\) are the forces applied by the breaks on cars A and B, respectively, then the ratio \(F_A/F_B\) is

The current passing through the battery in the given circuit, is:

A bob of heavy mass \(m\) is suspended by a light string of length \(l\). The bob is given a horizontal velocity \(v_0\) as shown in figure. If the string gets slack at some point \(P\) making an angle \(\theta\) from the horizontal, the ratio of the speed \(v\) of the bob at point \(P\) to its initial speed \(v_0\) is:

The output (Y) of the given logic implementation is similar to the output of an/a ________ gate.

The electric field in a plane electromagnetic wave is given by \(E_z = 60\cos(5x + 1.5\times10^9 t)\,V/m\). Then expression for the corresponding magnetic field is (here subscripts denote the direction of the field) :

A ball of mass 0.5 kg is dropped from a height of 40 m. The ball hits the ground and rises to a height of 10 m. The impulse imparted to the ball during its collision with the ground is (Take g = 9.8 m/s\(^2\))

AB is a part of an electrical circuit (see figure). The potential difference "\(V_A - V_B\)", at the instant when current i = 2 A and is increasing at a rate of 1 amp / second is:

A 2 amp current is flowing through two different small circular copper coils having radii ratio 1:2. The ratio of their respective magnetic moments will be

In a certain camera, a combination of four similar thin convex lenses are arranged axially in contact. Then the power of the combination and the total magnification in comparison to the power (\(p\)) and magnification (\(m\)) for each lens will be, respectively -

An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature 27\(^\circ\)C. The mass of the oxygen withdrawn from the cylinder is nearly equal to :

[Given, \(R = \frac{100}{12}\) J mol\(^{-1}\)K\(^{-1}\), and molecular mass of O\(_2\) = 32, 1 atm pressure = \(1.01\times10^5\) N/m]

In some appropriate units, time (\(t\)) and position (\(x\)) relation of a moving particle is given by \(t = x^2 + x\). The acceleration of the particle is

To an ac power supply of 220 V at 50 Hz, a resistor of 20 \(\Omega\), a capacitor of reactance 25 \(\Omega\) and an inductor of reactance 45 \(\Omega\) are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively -

The Sun rotates around its centre once in 27 days. What will be the period of revolution if the Sun were to expand to twice its present radius without any external influence? Assume the Sun to be a sphere of uniform density.

A model for quantized motion of an electron in a uniform magnetic field \(B\) states that the flux passing through the orbit of the electron is \(n(h/e)\) where \(n\) is an integer, \(h\) is Planck's constant and \(e\) is the magnitude of electron's charge. According to the model, the magnetic moment of an electron in its lowest energy state will be (\(m\) is the mass of the electron)

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity \(2K\) while that in the middle has thermal conductivity \(K\). The left end of the combination is maintained at temperature \(3T\) and the right end at \(T\). The rods are thermally insulated from outside. In steady state, temperature at the left junction is \(T_1\) and that at the right junction is \(T_2\). The ratio \(T_1/T_2\) is

The plates of a parallel plate capacitor are separated by \(d\). Two slabs of different dielectric constant \(K_1\) and \(K_2\) with thickness \(\frac{3}{8}d\) and \(\frac{d}{2}\), respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If \(K_1 = 1.25\,K_2\), the value of \(K_1\) is :

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

A uniform rod of mass 20 kg and length 5 m leans against a smooth vertical wall making an angle of \(60^\circ\) with it. The other end rests on a rough horizontal floor. The friction force that the floor exerts on the rod is (take g = 10 m/s\(^2\))

In an oscillating spring mass system, a spring is connected to a box filled with sand. As the box oscillates, sand leaks slowly out of the box vertically so that the average frequency \(\omega(t)\) and average amplitude \(A(t)\) of the system change with time \(t\). Which one of the following options schematically depicts these changes correctly?

A balloon is made of a material of surface tension \(S\) and its inflation outlet (from where gas is filled in it) has small area \(A\). It is filled with a gas of density \(\rho\) and takes a spherical shape of radius \(R\). When the gas is allowed to flow freely out of it, its radius \(r\) changes from \(R\) to 0 (zero) in time \(T\). If the speed \(v(r)\) of gas coming out of the balloon depends on \(r\) as \(r^a\) and \(T \propto S^{\alpha}A^{\beta}\rho^{\gamma}R^{\delta}\) then

Consider the diameter of a spherical object being measured with the help of a Vernier callipers. Suppose its 10 Vernier Scale Divisions (V.S.D.) are equal to its 9 Main Scale Divisions (M.S.D.). The least division in the M.S. is 0.1 cm and the zero of V.S. is at \(x = 0.1\) cm when the jaws of Vernier callipers are closed.

If the main scale reading for the diameter is M = 5 cm and the number of coinciding vernier division is 8, the measured diameter after zero error correction, is

A parallel plate capacitor made of circular plates is being charged such that the surface charge density on its plates is increasing at a constant rate with time. The magnetic field arising due to displacement current is :

An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster's angle. Then-

Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is q and the force of repulsion between them is F. A third identical uncharged conducting sphere is brought in contact with sphere A first and then with B and finally removed from both. New force of repulsion between spheres A and B (Radii of A and B are negligible compared to the distance of separation so that for calculating force between them they can be considered as point charges) is best given as :

A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contains \(n_1 = 5\) and \(n_2 = 4\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :

A particle of mass \(m\) is moving around the origin with a constant force \(F\) pulling it towards the origin. If Bohr model is used to describe its motion, the radius \(r\) of the \(n^{th}\) orbit and the particle's speed \(v\) in the orbit depend on \(n\) as

The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury ?

A body weighs 48 N on the surface of the earth. The gravitational force experienced by the body due to the earth at a height equal to one-third the radius of the earth from its surface is :

A wire of resistance R is cut into 8 equal pieces. From these pieces two equivalent resistances are made by adding four of these together in parallel. Then these two sets are added in series. The net effective resistance of the combination is :

De-Broglie wavelength of an electron orbiting in the \(n = 2\) state of hydrogen atom is close to (Given Bohr radius = 0.052 nm)

An electric dipole with dipole moment \(5\times10^{-6}\) Cm is aligned with the direction of a uniform electric field of magnitude \(4\times10^{5}\) N/C. The dipole is then rotated through an angle of \(60^\circ\) with respect to the electric field. The change in the potential energy of the dipole is :

A constant voltage of 50 V is maintained between the points A and B of the circuit shown in the figure. The current through the branch CD of the circuit is :

A photon and an electron (mass \(m\)) have the same energy \(E\). The ratio \(\left(\lambda_{photon}/\lambda_{electron}\right)\) of their de Broglie wavelengths is: (\(c\) is the speed of light)

Which of the following options represent the variation of photoelectric current with property of light shown on the x-axis?

A. Photoelectric current vs Intensity of light: straight line through origin rising

B. Photoelectric current vs Intensity of light: horizontal constant line

C. Photoelectric current vs Frequency of light: straight line through origin rising

D. Photoelectric current vs Frequency of light: line starting from a positive intercept on the x-axis (threshold) and rising

A sphere of radius \(R\) is cut from a larger solid sphere of radius \(2R\) as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is :

A full wave rectifier circuit with diodes (\(D_1\)) and (\(D_2\)) is shown in the figure. If input supply voltage \(V_{in} = 220\sin(100\pi t)\) volt, then at \(t = 15\) msec

Two gases \(A\) and \(B\) are filled at the same pressure in separate cylinders with movable pistons of radius \(r_A\) and \(r_B\), respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas \(A\) and \(B\) are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio \(r_A/r_B\) is equal to

A physical quantity \(P\) is related to four observations \(a\), \(b\), \(c\) and \(d\) as follows:

\(P = a^3b^2 / c\sqrt{d}\)

The percentage errors of measurement in \(a\), \(b\), \(c\) and \(d\) are 1%, 3%, 2%, and 4% respectively. The percentage error in the quantity \(P\) is

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at \(22.5^\circ\) from the polarization axis of one of the polaroid, is (\(I_0\) is the intensity of polarised light after passing through the first polaroid):

Two identical point masses P and Q, suspended from two separate massless springs of spring constants \(k_1\) and \(k_2\), respectively, oscillate vertically. If their maximum speeds are the same, the ratio (\(A_Q/A_P\)) of the amplitude \(A_Q\) of mass \(Q\) to the amplitude \(A_P\) of mass \(P\) is:

A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to :

Match List I with List II.

List I (Spectral Lines of Hydrogen for transitions from): A. \(n_2=3\) to \(n_1=2\); B. \(n_2=4\) to \(n_1=2\); C. \(n_2=5\) to \(n_1=2\); D. \(n_2=6\) to \(n_1=2\)

List II (Wavelengths (nm)): I. 410.2; II. 434.1; III. 656.3; IV. 486.1

Choose the correct answer from the options given below :

Match List-I with List-II.

List-I (Material): A. Diamagnetic; B. Ferromagnetic; C. Paramagnetic; D. Non-magnetic

List-II (Susceptibility (\(\chi\))): I. \(\chi=0\); II. \(0>\chi\ge-1\); III. \(\chi\gg1\); IV. \(0<\chi<\epsilon\) (a small positive number)

Choose the correct answer from the options given below:

In a uniform magnetic field of 0.049 T, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is \(9.8\times10^{-6}\) kg m\(^2\). If the magnitude of magnetic moment of the needle is \(x\times10^{-5}\) Am\(^2\); then the value of 'x' is :

An unpolarised light beam strikes a glass surface at Brewster's angle. Then

Consider the following statements A and B and identify the correct answer :

A. For a solar-cell, the I-V characteristics lies in the IV quadrant of the given graph.

B. In a reverse biased \(pn\) junction diode, the current measured in (\(\mu A\)), is due to majority charge carriers.

A light ray enters through a right angled prism at point \(P\) with the angle of incidence \(30^\circ\) as shown in figure. It travels through the prism parallel to its base \(BC\) and emerges along the face \(AC\). The refractive index of the prism is:

A particle moving with uniform speed in a circular path maintains :

The graph which shows the variation of \(\left(\frac{1}{\lambda^2}\right)\) and its kinetic energy, \(E\) is (where \(\lambda\) is de Broglie wavelength of a free particle) :

A wire of length 'l' and resistance 100 \(\Omega\) is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:

The moment of inertia of a thin rod about an axis passing through its mid point and perpendicular to the rod is 2400 g cm\(^2\). The length of the 400 g rod is nearly :

The output (\(Y\)) of the given logic gate is similar to the output of an/a :

In a vernier calipers, \((N+1)\) divisions of vernier scale coincide with \(N\) divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is :

At any instant of time \(t\), the displacement of any particle is given by \(2t-1\) (SI unit) under the influence of force of 5N. The value of instantaneous power is (in SI unit):

A thin spherical shell is charged by some source. The potential difference between the two points \(C\) and \(P\) (in \(V\)) shown in the figure is:

(Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)

A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 Nm\(^{-1}\), then the excess force required to take it away from the surface is :

A logic circuit provides the output \(Y\) as per the following truth table :

| A | B | Y |

|---|---|---|

| 0 | 0 | 1 |

| 0 | 1 | 0 |

| 1 | 0 | 1 |

| 1 | 1 | 0 |

The expression for the output \(Y\) is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : The potential (\(V\)) at any axial point, at 2 m distance(\(r\)) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, \(4\times10^{-6}\) C m, is \(\pm9\times10^3\) V.

(Take \(\frac{1}{4\pi\epsilon_0}=9\times10^9\) SI units)

Reason R : \(V=\pm\frac{2P}{4\pi\epsilon_0 r^2}\), where \(r\) is the distance of any axial point, situated at 2 m from the centre of the dipole.

In the light of the above statements, choose the correct answer from the options given below:

The terminal voltage of the battery, whose emf is 10 \(V\) and internal resistance 1 \(\Omega\), when connected through an external resistance of 4 \(\Omega\) as shown in the figure is :

In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:

In an ideal transformer, the turns ratio is \(\frac{N_p}{N_s}=\frac{1}{2}\). The ratio \(V_s : V_p\) is equal to (the symbols carry their usual meaning) :

A tightly wound 100 turns coil of radius 10 cm carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as \(4\pi\times10^{-7}\) SI units):

Given below are two statements :

Statement I : Atoms are electrically neutral as they contain equal number of positive and negative charges.

Statement II : Atoms of each element are stable and emit their characteristic spectrum.

In the light of the above statements, choose the most appropriate answer from the options given below :

The quantities which have the same dimensions as those of solid angle are :

If \(c\) is the velocity of light in free space, the correct statements about photon among the following are :

A. The energy of a photon is \(E=h\nu\).

B. The velocity of a photon is \(c\).

C. The momentum of a photon, \(p=\frac{h\nu}{c}\).

D. In a photon-electron collision, both total energy and total momentum are conserved.

E. Photon possesses positive charge.

Choose the correct answer from the options given below :

A bob is whirled in a horizontal plane by means of a string with an initial speed of \(\omega\) rpm. The tension in the string is \(T\). If speed becomes \(2\omega\) while keeping the same radius, the tension in the string becomes :

If \(x=5\sin\left(\pi t+\frac{\pi}{3}\right)m\) represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are :

A thermodynamic system is taken through the cycle \(abcda\). The work done by the gas along the path \(bc\) is :

\({}^{290}_{82}X \xrightarrow{\alpha} Y \xrightarrow{e^+} Z \xrightarrow{\beta^-} P \xrightarrow{e^-} Q\)

In the nuclear emission stated above, the mass number and atomic number of the product \(Q\) respectively, are :

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity \(v_1\) while body B is at rest before collision. The velocity of the system after collision is \(v_2\). The ratio \(v_1 : v_2\) is :

In the following circuit, the equivalent capacitance between terminal \(A\) and terminal \(B\) is :

A horizontal force 10 \(N\) is applied to a block \(A\) as shown in figure. The mass of blocks \(A\) and \(B\) are 2 kg and 3 kg, respectively. The blocks slide over a frictionless surface. The force exerted by block \(A\) on block \(B\) is :

A wheel of a bullock cart is rolling on a level road as shown in the figure below. If its linear speed is \(v\) in the direction shown, which one of the following options is correct (\(P\) and \(Q\) are any highest and lowest points on the wheel, respectively)?

The mass of a planet is \(\frac{1}{10}\)th that of the earth and its diameter is half that of the earth. The acceleration due to gravity on that planet is :

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are \(8\times10^8\) N m\(^{-2}\) and \(2\times10^{11}\) N m\(^{-2}\), is :

If the monochromatic source in Young's double slit experiment is replaced by white light, then

A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object is:

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then

A. the charge stored in it, increases.

B. the energy stored in it, decreases.

C. its capacitance increases.

D. the ratio of charge to its potential remains the same.

E. the product of charge and voltage increases.

Choose the most appropriate answer from the options given below:

A 10 \(\mu F\) capacitor is connected to a 210 V, 50 Hz source as shown in figure. The peak current in the circuit is nearly (\(\pi=3.14\)):

Choose the correct circuit which can achieve the bridge balance.

Two heaters A and B have power rating of 1 kW and 2 kW, respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two cases is:

The velocity (\(v\)) - time (\(t\)) plot of the motion of a body is shown below :

The acceleration (\(a\)) - time (\(t\)) graph that best suits this motion is :

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is \(\frac{x}{2}\) times its original time period. Then the value of \(x\) is:

A metallic bar of Young's modulus, \(0.5\times10^{11}\) N m\(^{-2}\) and coefficient of linear thermal expansion \(10^{-5}\,{}^\circ\)C\(^{-1}\), length 1 m and area of cross-section \(10^{-3}\) m\(^2\) is heated from \(0^\circ\)C to \(100^\circ\)C without expansion or bending. The compressive force developed in it is:

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to :

A. hold the sheet there if it is magnetic.

B. hold the sheet there if it is non-magnetic.

C. move the sheet away from the pole with uniform velocity if it is conducting.

D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar.

Choose the correct statement(s) from the options given below:

The property which is not of an electromagnetic wave travelling in free space is that :

A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates :

An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle \(60^\circ\) with each other. The magnetic moment of this new magnet is:

The minimum energy required to launch a satellite of mass \(m\) from the surface of earth of mass \(M\) and radius \(R\) in a circular orbit at an altitude of \(2R\) from the surface of the earth is:

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures \(P_1\), \(P_2\) and \(P_3\) compared with those of Charles's law represented as dotted lines.

Then the correct relation is:

A force defined by \(F=\alpha t^2+\beta t\) acts on a particle at a given time \(t\). The factor which is dimensionless, if \(\alpha\) and \(\beta\) are constants, is:

The work functions of Caesium (Cs), Potassium (K) and Sodium (Na) are 2.14 eV, 2.30 eV and 2.75 eV respectively. If incident electromagnetic radiation has an incident energy of 2.20 eV, which of these photosensitive surfaces may emit photoelectrons?

The net magnetic flux through any closed surface is :

If the galvanometer \(G\) does not show any deflection in the circuit shown, the value of \(R\) is given by :

A 12 V, 60 W lamp is connected to the secondary of a step down transformer, whose primary is connected to ac mains of 220 V. Assuming the transformer to be ideal, what is the current in the primary winding?

A full wave rectifier circuit consists of two p-n junction diodes, a centre-tapped transformer, capacitor and a load resistance. Which of these components remove the ac ripple from the rectified output?

In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of \(2.0\times10^{10}\,\mathrm{Hz}\) and amplitude \(48\,\mathrm{V\,m^{-1}}\). Then the amplitude of oscillating magnetic field is : (Speed of light in free space \(= 3\times10^{8}\,\mathrm{m\,s^{-1}}\))

A metal wire has mass \((0.4\pm0.002)\) g, radius \((0.3\pm0.001)\) mm and length \((5\pm0.02)\) cm. The maximum possible percentage error in the measurement of density will nearly be:

Light travels a distance \(x\) in time \(t_1\) in air and \(10x\) in time \(t_2\) in another denser medium. What is the critical angle for this medium?

An electric dipole is placed at an angle of \(30^\circ\) with an electric field of intensity \(2\times10^{5}\,\mathrm{N\,C^{-1}}\). It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm.

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight \(W\) attached at its free end. The longitudinal stress at any point of cross-sectional area \(A\) of the wire is :

In hydrogen spectrum, the shortest wavelength in the Balmer series is \(\lambda\). The shortest wavelength in the Bracket series is :

The temperature of a gas is \(-50^\circ\) C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?

A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is :

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is :

The angular acceleration of a body, moving along the circumference of a circle, is :

Given below are two statements:

Statement I : Photovoltaic devices can convert optical radiation into electricity.

Statement II : Zener diode is designed to operate under reverse bias in breakdown region.

In the light of the above statements, choose the most appropriate answer from the options given below :

If \(\oint_S \vec{E}\cdot d\vec{S}=0\) over a surface, then :

Resistance of a carbon resistor determined from colour codes is \((22000\pm5\%)\,\Omega\). The colour of third band must be :

The magnetic energy stored in an inductor of inductance \(4\,\mu\mathrm{H}\) carrying a current of 2 A is :

In a series \(LCR\) circuit, the inductance \(L\) is 10 mH, capacitance \(C\) is \(1\,\mu\)F and resistance \(R\) is \(100\,\Omega\). The frequency at which resonance occurs is :

The magnitude and direction of the current in the following circuit is

The minimum wavelength of \(X\)-rays produced by an electron accelerated through a potential difference of \(V\) volts is proportional to:

The errors in the measurement which arise due to unpredictable fluctuations in temperature and voltage supply are :

For Young's double slit experiment, two statements are given below:

Statement I : If screen is moved away from the plane of slits, angular separation of the fringes remains constant.

Statement II : If the monochromatic source is replaced by another monochromatic source of larger wavelength, the angular separation of fringes decreases.

In the light of the above statements, choose the correct answer from the options given below:

A bullet is fired from a gun at the speed of \(280\,\mathrm{m\,s^{-1}}\) in the direction \(30^\circ\) above the horizontal. The maximum height attained by the bullet is \((g=9.8\,\mathrm{m\,s^{-2}},\ \sin30^\circ=0.5)\) :

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

The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly : (surface tension of soap solution \(=0.03\,\mathrm{N\,m^{-1}}\))

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to \(\left(\frac{1}{16}\right)^{th}\) of its initial value?

The potential energy of a long spring when stretched by 2 cm is \(U\). If the spring is stretched by 8 cm, potential energy stored in it will be :

The equivalent capacitance of the system shown in the following circuit is :

A vehicle travels half the distance with speed \(v\) and the remaining distance with speed \(2v\). Its average speed is:

The ratio of radius of gyration of a solid sphere of mass \(M\) and radius \(R\) about its own axis to the radius of gyration of the thin hollow sphere of same mass and radius about its axis is :

Two bodies of mass \(m\) and \(9m\) are placed at a distance \(R\). The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (\(G\) = gravitational constant) :

The venturi-meter works on :

An ac source is connected to a capacitor C. Due to decrease in its operating frequency :

The radius of inner most orbit of hydrogen atom is \(5.3\times10^{-11}\) m. What is the radius of third allowed orbit of hydrogen atom?

The resistance of platinum wire at \(0^\circ\)C is \(2\,\Omega\) and \(6.8\,\Omega\) at \(80^\circ\)C. The temperature coefficient of resistance of the wire is :

The net impedance of circuit (as shown in figure) will be :

For the following logic circuit, the truth table is:

10 resistors, each of resistance \(R\) are connected in series to a battery of emf \(E\) and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased \(n\) times. The value of \(n\) is :

Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15 (\(g=10\,\mathrm{m\,s^{-2}}\)).

The \(x\)-\(t\) graph of a particle performing simple harmonic motion is shown in the figure. The acceleration of the particle at \(t=2\) s is :

A satellite is orbiting just above the surface of the earth with period \(T\). If \(d\) is the density of the earth and \(G\) is the universal constant of gravitation, the quantity \(\frac{3\pi}{Gd}\) represents :

A very long conducting wire is bent in a semi-circular shape from \(A\) to \(B\) as shown in figure. The magnetic field at point \(P\) for steady current configuration is given by :

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

Two thin lenses are of same focal lengths (\(f\)), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be :

A wire carrying a current \(I\) along the positive \(x\)-axis has length \(L\). It is kept in a magnetic field \(\vec{B}=(2\hat{i}+3\hat{j}-4\hat{k})\) T. The magnitude of the magnetic force acting on the wire is :

A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels 24 cm through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

An electric dipole is placed as shown in the figure. The electric potential (in \(10^2\) V) at point P due to the dipole is (\(\epsilon_0\) = permittivity of free space and \(\frac{1}{4\pi\epsilon_0}=K\)):

A horizontal bridge is built across a river. A student standing on the bridge throws a small ball vertically upwards with a velocity \(4\,\mathrm{m\,s^{-1}}\). The ball strikes the water surface after 4 s. The height of bridge above water surface is (Take \(g=10\,\mathrm{m\,s^{-2}}\)) :

Two resistors of resistance, \(100\,\Omega\) and \(200\,\Omega\) are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in \(100\,\Omega\) to that in \(200\,\Omega\) in a given time is :

Two hollow conducting spheres of radii \(R_1\) and \(R_2\) (\(R_1 >> R_2\)) have equal charges. The potential would be :

When two monochromatic lights of frequency, \(\nu\) and \(\frac{\nu}{2}\) are incident on a photoelectric metal, their stopping potential becomes \(\frac{V_s}{2}\) and \(V_s\) respectively. The threshold frequency for this metal is :

As the temperature increases, the electrical resistance :

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :

Match List - I with List - II :

List - I (Electromagnetic waves): (a) AM radio waves (b) Microwaves (c) Infrared radiations (d) X-rays

List - II (Wavelength): (i) \(10^{-10}\) m (ii) \(10^{2}\) m (iii) \(10^{-2}\) m (iv) \(10^{-4}\) m

Choose the correct answer from the options given below :

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is :

A biconvex lens has radii of curvature, 20 cm each. If the refractive index of the material of the lens is 1.5, the power of the lens is :

The graph which shows the variation of the de Broglie wavelength (\(\lambda\)) of a particle and its associated momentum (p) is :

When light propagates through a material medium of relative permittivity \(\epsilon_r\) and relative permeability \(\mu_r\), the velocity of light, \(v\) is given by : (c - velocity of light in vacuum)

In the given nuclear reaction, the element X is :

\({}^{22}_{11}\text{Na} \rightarrow X + e^{+} + \nu\)

An ideal gas undergoes four different processes from the same initial state as shown in the figure below. Those processes are adiabatic, isothermal, isobaric and isochoric. The curve which represents the adiabatic process among 1, 2, 3 and 4 is :

The ratio of the distances travelled by a freely falling body in the \(1^{st}\), \(2^{nd}\), \(3^{rd}\) and \(4^{th}\) second :

Two objects of mass 10 kg and 20 kg respectively are connected to the two ends of a rigid rod of length 10 m with negligible mass. The distance of the center of mass of the system from the 10 kg mass is :

The energy that will be ideally radiated by a 100 kW transmitter in 1 hour is :

An electric lift with a maximum load of 2000 kg (lift + passengers) is moving up with a constant speed of 1.5 \(\text{ms}^{-1}\). The frictional force opposing the motion is 3000 N. The minimum power delivered by the motor to the lift in watts is : (g = 10 \(\text{ms}^{-2}\))

A copper wire of length 10 m and radius \((10^{-2}/\sqrt{\pi})\) m has electrical resistance of \(10\,\Omega\). The current density in the wire for an electric field strength of 10 (V/m) is :

If a soap bubble expands, the pressure inside the bubble :

Given below are two statements :

Statement I : Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only.

Statement II : Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q.

In light of above statements choose the most appropriate answer from the options given below :

A shell of mass m is at rest initially. It explodes into three fragments having mass in the ratio 2 : 2 : 1. If the fragments having equal mass fly off along mutually perpendicular directions with speed \(v\), the speed of the third (lighter) fragment is :

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball (\(v\)) as a function of time (t) is :

The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in rad/s\(^2\) is :

The peak voltage of the ac source is equal to :

The dimensions \([\text{MLT}^{-2}\text{A}^{-2}]\) belong to the :

The displacement-time graphs of two moving particles make angles of \(30°\) and \(45°\) with the x-axis as shown in the figure. The ratio of their respective velocity is :

In the given circuits (a), (b) and (c), the potential drop across the two p-n junctions are equal in :

The angle between the electric lines of force and the equipotential surface is :

Plane angle and solid angle have :

In a Young's double slit experiment, a student observes 8 fringes in a certain segment of screen when a monochromatic light of 600 nm wavelength is used. If the wavelength of light is changed to 400 nm, then the number of fringes he would observe in the same region of the screen is :

A light ray falls on a glass surface of refractive index \(\sqrt{3}\), at an angle \(60°\). The angle between the refracted and reflected rays would be :

In half wave rectification, if the input frequency is 60 Hz, then the output frequency would be :

A body of mass 60 g experiences a gravitational force of 3.0 N, when placed at a particular point. The magnitude of the gravitational field intensity at that point is :

A square loop of side 1 m and resistance \(1\,\Omega\) is placed in a magnetic field of 0.5 T. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is :

Let \(T_1\) and \(T_2\) be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio \(T_1 : T_2\) is :

A long solenoid of radius 1 mm has 100 turns per mm. If 1 A current flows in the solenoid, the magnetic field strength at the centre of the solenoid is :

Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :

The volume occupied by the molecules contained in 4.5 kg water at STP, if the intermolecular forces vanish away is :

Two transparent media A and B are separated by a plane boundary. The speed of light in those media are \(1.5 \times 10^{8}\) m/s and \(2.0 \times 10^{8}\) m/s, respectively. The critical angle for a ray of light for these two media is :

Match List - I with List - II :

List - I: (a) Gravitational constant (G) (b) Gravitational potential energy (c) Gravitational potential (d) Gravitational intensity

List - II: (i) \([L^{2}T^{-2}]\) (ii) \([M^{-1}L^{3}T^{-2}]\) (iii) \([LT^{-2}]\) (iv) \([ML^{2}T^{-2}]\)

Choose the correct answer from the options given below :

A series LCR circuit with inductance 10 H, capacitance 10 \(\mu\)F, resistance \(50\,\Omega\) is connected to an ac source of voltage, \(V = 200 \sin(100\,t)\) volt. If the resonant frequency of the LCR circuit is \(\nu_0\) and the frequency of the ac source is \(\nu\), then :

A ball is projected with a velocity, \(10\ \text{ms}^{-1}\), at an angle of \(60°\) with the vertical direction. Its speed at the highest point of its trajectory will be :

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is :

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The stretching of a spring is determined by the shear modulus of the material of the spring.

Reason (R) : A coil spring of copper has more tensile strength than a steel spring of same dimensions.

In the light of the above statements, choose the most appropriate answer from the options given below :

The truth table for the given logic circuit is :

A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is :

A wheatstone bridge is used to determine the value of unknown resistance X by adjusting the variable resistance Y as shown in the figure. For the most precise measurement of X, the resistances P and Q :

The area of a rectangular field (in \(\text{m}^2\)) of length 55.3 m and breadth 25 m after rounding off the value for correct significant digits is :

A big circular coil of 1000 turns and average radius 10 m is rotating about its horizontal diameter at 2 rad \(\text{s}^{-1}\). If the vertical component of earth's magnetic field at that place is \(2 \times 10^{-5}\) T and electrical resistance of the coil is \(12.56\,\Omega\), then the maximum induced current in the coil will be :

Two point charges \(-q\) and \(+q\) are placed at a distance of L, as shown in the figure.

The magnitude of electric field intensity at a distance R (R>>L) varies as :

A capacitor of capacitance C = 900 pF is charged fully by 100 V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900 pF as shown in figure (b). The electrostatic energy stored by the system (b) is :

Consider the following statements (A) and (B) and identify the correct answer.

(A) A zener diode is connected in reverse bias, when used as a voltage regulator.

(B) The potential barrier of p-n junction lies between 0.1 V to 0.3 V.

A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by

\(V = V_0 \sin\omega t\)

The displacement current between the plates of the capacitor, would then be given by :

A body is executing simple harmonic motion with frequency 'n', the frequency of its potential energy is :

The equivalent capacitance of the combination shown in the figure is :

Find the value of the angle of emergence from the prism. Refractive index of the glass is \(\sqrt{3}\).

A dipole is placed in an electric field as shown. In which direction will it move ?

Match Column - I and Column - II and choose the correct match from the given choices.

Column - I: (A) Root mean square speed of gas molecules; (B) Pressure exerted by ideal gas; (C) Average kinetic energy of a molecule; (D) Total internal energy of 1 mole of a diatomic gas

Column - II: (P) \(\frac{1}{3}nm\bar{v}^2\); (Q) \(\sqrt{\frac{3RT}{M}}\); (R) \(\frac{5}{2}RT\); (S) \(\frac{3}{2}k_BT\)

A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm will be :

If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.

A cup of coffee cools from 90°C to 80°C in t minutes, when the room temperature is 20°C. The time taken by a similar cup of coffee to cool from 80°C to 60°C at a room temperature same at 20°C is :

A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively :

The velocity of a small ball of mass M and density d, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \(\frac{d}{2}\), then the viscous force acting on the ball will be :

For a plane electromagnetic wave propagating in x-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively ?

Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.

Column - I: (A) Drift Velocity; (B) Electrical Resistivity; (C) Relaxation Period; (D) Current Density

Column - II: (P) \(\frac{m}{ne^2\rho}\); (Q) \(nev_d\); (R) \(\frac{eE}{m}\tau\); (S) \(\frac{E}{J}\)

A spring is stretched by 5 cm by a force 10 N. The time period of the oscillations when a mass of 2 kg is suspended by it is :

A parallel plate capacitor has a uniform electric field '\(\vec{E}\)' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is : (\(\varepsilon_0\) = permittivity of free space)

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of \(10^5\) m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

A lens of large focal length and large aperture is best suited as an objective of an astronomical telescope since :

A radioactive nucleus \(^A_ZX\) undergoes spontaneous decay in the sequence

\(^A_ZX \to {}_{Z-1}B \to {}_{Z-3}C \to {}_{Z-2}D\), where Z is the atomic number of element X. The possible decay particles in the sequence are :

An inductor of inductance L, a capacitor of capacitance C and a resistor of resistance 'R' are connected in series to an ac source of potential difference 'V' volts as shown in figure.

Potential difference across L, C and R is 40 V, 10 V and 40 V, respectively. The amplitude of current flowing through LCR series circuit is \(10\sqrt{2}\) A. The impedance of the circuit is :

The escape velocity from the Earth's surface is \(v\). The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :

A screw gauge gives the following readings when used to measure the diameter of a wire

Main scale reading : 0 mm

Circular scale reading : 52 divisions

Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :

Water falls from a height of 60 m at the rate of 15 kg/s to operate a turbine. The losses due to frictional force are 10% of the input energy. How much power is generated by the turbine ? (g = 10 m/s\(^2\))

A small block slides down on a smooth inclined plane, starting from rest at time t = 0. Let \(S_n\) be the distance travelled by the block in the interval t = n − 1 to t = n. Then, the ratio \(\frac{S_n}{S_{n+1}}\) is :

Polar molecules are the molecules :

A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

In a potentiometer circuit a cell of EMF 1.5 V gives balance point at 36 cm length of wire. If another cell of EMF 2.5 V replaces the first cell, then at what length of the wire, the balance point occurs ?

Two charged spherical conductors of radius \(R_1\) and \(R_2\) are connected by a wire. Then the ratio of surface charge densities of the spheres (\(\sigma_1/\sigma_2\)) is :

An electromagnetic wave of wavelength '\(\lambda\)' is incident on a photosensitive surface of negligible work function. If 'm' mass is of photoelectron emitted from the surface has de-Broglie wavelength \(\lambda_d\), then :

The electron concentration in an n-type semiconductor is the same as hole concentration in a p-type semiconductor. An external field (electric) is applied across each of them. Compare the currents in them.

The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of \(3.3\times10^{-3}\) watt will be : (h = \(6.6\times10^{-34}\) Js)

If E and G respectively denote energy and gravitational constant, then \(\frac{E}{G}\) has the dimensions of :

The effective resistance of a parallel connection that consists of four wires of equal length, equal area of cross-section and same material is 0.25 Ω. What will be the effective resistance if they are connected in series ?

The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be :

A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is :

Two conducting circular loops of radii \(R_1\) and \(R_2\) are placed in the same plane with their centres coinciding. If \(R_1 >> R_2\), the mutual inductance M between them will be directly proportional to :

In the product

\(\vec{F} = q(\vec{v}\times\vec{B}) = q\,\vec{v}\times(B\hat{i}+B\hat{j}+B_0\hat{k})\)

For q = 1 and \(\vec{v} = 2\hat{i}+4\hat{j}+6\hat{k}\) and \(\vec{F} = 4\hat{i}-20\hat{j}+12\hat{k}\)

What will be the complete expression for \(\vec{B}\) ?

For the given circuit, the input digital signals are applied at the terminals A, B and C. What would be the output at the terminal y ?

A series LCR circuit containing 5.0 H inductor, 80 μF capacitor and 40 Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be :

A uniform rod of length 200 cm and mass 500 g is balanced on a wedge placed at 40 cm mark. A mass of 2 kg is suspended from the rod at 20 cm and another unknown mass 'm' is suspended from the rod at 160 cm mark as shown in the figure. Find the value of 'm' such that the rod is in equilibrium. (g = 10 m/s\(^2\))

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of :

A car starts from rest and accelerates at 5 m/s\(^2\). At t = 4 s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t = 6 s ? (Take g = 10 m/s\(^2\))

Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of,

(i) an equilateral triangle of side 'a'.

(ii) a square of side 'a'.

The magnetic dipole moments of the coil in each case respectively are :

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

A step down transformer connected to an ac mains supply of 220 V is made to operate at 11 V, 44 W lamp. Ignoring power losses in the transformer, what is the current in the primary circuit ?

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution.

If this particle were projected with the same speed at an angle 'θ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, θ, is then given by :

A particle of mass 'm' is projected with a velocity \(v = kV_e\) (k < 1) from the surface of the earth. (\(V_e\) = escape velocity)

The maximum height above the surface reached by the particle is :

Three resistors having resistances \(r_1\), \(r_2\) and \(r_3\) are connected as shown in the given circuit. The ratio \(\frac{i_3}{i_1}\) of currents in terms of resistances used in the circuit is :

From a circular ring of mass 'M' and radius 'R' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is 'K' times 'MR\(^2\)'. Then the value of 'K' is :

For which one of the following, Bohr model is not valid ?

The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is : (c = speed of electromagnetic waves)

The Brewsters angle \(i_b\) for an interface should be :

A cylinder contains hydrogen gas at pressure of 249 kPa and temperature \(27^\circ\)C.

Its density is : (R = 8.3 J mol\(^{-1}\) K\(^{-1}\))

A ray is incident at an angle of incidence \(i\) on one surface of a small angle prism (with angle of prism A) and emerges normally from the opposite surface. If the refractive index of the material of the prism is \(\mu\), then the angle of incidence is nearly equal to :

Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is :

The energy equivalent of 0.5 g of a substance is :

A body weighs 72 N on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth ?

The solids which have the negative temperature coefficient of resistance are :

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is :

A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale.

The pitch of the screw gauge is :

In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be :

Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass.

The centre of mass of the system from the 5 kg particle is nearly at a distance of :

Find the torque about the origin when a force of \(3\hat{j}\) N acts on a particle whose position vector is \(2\hat{k}\) m.

Light with an average flux of 20 W/cm\(^2\) falls on a non-reflecting surface at normal incidence having surface area 20 cm\(^2\). The energy received by the surface during time span of 1 minute is :

A spherical conductor of radius 10 cm has a charge of \(3.2\times10^{-7}\) C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the centre of the sphere ?

\(\left(\frac{1}{4\pi\epsilon_0} = 9\times10^9\ \text{N m}^2/\text{C}^2\right)\)

In a certain region of space with volume 0.2 m\(^3\), the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is :

The increase in the width of the depletion region in a p-n junction diode is due to :

A 40 \(\mu\)F capacitor is connected to a 200 V, 50 Hz ac supply. The rms value of the current in the circuit is, nearly :

The mean free path for a gas, with molecular diameter d and number density n can be expressed as :

For transistor action, which of the following statements is correct ?

Light of frequency 1.5 times the threshold frequency is incident on a photosensitive material. What will be the photoelectric current if the frequency is halved and intensity is doubled ?

When a uranium isotope \(^{235}_{92}\)U is bombarded with a neutron, it generates \(^{89}_{36}\)Kr, three neutrons and :

The energy required to break one bond in DNA is \(10^{-20}\) J. This value in eV is nearly :

Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is :

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L\(_1\) when mass M is suspended from its free end. The expression for Young's modulus is :

The average thermal energy for a mono-atomic gas is : (\(k_B\) is Boltzmann constant and T, absolute temperature)

Which of the following graph represents the variation of resistivity (\(\rho\)) with temperature (T) for copper ?

The color code of a resistance is given below :

(figure: colour bands Yellow, Violet, Brown, Gold)

The values of resistance and tolerance, respectively, are :

In Young's double slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes :

The capacitance of a parallel plate capacitor with air as medium is 6 \(\mu\)F. With the introduction of a dielectric medium, the capacitance becomes 30 \(\mu\)F. The permittivity of the medium is :

(\(\epsilon_0 = 8.85\times10^{-12}\) C\(^2\) N\(^{-1}\) m\(^{-2}\))

Dimensions of stress are :

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

A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is \(\frac{\pi}{3}\). If instead C is removed from the circuit, the phase difference is again \(\frac{\pi}{3}\) between current and voltage. The power factor of the circuit is :

A short electric dipole has a dipole moment of \(16\times10^{-9}\) C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of \(60^\circ\) with the dipole axis is :

\(\left(\frac{1}{4\pi\epsilon_0} = 9\times10^9\ \text{N m}^2/\text{C}^2\right)\)

An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m\(^{-1}\). The permeability of the material of the rod is :

(\(\mu_0 = 4\pi\times10^{-7}\) T m A\(^{-1}\))

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is :

(\(\mu_0 = 4\pi\times10^{-7}\) T m A\(^{-1}\))

A charged particle having drift velocity of \(7.5\times10^{-4}\) m s\(^{-1}\) in an electric field of \(3\times10^{-10}\) V m\(^{-1}\), has a mobility in m\(^2\) V\(^{-1}\) s\(^{-1}\) of :

The quantities of heat required to raise the temperature of two solid copper spheres of radii \(r_1\) and \(r_2\) (\(r_1 = 1.5\,r_2\)) through 1 K are in the ratio :

An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is \(1.227\times10^{-2}\) nm, the potential difference is :

Taking into account of the significant figures, what is the value of 9.99 m \(-\) 0.0099 m ?

A ball is thrown vertically downward with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with a velocity of 80 m/s. The height of the tower is : (g = 10 m/s\(^2\))

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :

A resistance wire connected in the left gap of a metre bridge balances a 10 \(\Omega\) resistance in the right gap at a point which divides the bridge wire in the ratio 3 : 2. If the length of the resistance wire is 1.5 m, then the length of 1 \(\Omega\) of the resistance wire is :

For the logic circuit shown, the truth table is :

(figure: A and B each pass through a NOT gate; both outputs feed a NOR-type gate (OR gate with output bubble) giving Y)

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes \((L+l)\). The elastic potential energy stored in the extended wire is :

A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when :

Ionized hydrogen atoms and \(\alpha\)-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths \(r_H : r_\alpha\) will be :

Body A of mass 4m moving with speed \(u\) collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :

In a double slit experiment, when light of wavelength 400 nm was used, the angular width of the first minima formed on a screen placed 1 m away, was found to be \(0.2^\circ\). What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water ? (\(\mu_{water} = 4/3\))

In which of the following devices, the eddy current effect is not used ?

A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of \(2.5\times10^{-2}\) N/m. The pressure inside the bubble equals at a point \(Z_0\) below the free surface of water in a container. Taking \(g = 10\) m/s\(^2\), density of water \(= 10^3\) kg/m\(^3\), the value of \(Z_0\) is :

Which colour of the light has the longest wavelength ?

A disc of radius 2 m and mass 100 kg rolls on a horizontal floor. Its centre of mass has speed of 20 cm/s. How much work is needed to stop it ?

The displacement of a particle executing simple harmonic motion is given by

\(y = A_0 + A\sin\omega t + B\cos\omega t\).

Then the amplitude of its oscillation is given by :