The value of acceleration due to gravity at a height of 10km from the surface of earth is x. At what depth inside the earth is the value of the acceleration due to gravity has the same value x ?

Young’s modulus of a perfect rigid body is 

A wheel starting from rest gains an angular velocity of 10 rad/s after uniformly accelerated for 5 sec. The total angle through which it has turned is 

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged if the density of ice is \(\rho _i=0.917\,g\,cm^{-3}\) ? 

A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature are allowed to cool down under similar conditions. Then the 

In an adiabatic expansion of an ideal gas the product of pressure and volume 

A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction of the heat energy is converted into work ? 

A tray of mass 12 kg is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of 1.5 s. The spring constant of each spring is

A train whistling at constant frequency ‘n’ is moving towards a station at a constant speed V. The train goes past a stationary observer on the station. The frequency ‘n’ of the sound as heard by the observer is plotted as a function of time ‘t’. Identify the correct curve

When a certain photosensitive surface is illuminated with monochromatic light of frequency \('\nu'\), the stopping potential for photoelectric current is \(\Large\frac{V_0}{3}\). When  the same surface is illuminated by monochromatic light of frequency '\(\Large\frac{\nu}{3}\)' the stopping potential is '\(V_0\)'. The threshold frequency for photoelectric emission is

Which one of the following is NOT correct ? 

A galvanometer of resistance 100Ω is connected to a battery of 2V with a resistance of 1900Ω in series. The deflection obtained is 30 divisions. To reduce this deflection by 10 divisions the additional resistance required to be connected in series is 

A transverse wave is travelling on a string with velocity 'V'. The extension in the string is 'x'. If the string is extended by 50%, then the speed of wave along the string will be nearly (Hooke's law is obeyed) 

Glass has refractive index \(\Large\frac{3}{2}\) and water has refractive index \(\Large\frac{4}{3}\) . If the speed of light in glass is \(2 ×10^8\, m/s\), then the speed of light in water will be 

If the errors involved in the measurements of a side and mass of a cube are 2% and 4% respectively, what is the maximum permissible error in the density of the material ? 

A solid sphere is rolling down a frictionless surface with translational velocity 'V'. It climbs the inclined plane from 'A' to 'B' and then moves away from 'B' on the smooth horizontal surface. The value of 'V' should be

A wall is hit elastically and normally by 'n' balls per second. If 'm' is the mass and 'u' is velocity for each molecule, the force exerted by the balls on the wall is 

If two non-zero vectors \(\vec{P} \) and \(\vec{Q} \) are perpendicular to each other then the magnitude of their vector product is \((sin\,90^{\circ}=cos\,0^{\circ}=1) \)

An object with mass 5 kg is acted upon by a force, \(\vec{F}=(-3\hat{i}+4\hat{j})N \). If it’s initial velocity at \(t=0 \)  is  \(\vec{v}=(6\hat{i}-12\hat{j})ms^{-1} \) , the time at which it will just have a velocity along y-axis is

A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from A to B, the angular momentum of the particle about 'O' 

A wire is stretched such that it’s volume remains constant. The Poisson's ratio of the material of the wire is 

Light of certain frequency and intensity incident on a photosensitive material causes photoelectric effect. If both the frequency and intensity are doubled. The photoelectric saturation current becomes. 

The phenomenon involved in the reflection of radio-waves by ionosphere is similar to 

A point charge ‘q’ is placed at the corner of a cube of side ‘a’ as shown in the figure. What is the electric flux through the face ABCD ?

The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitude of the field at A is \(40Vm^{−1}\) , what is the force on \(20μC\) charge kept at B?

An infinitely long thin straight wire has uniform charge density of \({\Large\frac{1}{ 4} }×10^{−2}\, cm^{−1}\) . What is the magnitude of electric field at a distance 20 cm from the axis of the wire ? 

A dipole moment ‘ P ’ and moment of inertia \(I\) is placed in a uniform electric field \(\vec{E}\) . If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is

The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is 6μF . The value of capacitance of each capacitor is 

Figure shows three points A, B and C in a region of uniform electric field \(\vec{E}\) . The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good ? (\(V_A,V_B\) and \(V_C\) represent the electric potential at points A, B and C respectively)

When a soap bubble is charged ? 

A hot filament liberates an electron with zero initial velocity. The anode potential is 1200 V. The speed of the electron when it strikes the anode is 

A metal rod of length 10 cm and a rectangular cross - section of \(1 \,cm × {\Large\frac{1 }{2} }cm\) is connected to a battery across opposite faces. The resistance will be 

A car has a fresh storage battery of e.m.f 12 V and internal resistance \(2×10^{−2}\, Ω\). If the starter motor draws a current of 80 A. Then the terminal voltage when the starter is on is 

A potentiometer has a uniform wire of length 5 m. A battery of emf 10 V and negligible internal resistance is connected between its ends. A secondary cell connected to the circuit gives balancing length at 200 cm. The emf of the secondary cell is 

The colour code for a carbon resistor of resistance \(0.25\,kΩ±10\%\) is 

Each resistance in the given cubical network has resistance of 1Ω and equivalent resistance between A and B is 

I-V characteristic of a copper wire of length L and area of cross-section A is shown in figure. The slope of the curve becomes

In the given figure, the magnetic field at ‘O’.

The magnetic field at the origin due to a current element  \(\overrightarrow{idl} \) placed at a point with vector position \(\vec{r}\) is

A long cylindrical wire of radius R carries a uniform current I flowing through it. The variation of magnetic field with distance ‘r’ from the axis of the wire is shown by

A cyclotron is used to accelerate protons \(\left ( _{1}^{1}\textrm{H} \right ) \) , Deuterons \(\left ( _{1}^{2}\textrm{H} \right ) \) and \(α-\)particles \(\left ( _{2}^{4}\textrm{He} \right )\) . While exiting under similar conditions, the minimum K.E. is gained by 

A paramagnetic sample shows a net magnetization of \(8\,Am^{−1}\) when placed in an external magnetic field of 0.6 T at a temperature of 4K. When the same sample is placed in an external magnetic field of 0.2 T at a temperature of 16 K. the magnetization will be

The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is ‘x’ . if the current and the radius both are doubled. The new ratio will become 

In a permanent magnet at room temperature 

A rod of length 2 m slides with a speed of \(5ms^{−1}\) on a rectangular conducting frame as shown in figure. There exists a uniform magnetic filed of 0.04 T perpendicular to the plane of the figure. If the resistance of the rod is \(3Ω\). The current through the rod is  

The current in a coil of inductance 0.2 H changes from 5A to 2A in 0.5 sec. The magnitude of the average induced emf in the coil is 

In the given circuit the peak voltage across C, L and R are 30 V, 110 V and 60 V respectively. The rms value of the applied voltage is 

The power factor of R-L circuit is \(\Large\frac{1}{\sqrt3}\) . If the inductive reactance is 2 Ω. The value of resistance is

In the given circuit, the resonant frequency is 

A light beam of intensity \(20\,W/cm^2\) is incident normally on a perfectly reflecting surface of sides 25 cm × 15 cm. The momentum imparted to the surface by the light per second is 

An object approaches a convergent lens from the left of the lens with a uniform speed 5 m/s and stops at the focus, the image 

The refracting angle of prism is A and refractive index of material of prism is \(cot\,\Large\frac{A}{2}\) . The angle of minimum deviation is 

The following figure shows a beam of light converging at point P. When a concave lens of focal length 16 cm is introduced in the path of the beam at a place shown by dotted line such that OP becomes the axis of the lens, the beam converges at a distance x from the lens. The value of x will be equal to 

Three polaroid sheets \(P_1\),\(P_2\) and \(P_3\) are kept parallel to each other such that the angle between pass axes of \(P_1\) and \(P_2\) is \(45^∘\) and that between \(P_2\) and \(P_3\) is \(45^∘\). If unpolarised beam of light of intensity 128 \(Wm^{−2}\) is incident on \(P_1\). What is the intensity of light coming out of \(P_3\) ? 

Two poles are separated by a distance of 3.14 m. The resolving power of human eye is 1 minute of an arc. The maximum distance from which he can identify the two poles distinctly is 

In young’s Double Slit Experiment, the distance between the slits and the screen is 1.2 m and the distance between the two slits is 2.4 mm. If a thin transparent mica sheet of thickness 1μm and R.I. 1.5 is introduced between one of the interfering beams, the shift in the position of central bright fringe is 

The de-Broglie wavelength associated with electron of hydrogen atom in this ground state is 

The following graph represents the variation of photo current with anode potential for a metal surface. Here \(I_1\), \(I_2\) and \(I_3\) represents intensities and \(γ_1\),\( γ_2\), \(\gamma_3\) represent frequency for curves 1, 2 and 3 respectively, then  

The period of revolution of an electron revolving in \(n^{th}\) orbit of H-atom is proportional to 

Angular momentum of an electron in hydrogen atom is \(\Large\frac{3h}{2\pi}\) (h is the Planck’s constant). The K.E. of the electron is 

A beam of fast moving alpha particles were directed towards a thin film of gold. The parts A, B and C of the transmitted and reflected beams corresponding to the incident parts A, B and C of the beam are shown  in the adjoining diagram. The number of alpha particles in 

Two protons are kept at a separation of 10 nm. Let \(F_n\) and \(F_e\) the nuclear force and the electromagnetic force between them 

During a \(β\)− decay 

A radio-active elements has half-life of 15 years. What is the fraction that will decay in 30 years? 

A 220 V A.C supply is connected between points A and B as shown in figure what will be the potential difference V across the capacitor? 

In the following circuit what are P and Q :

A positive hole in a semiconductor is 

Two long straight parallel wires are a distance 2d apart. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field B along the line xx’ is given by

A cylindrical wire has a mass \((0.3±0.003)g\), radius \((0.5±0.005)mm\) and length \((6±0.06)cm\). The maximum percentage error in the measurement of its density is 

At a metro station, a girl walks up a stationary escalator in 20 sec. If she remains stationary on the escalator, then the escalator take her up in 30 sec. The time taken by her to walk up on the moving escalator will be 

Rain is falling vertically with a speed of \(12\,ms^{−1}\) . A woman rides a bicycles with a speed of \(12\,ms^{−1}\) in east to west direction. What is the direction in which she should hold her umbrella? 

One end of a string of length ′l′ is connected to a particle of mass ‘m’ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed ‘v’, the net force on the particle (directed towards the centre) is : (T is the tension in the string) 

A body is initially at rest. It undergoes onedimensional motion with constant acceleration. The power delivered to it at time ‘t’ is proportional to 

A thin uniform rectangular plate of mass 2 kg is placed in X-Y plane as shown in figure. The moment of inertial about x-axis is \(I_x=0.2\,kg\,m^2\) and the moment of inertia about y-axis is \(I_y=0.3\,kg\,m^2\) . The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is

The angular spread of central maximum, in diffraction pattern, does not depend on

An eagle flies at constant velocity horizontally across the sky, carrying a mouse and releases the mouse while in flight. From the eagle’s perspective, the mouse falls vertically with speed \(v_1\) . From an observer on the ground’s perspective, the mouse falls at an angle with speed \(v_2\) . What is the speed of the eagle with respect to the observer on the ground ?

A body slides down a frictionless inclined planes starting from rest. If \(S_n\) and \(S_{n+1}\) be the distance travelled by the body during \(n^{th}\) and \((n+1)^{th}\) seconds, then the ratio   \(\frac{S_{n+1}}{S_n}\) is

The linear momentum of a particle moving in \(X-Y\) planes under the influence of a force is given as \(\vec{p}\,(t)=A\,(\hat{i}\,cos\,bt-\hat{j}\,sin\,bt)\) where \(A\) and \(b\) are constants. The angle between the force and momentum is

Which of the following expression has a dimensional formula different from others?

The acceleration (a) of an object varies as a function of its velocity (v) as \(a=\lambda \sqrt v\) where λ is a constant. If at t=0, v=0, then the velocity as a function of time (t) is given as

A car starts from rest to cover distance 'd' on a road where the coefficient of friction between the road and the tyres is µ. The minimum time in which car can cover this distance is proportional to 

A 1.5 m tall girl standing at a distance of 15 m from a fence 5 m high throws a stone of mass 0.25 Kg at an angle of \(45^{\circ}\) to the horizontal. The minimum velocity of the stone to be thrown to fly over the fence is 

A body of mass M in the form of an inclined plane with a \(45^{\circ}\) angle of inclination lies on a horizontal plane. A ball of mass 'm' moving horizontally with velocity '\(v_0\)' collides with the inclined plane. After the impact the ball bounces vertically upwards and the inclined plane begins to slide without friction along the horizontal plane. The velocity of the ball after the collision in its vertical travel is

A body can rotate in a vertical plane at the end of a string of length L. The horizontal velocity imparted to the body in its highest position, so that the tension in the string at the lowermost position is ten times the weight of the body, will be 

An empty container is put on the pan of a physical balance and the scale is adjusted to zero. Small identical balls of mass 10 g each are dropped into the container from rest from height 4.9 m at a constant rate of 100 balls per second. If the collision between each ball and container is completely inelastic, the reading of the balance after 5 second will be 

A ball of mass 'm' lying on a frictionless surface is attached to the two elastic springs of force constant 'k' as shown in the figure. The other two ends of the spring are connected to rigid wall. The ball can perform simple harmonic motion horizontally. The ratio of the velocity of the ball at positions equal to one half and one third of amplitude from the equilibrium position will be

The angular velocity of earth rotation, at which the bodies at the equator become weightless, is (Radius of earth = 6400 Km) 

If the telecast is to cover a range of 64km, the height of TV tower should be (Radius of earth,R=6400Km) 

The excess of pressure inside a soap bubble is twice the excess of pressure inside another soap bubble. The volume of first bubble is 'n' times the volume of second bubble. The value of 'n' must be 

Acceleration due to gravity at height 'h' above the surface of the earth is (R=Radius of the earth)

When an a.c. source is connected across a pure inductor of self inductance (L) then e.m.f. induced in it 

If angular momentum of a rotating body about a fixed axis is increased by 10%, its rotational kinetic energy will be increased by 

A point source is placed in air. The spherical wavefront has radius ‘\(r_a\)’ after time 't'. If the same point source is placed in the medium of refractive index '\(μ\)', the radius of spherical wavefront in the medium in same time t is

In a cyclotron the time required by positive ion to traverse semicircle does NOT depend upon

From the position of smaller angular displacement 'Ï´', the bob of simple pendulum of length 'L' is released then its linear displacement at time 't' is

The magnitude of the induced e.m.f. produced in the coil when a magnet is inserted into it does 'NOT' depend upon the 

The mass and radius of earth is \(M_e\) and \(R_e\) respectively and that of moon is \(M_m\) and \(R_m\) respectively. The distance between the centre of earth and that of moon is 'D' . The minimum speed required for a body (mass 'm') to project from a point midway between their centres to escape to infinity is

The rate of cooling of a body is \(2 ^\circ C/min\) when the body is at \(50 ^\circ C\) above the temperature of surroundings. When the body is at \(30 ^\circ C\) above the temperature of surroundings, its rate of cooling will be 

A charge 'q' is enclosed by a Gaussian spherical surface of radius 'R'. If, now, radius of the spherical surface is doubled the outward electric flux will

When an npn transistor is used as an amplifier 

A capillary tube is dipped in water, the water rises in it to a height 'h'. If `r' is the radius of bore of tube then

A particle performs simple harmonic motion from mean position, with period 8 s. The distance travelled by it between 1st and 2nd second of its motion is (A = amplitude of S. H. M.)

Which of the following statements is NOT true for a particle moving in circle with a constant angular speed? 

A sonometer wire of length \('L_1\,'\) is in unison with a tuning fork of frequency 'n'. When the vibrating length of the wire is reduced to \('L2\,’\) , it produces 'x' beats per second with the fork. The frequency of the fork is

The innermost orbit of the hydrogen atom has a diameter of \(1.06\, \mathring{A} \) , the diameter of the tenth orbit is

Two vibrating tuning forks produce waves which are represented by \(Y_1 = 4\, sin\, 500\,Ï€t\) and \(Y_2 = 4 \,sin \,506Ï€t\) . The number of beats produced per minute by these two waves is 

Dimensions of magnetic intensity are 

The S.I. unit of impulse is the same as that of 

Half-lives of two radioactive elements A and B are 20 minute and 40 minute respectively. Initially the samples have equal nuclei. After 80 minute, the ratio of decayed number of A and B nuclei will be 

In Biprism experiment the distance between the two virtual images of the slits in the magnified and diminished position are 2.4 mm and 0.6 mm  respectively. The distance between two coherent sources is 

A conical pendulum has bob of mass of 250g and a length of 1m. If the horizontal circle traced by the bob has a diameter of 120cm, then the tension in the string would be nearly (\(g=9.8m/s^2\) ) 

'M' kg weight is suspended from a weightless spring and it has period 'T'. If now '4m' kg weight is suspended from the same spring, the new period will be 

Bending of beam can be reduced by using 

In the formula for high resolving power microscope, the numerical aperture of the object of the microscope is given as

( \(\mu\) refractive index of oil and angle made by the object at the aperture = \(2\alpha\) ) 

A charged capacitor has charge \('Q_1\,'\) at potential \('V_1'\) . The charge on capacitor is increased to \('Q_2\,'\) so that its potential increases to \(V_2\), then the difference between final and initial energy stored in capacitor is

The component of the vector \(\vec{P}=\hat{i}P_x+\hat{j}P_y+\hat{k}P_z \) along the direction of \((\hat{i}-\hat{j}) \) is

Two long, straight wires are set parallel to each other. Both the wires carry a current 'I' in opposite directions and separation between them is '2R'. The magnetic induction at the midway between them is (\(μ_0\) = permeability of free space) 

A metal surface ejects electrons when irradiated by blue light, but not when irradiated by green light. The electrons will also be ejected by the surface, when irradiated by 

The ratio of magnetic induction along the axis to magnetic induction along the equator of a bar magnet for a point at the same distance (r) from the centre of magnet is 

The ratio of magnetization and magnetic intensity is called 

The sequence of harmonics of a pipe open at one end and closed at the other end is 250Hz and 350Hz. The resonating length of the air column in  its fundamental mode will be (velocity of sound in air = 340 m/s) 

In case of Light Emitting Diode (LED) light is emitted due to 

Three vessels A, B, C of different shapes have same base area and are filled with water up to same height 'h'. The respective forces exerted by water on the bases are \('F_A\,'\) , \('F_B\,'\) , \('F_C\,'\) and respective weights are \(`W_A\,'\), \('W_B\,'\), \('W_C \,'\). Then 

A wire suspended vertically is stretched by 1mm, when mass of 4kg is attached to the lower end. Energy gained by the wire is (Take \(g=10m/s^2 \) ) 

Work done by the force on the body is the measure of the change in its 

The dimensions of angular momentum are

When a resistance ' \(R_1\) ' is connected across the terminal of a cell of e.m.f. ' \(E_1\) ' the current is ‘ \(I_1\) '. When the resistance is changed to ' \(R_2\) ' the current is ‘ \(I_2\) '. The internal resistance of the cell is

In potentiometer experiment, the potential gradient can be increased by 

The bob of a simple pendulum has mass 2g and a charge of \(5.0\,\mu C\) . It is at rest in a uniform horizontal electric field of intensity \( 2000 \frac{V}{m}\) . At equilibrium, the angle that the pendulum makes with the vertical is: (take \(g=10\,\frac{m}{s^2}\) )

Consider a wire with density \((d)\) and stress \((\sigma)\) . For the same density, if the stress increases 2 times, the speed of the transverse waves along the wire changes by

Five moles of an ideal monoatomic gas with an initial temperature of \(150^\circ C\) expand and in the process absorb \(1500J\) of heat and does \(2500J\) of work. The final temperature of the gas in \(^\circ C\) is (ideal gas constant, \(R=8.314\,JK^{-1}mol^{-1}\) ) .

A flat mirror revolves at a constant angular velocity making \(n=0.4\) revolutions per second. With what velocity \((in\,\,ms^{-1})\) will a light spot move along a spherical screen with a radius of \(15\) metres, if the mirror is at the centre of curvature of the screen?

Consider a system of gas of a diatomic molecule in which the speed of sound at \(0^\circ C\) is \(1260\,ms^{-1}\) . Then, the molecular weight of the gas is (given, the gas constant \(R\) is \(8.314 \,J/mol\,K\))

An alternating voltage \(V=V_0sin\,\omega t\) is applied across a circuit and as a result, a current \(I=I_0\,sin\left (\omega t+\frac{\pi }{2} \right )\) flows in it. The power consumed per cycle is

If the coefficient of cubical expansion of a material is \(‘x’\) times of the coefficient of surfacial expansion, then value of \(‘x’\) is 

String \(AB\) of unstretched length, \(L\) is stretched by applying a force \(F\) at the mid-point \(C\) such that the segments \(AC\) and \(BC\) make an angle \('θ ' \)with \(AB\) as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio \(K\) . The force \(F\) is given by

An object moves along the circle with normal acceleration proportional to \(t^ {α}\) , where \(t\) is the time and \( α\) is a positive constant. The power developed by all the forces acting on the object will have time dependence proportional to

A ball moves one-fourth \(\Large (\frac{1^{th}}{4})\) of a circle of radius R in time T. Let  \(\large \nu_1\) and \(\large \nu_2\) be the magnitudes of mean speed and mean velocity vector. The ratio \(\Large \frac{\nu_1}{\nu_2}\) will be

A 4 kg object has a velocity, \(\large 3.0 \hat i \ m/s\) at some instant. Eight seconds later, its velocity is \(\large (8.0 \hat i+ 10.0\hat j) m/s\) . Assuming that the object is subjected to a constant net force, the magnitude of the force is

A block of mass 10 kg, initially at rest, makes a downward motion on 45° inclined plane. Then the distance travelled by the block after 2seconds is 
(Assume the coefficient of kinetic friction to be 0.3 and \(\large g = 10 \ ms^{-2}\))

Conservative forces are defined as the force for which,

A rocket motor consumes 100 kg of fuel per second exhausting it with a speed of 5 km/s. The speed of the rocket when its mass is reduced to \(\Large \frac{1}{20^{th}}\) of its initial mass, is (Assume initial speed to be zero and ignored gravitational and viscous forces.)

Ball A of mass 50 gm and speed 10 m/s collides with other ball B of mass 10 gm and speed 15 m/s travelling in opposite direction with each other. Determine the final speed of ball B, if the coefficient of restitution is \(\Large \frac{2}{5}\).
 

A solid sphere of mass 5 kg rolls on a plane surfaces. Find its kinetic energy at an instant when its centre moves with speed 4 m/s.

A body of mass 0.3 kg hangs by a spring with a force constant of 50 N/m. The amplitude of oscillations is damped and reaches \(\Large \frac{1}{e}\) of its original value in about 100 oscillations. If ω and ω′ are the angular frequencies of undamped and damped oscillations respectively, then percentage of \(\Large (\frac{\omega -\omega'}{\omega})\) is

If a planet of mass \(\large 6.4 \times 10^{23} kg\) can be compressed into a sphere such that the escape velocity from its surface is \(\large 8 \times 10^{4} m/s\), then what should be the radius of the sphere? (Gravitational constant, \(\large G = 6.6 \times 10^{-11} Nm^{-2} kg^{-2}\))

A horizontal aluminum rod of diameter 4 cm projected 6 cm from the wall. An object of mass 400 π kg is suspended from the end of the rod. The shearing modulus of aluminum is \(\large 3.0 \times 10^{10} \ N/m^2\).  The vertical deflection of the end of the rod is ( \(\large g=10 \ m/s^2\)).

A water tank kept on the ground has an orifice of 2 mm diameter on the vertical side. What is the minimum height of water above the orifice for which the output flow of water is found to be turbulent? (Assume, \(\large g=10 \ m/s^2, \rho_{water} =10^3 kg/m^3\), viscosity = 1 centi – poise)

A copper ball of radius 3.0 mm falls in an oil tank of viscosity 1 kg/ms. Then, the terminal velocity of the copper ball will be (Density of oil = \(\large 1.5 \times 10^3 \ kg/m^3\), Density of copper = \(\large 9 \times 10^3 \ kg/m^3\) and g = \(\large g=10 \ m/s^2\) )

The wavelength of the radiation emitted by a black body is 1 mm and Wien’s constant is \(\large 3 \times 10^{-3} mK\). Then the temperature of the black body will be

A hot body placed in air cools down to a lower temperature. The rate of decrease of temperature is
proportional to the temperature difference from the surrounding. The body loses 60% and 80% of maximum heat it can loose in time \(\large t_1\) and \(\large t_2\) respectively. The ratio \(\Large \frac{t_2}{t_1}\) will be

A Carnot engine with efficiency η operates between two heat reservoirs with temperatures \(\large T_1\) and \(\large T_2\), where \(\large T_1 > T_2\) . If only \(\large T_1\) is changed by 0.4%, the change in efficiency is \(\large \Delta \eta_1\), whereas if only \(\large T_2\) is changed by 0.2%, the efficiency is changed by \(\large \Delta \eta_2\). The ratio \(\Large \frac{\Delta \eta_1}{\Delta \eta_2}\) is approximately,

The scientific principle that forms the basis of the tokamak technology is 

If E and \(E_o\) represent the energies, t and \(t_0\) represent the times , in which of the following is dimensionally correct relation? 

A ball is dropped from a bridge that is 45 metre above the water . It falls directly into a boat which is moving with constant velocity. The boat is 12 m away from the point of impact when the ball is dropped . The speed of the boat is

(Take \(g=10\,m/s^2\))

A ball is dropped from a height H from rest. The ball travels \(\Large\frac{H}{2}\) in last 1.0 s. The total time taken by the ball to hit the ground is 

A planet is moving in a circular orbit. It completes 2 revolutions in 360 days. what is its angular frequency? 

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces 

A mass m is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, then with what acceleration will the mass release? (Assume g = acceleration due to gravity)

A particle of mass \(m_1\) collides with a particle of \(m_2\) at rest . After the elastic collision, the two particles moves at an angle of 90° with respect to each other. The ratio \(\Large\frac{m_2}{m_1}\) is

A block of mass 100 g moving at a speed of 2 m/s compresses a spring through a distance 2 cm before its speed is halved. Find the spring constant of the spring 

A bullet of mass m moving horizontally with speed \(v_0\) hits a wooden block of mass M that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height h, then how much of the initial kinetic energy of the bullet is lost in the collision?

A ball of mass 100 g is dropped at time t = 0. A second ball of mass 200 g is dropped from the same point at t = 0.2 s. The distance between the center of mass of two balls and the release point at t = 0.4 s is: (Assume g = 10 \(m/s^2\))

A ball of mass M moving with a speed of 2 m/s hits another ball of mass 1 kg moving in the same direction with a speed of 1 m/s. If the kinetic energy of center of mass is \(\Large\frac{4}{3}\) Joule then the magnitude of M is 

A simple harmonic oscillator of frequency 1 Hz has a phase of 1 radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. ( time in seconds ( s)). 

A planet is revolving around the sun in which of the following is correct statement? 

The wrong statement in the following is 

The speed of the water in a river is 'V' near the surface. If the coefficient of viscosity of water is '\( η\) ' and the depth of the river is 'H', then the shearing stress between the horizontal layers of water is 

A steel rod at 25 °C is observed to be 1m long when measured by another metal scale which is correct at 0 °C. The exact length of steel rod at 0 °C is (\(∝_{steel}\) = \(12 ×10^{-6}\) / °C, \(∝_{metal} = 20 × 10^{-6} \)/ °C) 

Latent heat of vaporisation of water is \(22.6×10^5\) J/kg. The amount of heat needed to convert 100 kg of water into vapor at 100 °C is 

The P-V diagram shown below indicates two paths along which a sample of gas can be taken from state A to state B. The energy equal to 5 PV in the from of heat is required to be transferred if the Path -1 is chosen. How much energy in the from of heat should be transferred if Path-2 is chosen?

The Nobel laureate ABDUS SALAM is Known for discovery of 

The dimension of light year 

The position of an object moving along x-axis is given as \(x =a+ bt^2\) , where a, b are constants and t is time in seconds. The object covers a distance of 16 m in 2 secs. If the average velocity of the object between t = 3 s and t = 5 s is 28 m/s , the values of a and b are :

The following figure shows the speed-time graph of a particle moving along a fixed direction. The distance travelled by the particle between time t = 0 s to t = 6 s is 

vector \(\vec{a}=\hat{i}+2\hat{j}+2\hat{k} \) and \(\vec{b}=\hat{i}-\hat{j}+\hat{k} \) . What is the unit vector along \(\vec{a}+\vec{b} \)?

A particle aimed at a target, projected at an angle 15° with the horizontal is short of the target by 10 m. If the same particle projected at an angle of 45° with the horizontal then it is away from the target by 15 meters. The angle of projection to hit the target is

Two balls A and B of masses 50 kg and 20 kg are moving in a straight line in the same direction at speed of 9 km/h and 18 km/h respectively. Ball B hits A and reverses its direction at a speed of 27 km/h. The speed of the ball A after the collision is 

A simple pendulum is suspended from the ceiling of a car taking a turn of radius 10 m at a speed of 10 m/s. Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turm. (Assume g = 10 m/\(s^2\) ) 

In the diagram below the spring has a force constant of K, the block has a mass of m, and the height of hill is h. Determine the compression of the spring x such that the block just reaches to the  top of the hill. (Assume that there are no non-conservative forces involved.)

Two masses of 1 g and 4 g are moving with equal kinetic energy. The ratio of the magnitudes of their linear momentum is 

A solid body rotates with angular velocity \(\omega=at\,\hat{i} +bt^2\,\hat{i} \) where \(a=1\,rad/s^2 \) and \(b=0.5\,rad/ s^3 \) and t is in seconds. Calculate the angle between the vectors of the angular velocity and the angular acceleration at t = 1 sec.

A uniform wire of length ‘L’ with centre of mass at the origin is lying along the x - axis. The wire is bent in the form of a circle such that its lowest point is at the origin. Then the shift of centre of mass is

The function ( \(sin\omega t-cos\omega\,t\) ) represents the S. H. M having a time period T 

In an earth satellite moving in a circular orbit, a piece of metal (weighing 0.016 kg on the earth) is weighed by a spring balance while the metal is suspended in water. If the density of metal is 8 times of water density, then the recorded weight will be (g is acceleration due to gravity) 

Consider a metallic. wire of length 10 m. An external force applied results in an elongation of 5 mm. What is the potential energy stored per unit volume [Young's modulus of wire \(Y=16\times 10^{10}\,N/m^2 \) ]

A cylindrical block of wood of mass 10 kg and radius 10 cm is floating in water with its axis vertical. when it is depressed a little and then released it starts executing simple hormonic motion (SHM). The frequency of the SHM executed by the block 1s: (Assume \(g=10\,m/s^2 \) and let \(\rho \) is the density of the water)

50 g of ice at 0 °C is mixed with 50 g of water at 80 °C. If the latent heat of ice is 80 cal/g and specific heat of water is 1 cal/g °C, then the final temperature of mixture is 

In the case of black body for energy distribution, energy radiated by a blackbody which is given by, Planck's formula reduces to Rayleigh Jean's formula for 

An air conditioner (AC) removes heat at a rate of 1.2 kJ/sec from a room. A power of 400W is required to run the AC. The coefficient of performance (α ) of the AC is 10% of that of the refrigerator operating between outside and room temperature. If outside temperate is 3 7 °C, what will be room temperature?

For the following nuclear disintegration process \(\large ^{238} _{92} U \rightarrow ^{206} _{82} Pb + x [^{4} _ {2} He]+[^0 _{-2} e]\) then value of x is

If the radii of \(\large ^{64} _{30} Zn\) and \(\large ^{27} _{13} Al\) nuclei are \(\large R_1\) and \(\large R_2\) respectively then \(\Large \frac{R_1}{R_2} = \)

For PN junction, the intensity of electric field is \(\large 1 \times 10^6 \ V/m\) and the width of depletion region is 5000Å. The value of potential barrier = ________V.

The logic circuit in the figure represents characteristics of which logic gate ?

For PN junction, the width of space charge region is approximately  ___________   \(\mu m\).

A modulating signal of frequency\(5\,kHz\) and peak voltage of \(8V\) is used to modulate a carrier of frequency \(10\,MHz\)  and peak voltage \(10V\) . Then the amplitude of USB is __________ V .

The propagation of radio waves with frequency \(2\,MHz\) to \(30 \,MHz\) is due to __________ .

When two spheres having \(4Q\) and \(–2Q\) charge are placed at a certain distance, the force acting between them is F. Now they are connected by a conducing wire and again separated from each other. Now they are kept at a distance half of the previous one. The force acting between them is ___________ .

Charge of \(1\,\mu C\) each is placed on the five corners of a regular hexagon of side \(1m\). The electric field at its centre is _________ \(N/C\)

An electric dipole is placed in a non-uniform electric field, then___________

The unit of intensity of polarization is__________ .

In the figure area of each plate is \(A\) and the distance between consecutive plates is as shown in the figure. What is the effective capacitance between points \(A\,\&\,B\)

A moving positive charge approaches a negative charge. What will happen to the potential energy of the system ?

The heat produced per unit time, on passing electric current through a conductor at a given temperature, is directly proportional to the_________ .

A carbon resistor has three bands as brown, black and green in order. What will be the range of resistance it offers.

In the network shown in the figure the equivalent resistance between points \(X\&Y\) will be ______\(\Omega\). Value of each resistance is \(2\Omega\).

Shunt wire should be _________ .

The dimensional formula of effective torsional constant of spring is__________ .

There are \(50\) turns per cm length in a very long solenoid. It carries a current of \(2.5A\). The magnetic field at its centre on the axis is _________ T.

The gyromagnetic ratio of an electron = ______ specific charge of an electron.

Alnico is an alloy of _________

The focal length of a thin lens made from the material of refractive index \(1.5\) is \(15\) cm. When it is placed in a liquid of refractive index \(4/3\) , its focal length will be____________ cm.

Time taken by the sunlight to pass through a slab of \(4\) cm and refractive index \(1.5\) is____ sec.

If the tube length of astronomical telescope is \(96\) cm and magnifying power is \(15\) for normal setting, then the focal length of the objective is

___________ cm.

Photons of energy \(2eV\) and \(2.5eV\) successively illuminate a metal whose work function is \(0.5\, eV\) . The ratio of maximum speed of emitted electron is ________.

To increase de-Broglie wavelength of an electron from \(0.5\times10^{-10}m\) to \(10^{-10}m\), its energy should be ___________.

A wheel of radius \(2m\) having \(8\) conducting concentric spokes is rotating about its geometrical axis with an angular velocity of \(10\) rad/s in a uniform magnetic field of \(0.2\)T perpendicular to its plane. The value of induced emf between the rim of the wheel and centre is ______V

A coil of surface area \(200\,cm^2\)having \(25\) turns is held perpendicular to the magnetic field of intensity \(0.02\, Wb/m2\) . The resistance of the coil is \(1\Omega\). If it is removed from the magnetic field in \(1\,s\), the induced charge in the coil is_______ C.

The dimensional formula of JWL is ______. Take Q as the dimension of charge.

If in an A.C., L-C series circuit \(X_{C}> X_{L}\). Hence potential______.

In L-C-R, A.C. series circuit, \(L=9H\), \(R=10\Omega \) & \(C=100\mu F\) . Hence Q-factor of the circuit is _____.

The \(r\,m\,s\,\) speed of hydrogen molecule at a certain temperature is \(v\) . If the temperature is doubled and hydrogen gas dissociates into atomic hydrogen, the \(r\,m\,s\,\) speed will become

The activity of a radioactive element decreases in \(10\) years to \(1/5\) of initial activity \(A_0\) . After further next \(10\) years its activity will be

Four very long wires are arranged as shown, so that their cross-section forms a square, with connections at the ends so that current \(I\) flows through all four wires as shown. Length of each side of the formed such square is \(b\) . The magnetic field at the central point \(P\) (centre of the square) is

A nonconducting ring carries linear charge density \(\lambda\) . It is rotating with angular speed \(ω\) about its axis. The magnetic field at its centre is

A stationary source (see figure) emits sound waves of frequency \(f\) towards a stationary wall. If an observer moving with speed \(u\) in a direction perpendicular to the wall measures a frequency \(f'=\frac{11}{8}f\) at the instant shown, then \(u\) is related to the speed of sound \(V_S\) as

The front solid cylinder has mass \(\frac{M}{3}\) while the back one solid cylinder has mass \(\frac{2M}{3}\) . The centers of these cylinders are connected by massless rod as shown. Both the cylinders have same radii \(R\) . The system is released from rest on the inclined plane. The cylinders roll down. The speed of the rod after system descending a vertical distance \(h\) is

Suppose a particle of mass \(m\) moving with potential energy \(U=\frac{kx^2}{2}+Ae^{-ax^2}\) has velocity \(v_a\) when its position is \(x = a\) . Here \(k, A\) and \(α\) are constants. The particle will be able to pass the origin if

A rectangular wire loop with length \(a\) and width \(b\) lies in the \(xy\) plane as shown. Within the loop there is a time dependent magnetic field given by \(\overrightarrow{B}=c\,[(x\,cos\,\omega t)\hat{i}+(y\,sin\,\omega t)\hat{k}]\) Here \(c\) and \(ω\) are constants. The magnitude of emf induced in the loop as a function of time is

A Tennis ball with (small) mass \(m_2\) sits on the top of a basketball with (large) mass \(m_1\) . The bottom of the basketball is at a height \(h\) above the ground and the bottom of the tennis ball is at a height \((h + d)\) above the ground. The balls are dropped from rest. Here all collisions are elastic and \(m_1 >> m_2\) . To what approximate height from the ground the tennis ball bounce ?

An ellipse has uniform linear positive charge density in upper half (total upper half part charge \(+Q\)) and uniform linear negative charge density in lower half (total lower half part charge \(–Q\)) as shown in figure. Here semi minor axis \(b < a\) semi major axis. Select the correct statement about the magnitude of electric dipole moment \(P\) of the ellipse

Consider the circuit shown below. The current in the \(4\Omega\)  resistor is

A metal rod of Young’s modulus \(1.5 × 10^{10}\, N/m^2\) undergoes an elastic strain of 0.06%. The energy stored per unit volume of the rod is 

A piece of ice containing a piece of iron inside it is floating on water in a container. When ice melts completely, the level of water in the container will 

A uniform circular disc of mass 'M' and radius 'R' is rotating in a horizontal plane about an axis passing through its centre of mass and perpendicular to its plane with an angular velocity ω. Another disc of same radius but mass (\(\Large\frac{M}{2}\)) is placed gently on the first disc. The angular velocity of the system now is 

The period of a simple pendulum hanging from the ceiling of a stationary cart is \(T_0\). When the cart rolls without friction down the inclined plane with angle of inclination \( θ\), the period of oscillation 

Four identical rings of radius R and mass M are placed at the corner of a square in x-y plane such that each ring touches the two rings tangentially. The moment of inertia of this system about z-axis passing through the centre of the square is 

A police car moving at 5.4 Km/Hr sounds siren emitting frequency of 550 Hz which is reflected back from a stationary object some distance ahead of the car. The number of beats heard per second by an observer sitting in the car is (Assume velocity of sound in air= 330 m/sec) 

A uniform string of mass M and length L is hanging from the ceiling. If a transverse wave travels along the length of the string, then the time taken by it to travel the whole length is

In an organ pipe open at one and closed at the other end, two successive harmonics have frequencies 560 Hz and 720 Hz. The length of the pipe is (Assume the velocity of sound in air =330 m/sec) 

The equation of the displacement of a wave is y (in cm) = \(10(\sqrt3\,sin\,2\pi t+cos\,2\pi t)\). The amplitude of the wave is

200 gram of ice at \(-10 ^{\circ}C\) is mixed with 200 gram of water at \(6 ^{\circ}C\) in a calorimeter. If the specific heat of ice and water are 0.5 and 1.0 cal/gm \( ^{\circ}C\) respectively and the latent heat of ice is 80 cal/gm, the temperature of the mixture in thermal equilibrium is 

An ideal gas having pressure P, volume V and temperature T is allowed to expand adiabatically until its volume becomes 4V while its temperature falls to \(\Large\frac{T}{2}\). The adiabatic exponent of the gas is 

If the Wien’s constant b=0.3 \(cm-K\), then the temperature of the sun having maximum intensity of radiation at 6000 \(A^0\) wavelength is 

A Carnot engine works between \(727^{\circ}C\) and \(27^{\circ}C\). The efficiency of the engine is 

The entropy remains constant in 

Two identically charged spherical balls of mass 'm' are suspended by strings of length l each from the same point. At the point of suspension, there is a third ball of same charge. The charge of the balls for the angle between the strings in equilibrium position being \(90^{\circ}\) is 

The circuit shown in the figure has four batteries of emf E and internal resistance 'r', two resistances R each and a parallel plate capacitor with plates of length l and the distance between them as 'd'. An electron having charge 'e' enters the capacitor plates at velocity 'v' parallel to the plates. The angle to the plates with which the electron come out of the capacitor is

A battery of EMF 4V and internal resistance 1 Ohm is connected with three 45 Ohms resistances, a voltmeter and an ammeter in the electrical circuit as shown in the figure. The reading of the voltmeter and ammeter are

The filament of an electric kettle is made up of three sections of equal resistances. These sections are connected in parallel and the water begins to boil in 9 minutes. If these resistances are connected in series, then the time taken by the same mass of water in the kettle to boil is 

Two conducting spheres A and B of radii 1 cm and 2 cm carrying charge \(5 × 10^{–8} C \) and \(1 \times 10^{–7} C\) respectively are kept far apart. If the spheres are joined by a conducting wire, then 

A piece of platinum and germanium are heated above the room temperature, then the resistance of 

The ratio of electrostatic force \(F_e\) and gravitational force \(F_g\) acting between a proton and an electron distant r from each other is approximately 

An electron is moving in a circular orbit of radius r with angular velocity ω. The magnetic field at its centre will be

In an ammeter, 0.2 % of the main current flows from the coil of the galvanometer. If the resistance of the coil of galvanometer is G, then the resistance of the ammeter will be

 A long straight conductor carrying current I and a square frame of side a are in the same plane as shown in the figure. This frame moves with a constant velocity v right side. The induced emf in the frame will be proportional to

The angle of dip at a place is \(30^{\circ}\). If horizontal component of earth’s magnetic field is H, the total field intensity is

The magnetic susceptibility is positive and small for a 

The phenomenon of propagation of light in an optical fiber is due to 

The resolving power of a microscope can be increased by 

The convex side of a plano-convex lens of radius of curvature 60 cm and refractive index 1.5 is silver plated to obtain a special type of concave mirror. The focal length of the mirror is 

A monochromatic beam of light of wavelength 600 nm in vacuum enters a medium of refractive index (4/3). Its wavelength and frequency in the medium will be 

A thin mica sheet of refractive index 1.4 is used to cover one slit of Young’s double slit experiment being performed using monochromatic beam of light of wavelength 6000 \(A^0\). If at the central point is now found the fifth bright fringe, the thickness of the mica sheet is 

An unpolarized light wave is incident from air on a glass surface at the Brewster angle. The angle between the reflected and the refracted wave is 

A prism of angle of prism 60\(^{\circ}\) has angle of minimum deviation 40\(^{\circ}\). The angle of incidence in this position is 

If the common-base current gain of a transistor is 0.96, then its common-emitter current gain will be 

The work function of a metal is 2.0 eV. The stopping potential for the light of wavelength 4000 A\(^{\circ}\)will be 

A 1 milliwatt laser source is emitting light of wavelength 555 nm. The number of photons emitted per second are approximately (Planck’s constant = \(6.6 × 10^{–34}\, m^2 \,Kg/s\)) 

If V be the accelerating voltage of the tube, the maximum frequency of continuous x-rays produced depends on V as 

Hydrogen atoms in its ground state are excited by monochromatic radiation of photon energy 12.8 eV. If the ionization potential of hydrogen atom is 13.6 eV, the number of spectral lines emitted according to Bohr theory will be 

The half life of a radioactive substance is 7.5 seconds. The fraction of substance left after one minute is 

The output equation of the logical circuit shown in figure is 

The number of atoms in the lower and upper energy states of a material are \(N_1\) and \(N_2\) respectively. For population inversion between these two levels 

Two vessels separately contain two ideal gases A and B at the same temperature. The pressure of gas A is three times the pressure of gas B. Under these conditions, the density of gas A is found to be two times the density of B. The ratio of molecular weights of gas A and B, i.e. \(\Large\frac{M_A}{M_B} \) is 

Two coherent plane waves of identical frequency, polarization and intensity

(\(I\)) interfere at a point where they differ in phase by 60°. What is the resulting intensity? 

The position of final image formed by the given lens combination from the third lens will be at a distance of (\(f_1 =+ 10\), \(f_2=-10\,cm\) and \(f_3= +30 cm\)) 

An object is placed at a distance of 40 cm in front of a concave minor of focal length 20 cm. The image produced is 

Two beams of monochromatic light with intensities 64 mW and 4 mW interfere constructively to produce an intensity of 100 mW. If one of the beams is shifted by an angle θ, the intensity is reduced to 84 mW. The magnitude of θ is 

A particle of mass \(2 × 10^{-6}\, kg\) with a charge \(5 × 10^{- 6}\, C\) is hanging in air above a similarly charged conducting surface. The charge density of the smface is (Assume \({\Large\epsilon _o} = 8.85 × 10^{-12}\, C^2 N^{-1} M^{-2}\) and g = 10 m/s2 ) 

Find the equivalent capacitance between point A & B. 

A circular wire has current density \(J=\left ( 2\times\,10^{10}{\Large\frac{A}{m^2}} \right )r^2\) where r is the radial distance, out of the wire radius is 2 mm. The end-to-end potential applied to the wire is 50 V. How much energy (in joule) is converted to thermal energy in 100 s? 

The resistance in following circuit are \(R_1= R_2= R_3 =6.0 \,Ω\). The emf of the battery is 12 volts. When switch S is closed, the potential across resistance \(R_1\) is changed by an amount. 

Figure below shows three circuits consisting of concentric circular arcs and straight radial lines. The center of the circle is shown by the dot. Saine current flows through each of the circuits. If \(B_1, B_2, B_3\) are the magnitudes of the magnetic field at the center. Which of the following is true?

A charged particle moves through a magnetic field perpendicular to its direction. Then 

The length \(l\) 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 into three equal parts of length \(\Large\frac{l}{3}\) each. If these parts are placed on each other with their like poles together, then the time period of this combination is 

Two straight conducting rails form a right angle as shown below. A conducting bar in contact with the rails starts at the vertex at time t = 0 and moves with constant velocity of v = 5 m/s along them. A magnetic field with B = 0.1 T is directed out of the page. The absolute value of the emf around the triangle at the time t = 4 swill be? 

A current of 6 A is flowing at 220 V in the primary coil of a transformer. If the voltage produced in the secondary coil is 1100 V and 40 % of power is lost, then the current in the secondary coil will be: 

The phase difference between the following two waves \(y_2\) and \(y_1\) is: \(y_1=s\,sin(\omega t-kx) \)

\(y_2=b\,cos\left ( wt-kx+{\Large\frac{\pi}{3} }\right ) \)

A beam of photons with an energy of 10.5 eV strike a metal plate. The photoelectrons are emitted with maximum velocity of \(1.6 \times10^6\) m /s. The work function of the metal is (Assume mass of electron = \(9 × 10^{-31}\) kg and Charge of electron = \(1.6 × 10^{-19}\) C) 

In the hydrogen atom spectrum , let \(E_1\) and \(E_2\) are energies for the transition \(n = 2 \rightarrow n = 1\) and \(n = 3\rightarrow n = 2\) respectively. The ratio \(E_2\)/\(E_1\) is 

What is the binding energy of \(_{14}^{29}\textrm{Si}\) whose atomic mass is 28.976495 u

Mass of proton = 1.007276 u

Mass of neutron = 1.008664 u

(Neglect the electron mass) (Assume 1 u = 931.5 Me V) 

Which of the following statements is incorrect? 

A piece of copper and another of germanium are cooled from room temperature to 77 °K. The resistance of 

A carrier signal of frequency \(\nu_1\) and peak voltage of \(V_1\) is modulated by a message signal of frequency \(\nu_2\) and peak voltage of \(V_2\) . Let m be the modulation index and \(\nu_+,\nu_-\)  be side bands produced. The correct statement is

Pressure versus temperature graph of an ideal gas at constant volume V is shown by the straight-line A. Now mass of the gas is doubled and the volume is halved then the corresponding pressure versus temperature graph will be shown by the line

A standing wave can be produced by combining 

In which colour have maximum dispersion 

A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal length is \(\Large\frac{5}{3} \) . If their equivalent focal length is 45 cm, the  individual focal lengths of concave and convex lens are respectively.

A thin transparent sheet of thickness 't' is placed in front of a Young's double slit. The fringe width will be (µ >1) 

Four point charges \(q_A = 2μC, q_B = -5µC, q_C = 2µC, q_D = -5µ\)C are located at the corners of a square ABCD of side 10 cm. The force acting on a charge of 1μC placed at centre of the square is  

N number of charges, +Q each, are placed maintaining equal distance on the circumference of a circle of radius R. The net electrostatic potential at the centre of the circle is 

Resistivity of the material of a conductor having uniform area of cross-section varies along its length on x , according to the relation \(\rho=\rho _0(a+bx) \); if L is length and A is cross-section area of conductor, then resistance of the conductor given by ( \( \rho _0 \) ,a,b are constants)

Thirteen resistors each of resistance 'R are connected in the circuit as shown in the following figure. Net resistance between A and B is 

A conducting circular loop of radius r carries a constant current i. It is placed in an uniform magnetic field \(\vec{B_0} \) such that \(\vec{B_0} \) is perpendicular to the plane of the loop. The magnetic force acting on the loop is .

Let \(\vec{B_1} \) is the magnetic field at the centre of the current carrying coil of radius R and \(\vec{B_2} \) is the magnetic field on the axis of same circular coil at the distance of 3R. Then the ratio \({\Large\frac{\left|\vec{B_1} \right|}{\left|\vec{B_2} \right|}} \)

A magnetic needle kept in a non-uniform magnetic field experiences 

A coil of wire of area \( 0.2\,m^2 \) containing 1000 turns is placed in a magnetic field of induction \(\sqrt2\,T \) . At time t = 0, the axis of the coil and the direction of magnetic field are along z-direction. The coil is rotated by an angle 45° in 2s about y-axis. Assuming the constant angular speed, the average e.m.f induced in the coil is approximately  

Three identical emf sources are attached to a single circuit element: a resistor, a capacitor, or an inductor. The current amplitude is then measured as a function of frequency. Which one of the following curve corresponds to inductive circuit? 

A plane electromagnetic wave of frequency 30 MHz is travelling along \(\hat{k} \) - direction. At a particular point of space and time of propagation,  if the electric field is given by \( \vec{E}=30\,Volts/meter(-\hat{i}) \) , then the corresponding magnetic field is 

In the experimental study of photoelectric effect, if \(V_o\) is the stopping potential and \(\nu\) is the frequency of the incident light on the metal the slope of graph plotted for \(V_o\) versus \(\nu\) is (where h, e and \(\phi_0\) are Planck's constant, charge of electron and work function of the metal respectively.) 

The series corresponding to lowest wavelength transition in H - atom. 

The equation \(4_{1}^{1}\textrm{H^+}\rightarrow _{2}^{4}\textrm{He}^{2+}+2e^{+1}+26\,MeV \) represents. 

The universal gates are 

What is the output of given logic circuit below if A = 0 , B = 1 and A = 1, B = 0 

 A message signal 15 sin(100πt) is used to modulate a carrier signal \( 45\,sin(3\times10^6\pi t) \). The modulation index is