AIPMT 2015

A series R-C circuit is connected to an alternating voltage source. Consider two situations :
(a)  When capacitor is air filled.
(b)  When capacitor is mica filled.
Current through resistor is \(I\) and voltage across capacitor is \(V\) ...

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is

A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference \(V\) is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is

A circuit contains an ammeter, a battery of 30 V and a resistance 40.8 ohm all connected in series. If the ammeter has a coil of resistance 480 ohm and a shunt of 20 ohm, the reading in the ammeter will be

Two metal wires of identical dimensions are connected in series. If \(\sigma\)1 and \(\sigma\)2 are the conductivity of the combination is

A potentiometer wire of length L and a resistance r are connected in series with a battery of e.m.f. E0 and a resistance r1. An unknown e.m.f. E is balanced at a length \(l\) of the potentiometer wire. The e.m.f. E will be given by

A photoelectric surface is illuminated successively by monochromatic light of wavelength \(\lambda\) and \(\lambda/2\). If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the ...

Light of wavelength 500 nm is incifent on a metal with work function 2.28 eV. The de Broglie wavelength of the emitted electron is

An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil ?

The energy of the em waves is of the order of 15 keV. To which part of the spectrum does it belong ?

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy \(-\) y + 2yz, the electric field (in N/C) at point (1, 1, 0) is

In an astronomical telescope in normal adjustment a straight black line of length L is drawn on inside part of objective lens. The eye-piece forms a real image of this line. The length of this image is \(I\). The magnification of the telesc...

A beam of light consisting of red, green and blue colours is incifent on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively.

The pris...

A remote-sensing satellite of earth revolves in a circular orbit at a height of 0.25 \(\times\) 106 m above the surface of earth. If earth's radius is 6.38 \(\times\) 106 m and g = 9.8 ms\(-\)2, then the orbital speed of the satellite i...

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,

The coefficient of performance of a refrigerator is 5. If the temperature inside freezer is \(-\)20oC, the temperature of the surroundings to which it rejects heat is

An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas ?

Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A a...

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30o, the box starts to slip and slides 4.0 m down the plank in 4.0 s.

The coefficients of static and kinet...

Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius \({r \over 2}\) and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they expr...

A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 weber/m2. The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of...

If vectors \(\overrightarrow A = \cos \omega t\widehat i + \sin \omega t\widehat j\) and \(\overrightarrow B = \cos {{\omega t} \over 2}\widehat i + \sin {{\omega t} \over 2}\widehat j\) are functions of time, then the value of t at which...

The positions vector of a particle \(\overrightarrow R\) as a function of time is given by \(\overrightarrow R\) = 4sin(2\(\pi\)t)\(\widehat i\) + 4cos(2\(\pi\)t)\(\widehat j\). Where R is in meters, t is in seconds and \(\widehat i\) a...

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the ...

A particle is executing a simple harmonic motion. Its maximum acceleration is \(\alpha\) and maximum velocity is \(\beta\). Them, its time period of vibration will be

The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same le...

The value of coefficient of volume expansion of glycerin is 5 \(\times\) 10\(-\)4 K\(-\)1. The fractional change in the density of glycerin for a rise of 40oC in its temperature, is

Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then

A force \(\overrightarrow F = \alpha \widehat i + 3\widehat j + 6\widehat k\) is acting at a point \(\overrightarrow r = 2\widehat i - 6\widehat j - 12\widehat k\). The value of \(\alpha\) for which angular momentum about origin is conse...

Point masses m1 and m2 are placed at the opposite ends of a rigid rod of length L, and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass ...

An automobile moves on a road with a speed of 54 km h\(-\)1. The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2. If the vehicle is brought to rest in 15 s, the magnitude of averag...

The input signal given to a CE amplifier having a voltage gain of 150 is Vi = 2cos(15t + \({\pi \over 3}\)). The corresponding output signal will be

In the given figure, a diode D is connected to an external resistance R = 100 \(\Omega\) and an e.m.f. of 3.5 V. If the barrier potential developed across the diode is 0.5 V, the current in the citcuit will be

If dimensions of critical velocity \(\upsilon\)c of a liquid flowing through a tube are expressed as \(\left[ {{\eta ^x}{\rho ^y}{r^z}} \right]\) where \(\eta ,\rho\) and r are the coefficient of viscosity of liquid, density of liquid and...

Two slits in Young's experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, \({{{I_{max}}} \over {{I_{min}}}}\) is

At the first minimum adjacent to the central maximum of a single-slit diffraction pattern, the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the midpoint of the slit is

A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 m s\(-\)1 at an angle of 60o with the source observer line as shown in the figu...

A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string i...

4.0 g of a gas occupies 22.4 litres at NTP. The specific heat capacity of the gas at constant volume is 5.0 J K\(-\)1 mol\(-\)1. If the speed of sound in this gas at NTP is 952 m s\(-\)1, then the heat capacity at constant pressure is
(Ta...

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

On a frictionless surface, a block of mass M moving at speed v collides elastically with another block of same mass M which is initially at rest. After collision the first block moves at an angle \(\theta\) to its initial direction and has...

A ball is thrown vertically downwards from a height of 20 m with an initial velocity v0. It collides with the ground, losses 50 percent of its energy in collision and rebounds to the same height. The initial velocity v0 is
(Take g = 10 m s...

The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury. If the density of mercury be 13.6 \(\times\) 103 kg/m3 and g = 10 m/s2 then the power (in watt) is

Two particles A and B, move with constant velocities \(\overrightarrow {{v_1}}\) and \(\overrightarrow {{v_2}}\). At the initial moment their position vectors are \(\overrightarrow {{r_1}}\) and \(\overrightarrow {{r_2}}\) respectively....