AIIMS 2017

A series R-C circuit is connected to AC voltage
source. Consider two cases; (A) When C is
without a dielectric medium and (B) When C
is filled with dielectric of constant 4. The
current I\(_R\) through the resistor and voltage V\(_C\) acros...

Assertion : The average value of alternating emf is \(63.39 \%\) of the peak value.
Reason : The rms value of alternating emf is \(70.72 \%\) of peak value.

A nuclear explosive is designed to deliver \(1 \mathrm{~MW}\) power in the form of heat energy. If the explosion is designed with nuclear fuel consisting of \(U^{235}\) to run a reactor at this power level for one year, then the amount of f...

Assertion : A beam of charged particles is employed in the treatment of cancer.
Reason : Charged particles on passing through a material medium lose their energy by causing ionization of the atoms along their path.

Assertion : In He-Ne laser, population inversion takes place between energy levels of neon atoms.
Reason : Helium atoms have a metastable energy level.

Assertion : In \(\alpha\)-decay atomic number of daughter nucleus reduces by 2 units from the parent nucleus.
Reason : An \(\alpha\)-particle carries four units of mass.

Two capacitors \(C\) and \(\frac{C}{2}\) are connected to a battery of \(V\) volts, as shown below

The work done in charging both the capacitors fully is

A parallel plate capacitor has an electric field of \(10^5 \mathrm{~Vm}^{-1}\) between the plates. If the charge on the capacitor plates is \(1 \mu \mathrm{C}\), the force on each capacitor plate is

A body of mass \(4 \mathrm{~kg}\) moving with velocity \(12 \mathrm{~m} / \mathrm{s}\) collides with another body of mass \(6 \mathrm{~kg}\) at rest. If two bodies stick together after collision, then the loss of kinetic energy of system is

The particle of mass \(m\) is moving in a circular path of constant radius \(r\) such that its centripetal acceleration \(a_c\) is varying with time \(t\) as \(a_c=k^2 r t^2\), where \(k\) is a constant. The power delivered to particle by t...

Assertion : For looping a vertical loop of radius, \(r\) the minimum velocity at lowest point should be \(\sqrt{5 g r}\).
Reason : In this event the velocity at the highest point will be zero.

A cylindrical conductor AB of non-uniform
area of cross-section carries a current of 5A.
The radius of the conductor at one end A is
0.5 cm. The current density at the other end of
the conductor is half of the value at A. The
radius of the ...

The effective resistance between p and q in
given figure is

Two batteries, one of emf \(18 \mathrm{~V}\) and internal resistance \(2 \Omega\) and the other of emf \(12 \mathrm{~V}\) and internal resistance \(1 \Omega\) are connected as shown. The voltmeter \(V\) will record a reading of

Assertion : A potentiometer is preferred over that of a voltmeter for measurement of emf of a cell.
Reason : Potentiometer does not draw any current from the cell.

Assertion : Photoelectric effect can take place only with an electron bound in the atom.
Reason : Electron is a fermion whereas proton is a boson.

Charges \(+q\) and \(-q\) are placed at points \(A\) and \(B\) respectively which are a distance \(2 L\) apart, \(C\) is the mid-point between \(A\) and \(B\). The work done in moving a charge \(+Q\) along the semicircle \(C R D\) is

Assertion : The electric field due to a dipole on its axis line at a distance \(r\) is \(E\). Then, electric field due to the same dipole on the equatorial line and at the same distance will be \(E / 2\).
Reason : Electric field due to dipo...

A lens of refractive index \(\mu\) is put in a liquid of refractive index \(\mu^{\prime}\). If the focal length of lens in air is \(f\), then its focal length in liquid will be

In the given figure, the angle of reflection is

A thin prism \(P_1\) of angle \(4^{\circ}\) and refractive index 1.54 is combined with another prism \(P_2\) of refractive index 1.72 produce dispersion without deviation, the angle of \(P_2\) is

A simple telescope, consisting of an objective of focal length \(60 \mathrm{~cm}\) and a single eye lens of focal length \(5 \mathrm{~cm}\) is focused on a distant object in such a way that parallel rays emerge from the eye lens. If the obj...

Assertion : The mirror used in search lights are parabolic and not concave spherical.
Reason : In concave spherical mirror, the image formed is always virtual.

Assertion : Angle of deviation depends on the angle of prism.
Reason : For thin prism \(\delta=(\mu-1) A\)
Where \(\delta=\) angle of deviation,
\(\mu=\) refractive index, \(A=\) angle of prism

A space ship is launched into a circular orbit
close to earth’s surface. What additional
velocity has now to be imparted to the
spaceship in the orbit to overcome the
gravitational pull?
(Radius of earth = 6400 km, g = 9.8 m/s\(^2\))

What is the maximum height attained by a body projected with a velocity equal to one-third of the escape velocity from the surface of the earth? (Radius of the earth \(=R\) )

Two satellites \(S_1\) and \(S_2\) are revolving round a planet in coplanar circular orbits of radii \(r_1\) and \(r_2\) in the same direction, respectively. Their respective periods of revolution are \(1 \mathrm{~h}\) and \(8 \mathrm{~h}\)...

The coefficient of cubical expansion of mercury is \(0.00018 /{ }^{\circ} \mathrm{C}\) and that of brass \(0.00006 /{ }^{\circ} \mathrm{C}\). If a barometer having a brass scale were to read \(74.5 \mathrm{~cm}\) at $$30^{\circ} \mathrm{C}$...

One mole of an ideal diatomic gas undergoes
transition from A to B along a path AB as
shown below.

The change in internal energy of the gas
during the transition is

Assertion : It is hotter over the top of a fire than at the same distance on the sides.
Reason : In the upward direction, the heat propagate through convection.

Assertion : In adiabatic expansion the product of \(p\) and \(V\) always decreases.
Reason : In adiabatic expansion process, work is done by the gas at the cost of internal energy of gas.

Assertion : The molecules of a monoatomic gas has three degrees of freedom.
Reason : The molecules of diatomic gas has five degrees of freedom.

Assertion : Molar heat capacity cannot be defined for isothermal process.
Reason : In isothermal process \(p\)-\(V\) versus \(T\) graph is a dot.

With what minimum acceleration can a fireman slide down a rope while breaking strength of the rope is \(2 / 3\) of the weight?

Four blocks of same mass connected by strings are pulled by a force \(F\) on a smooth horizontal surface as shown in figure. The tension \(T_1, T_2\) and \(T_3\) will be

A body of mass \(5 \times 10^{-3} \mathrm{~kg}\) is launched upon a rough inclined plane making an angle of \(30^{\circ}\) with the horizontal. Obtain the coefficient of friction between the body and the plane if the time of ascent is half ...

The angle of dip, if dip needle oscillating in vertical plane makes 40 oscillations per min in a magnetic meridian and 30 oscillations per minute in vertical plane at right angle to the magnetic meridian is

Assertion : The magnetism of magnet is due to the spin motion of electrons.
Reason : Dipole moment of electron is smaller than that due to orbit motion around nucleus.

Assertion : When \(\theta=45^{\circ}\) or \(135^{\circ}\), the value of \(R\) remains the same, only the sign changes.
Reason : \(R=\frac{u^2 \sin 2 \theta}{g}\)

What will be the a vs x graph for the following
graph?

In an experiment to measure the height of a bridge by dropping stone into water underneath. If the error in measurement of time is \(0.2 \mathrm{~s}\) at the end of \(4 \mathrm{~s}\), then the error in estimation of height of bridge will be...

A long wire having a semicircular loop of
radius r carries a current i as shown in figure.
The magnetic induction at the centre O due to
entire

A conductor lies along the z-axis at \(-1.5 \leq Z \leq 1.5 \mathrm{~m}\) and carries a fixed current of 10.0 \(\mathrm{A}\) in \(-a_z\) direction as shown in figure for a field \(B=3 \times 10^{-4} e^{-0.2 x} a_y \mathrm{~T}\), the total p...

Assertion : Cyclotron does not accelerate electron.
Reason : Mass of the electron is very small.

A load of mass $m$ falls from a height \(h\) on the scale pan hung from a spring as shown. If the spring constant is \(k\) and mass of the scale pan is zero and the mass \(m\) does not bounce relative to the pan, then the amplitude of vibr...

Assertion : A spring of force constant $k$ is cut into two pieces having lengths in the ratio 1 :
2. The force constant of series combination of the two parts is \(\frac{3 k}{2}\).
Reason : The spring connected in series are represented by ...

A boy is pushing a ring of mass \(3 \mathrm{~kg}\) and radius \(0.6 \mathrm{~m}\) with a stick as shown in figure. The stick applies a force of \(3 \mathrm{~N}\) on the ring and rolls it without slipping with an acceleration of 0.4 m/s$$^2$...

Assertion : The total kinetic energy of a rolling solid sphere is the sum of translational and rotational kinetic energies.
Reason : For all solid bodies, total kinetic energy is always twice of translational kinetic energy.

The current gain of a transistor in common emitter mode is 49. The change in collector current and emitter current corresponding to change in base current by \(5.0 \mu \mathrm{A}\), will be

A specimen of silicon is to be made \(P\)-type semiconductor for this one atom of indium, on an average, is doped in \(5 \times 10^7\) silicon atoms. If the number density of silicon is \(5 \times 10^{22}\) atom/\(\mathrm{m}^3\) then the nu...