AIIMS 2018

In a series R-C circuit shown in figure, the
applied voltage is 10 V and the voltage across
capacitor is found to be 8V. Then, the voltage
across R and the phase difference between
current and the applied voltage will
respectively be

An ideal coil of \(10 \mathrm{~H}\) is connected in series with a resistance of \(5 \Omega\) and a battery of \(5 \mathrm{~V}\). After \(2 \mathrm{~s}\), after the connection is made, the current flowing (in ampere) in the circuit is

In a circuit \(L, C\) and \(R\) are connected in series with an alternating voltage source of frequency \(f\). The current leads the voltage by \(45^{\circ}\). The value of \(C\) is

The half-life of a radioactive substance is \(20 \mathrm{~min}\). The approximate time interval \(\left(t_2-t_1\right)\) between the time \(t_2\), when \(\frac{2}{3}\) of it has decayed and time \(t_1\) when \(\frac{1}{3}\) of it had decaye...

Assertion If electrons in an atom were
stationary, then they would fall into the
nucleus.
Reason Electrostatic force of attraction acts
between negatively charged electrons and
positive nucleus.

Assertion Radioactive nuclei emits \(\beta^{-}\)-particles.
Reason Electrons exist inside the nucleus.

An infinite number of identical capacitors
each of capacitance 1 \(\mu\)F are connected as
shown in the figure. Then, the equivalent
capacitance between A and B is

Assertion A dielectric slab is inserted
between plates of an isolated charged
capacitor which remain same.
Reason Charge on an isolated system is
conserved.

Body of mass M is much heavier than the
other body of mass m. The heavier body with
speed v collides with the lighter body which
was at rest initially elastically. The speed of
lighter body after collision is

Three bodies having masses \(5 \mathrm{~kg}, 4 \mathrm{~kg}\) and \(2 \mathrm{~kg}\) is moving at the speed of \(5 \mathrm{~m} / \mathrm{s}, 4 \mathrm{~m} / \mathrm{s}\) and \(2 \mathrm{~m} / \mathrm{s}\) respectively along \(X\)-axis. The ...

Assertion Two particles moving in the same
direction do not lose all their energy in
completely inelastic collision.
Reason Principle of conservation of
momentum holds true for all kinds of
collisions.

A diode detector is used to detect and
amplitude modulated wave of 60%
modulation by using a condenser of capacity
250 pF in parallel with a load resistance
100 k\(\Omega\). Find the maximum modulated
frequency which could be detected by it...

A metal wire has a resistance of \(35 \Omega\). If its length is increased to double by drawing it, then its new resistance will be

In the circuit in the figure, if no current
flows through the galvanometer when the
key K is closed, the bridge is balanced. The
balancing condition for bridge is

In the circuit, shown the galvanometer \(G\) of resistance \(60 \Omega\) is shunted by a resistance \(r=0.02 \Omega\). The current through \(R\) is nearly \(1 \mathrm{~A}\). The value of resistance \(R\) (in ohm) is nearly

In the adjoining circuit diagram, the
readings of ammeter and voltmeter are 2 A
and 120 V, respectively. If the value of R is
75\(\Omega\), then the voltmeter resistance will be

Assertion Terminal voltage of a cell is greater
than emf of cell during charging of the cell.
Reason The emf of a cell is always greater
than its terminal voltage.

Assertion Bulb generally get fused when
they are switched on or off.
Reason When we switch on or off, a circuit
current changes in it rapidly.

The graph between the energy log E of an
electron and its de-Broglie wavelength log \(\lambda\) will be

A system \(S\) consists of two coils \(A\) and \(B\). The coil \(A\) carries a steady current \(I\). While the coil \(B\) is suspended nearby as shown in figure. Now, if the system is heated, so as to raise the temperature of two coils stea...

A circular loop of radius 0.3 cm lies parallel
to a much bigger circular loop of radius 20 cm.
The centre of the small loop on the axis of
the bigger loop. The distance between their
centres is 15 cm. If a current of 20 A flows
through the ...

A half ring of radius \(R\) has a charge of \(\lambda\) per unit length. The electric force on \(1 \mathrm{C}\) charged placed at the centre is

Positive charge \(Q\) is distributed uniformly over a circular ring of radius \(R\). A point particle having a mass \((m)\) and a negative charge \(-q\) is placed on its axis at a distance \(x\) from the centre. Assuming \(x < R\), find the...

Assertion Mass of a body decreases slightly
when it is negatively charged.
Reason Charging is due to transfer of electrons.

Assertion A convex mirror always make a
virtual image.
Reason The ray always diverge after
reflection from the convex mirror.

Two satellites \(A\) and \(B\) revolve round the same planet in coplanar circular orbits lying in the same plane. Their periods of revolutions are \(1 \mathrm{~h}\) and \(8 \mathrm{~h}\), respectively. The radius of the orbit of \(A\) is $$...

A planet is revolving around the sun in a circular orbit with a radius \(r\). The time period is \(T\). If the force between the planet and star is proportional to \(r^{-3 / 2}\), then the square of time period is proportional to

The weight of a body on the surface of the
earth is 63 N. What is the gravitational force
on it due to the earth at a height equal to
half the radius of the earth?

An ideal gas of mass \(m\) in a state \(A\) goes to another state \(B\) via three different processes as shown in figure. If \(Q_1, Q_2\) and \(Q_3\) denote the heat absorbed by the gas along the three paths, then

A gas consisting of a rigid diatomic molecules
was initially under standard condition. Then,
gas was compressed adiabatically to
one-fifth of its initial volume. What will be
the mean kinetic energy of a rotating
molecule in the final state...

Assertion In isothermal process, whole of
the heat energy supplied to the body is
converted into internal energy.
Reason According to the first law of
thermodynamics,
\(\Delta Q=\Delta U+\Delta W\)

Assertion Internal energy of an ideal gas
does not depend on volume of gas.
Reason Internal energy depends only on
temperature of gas.

A wooden wedge of mass \(M\) and inclination angle \((\alpha)\) rest on a smooth floor. A block of mass $m$ is kept on wedge. A force \(F\) is applied on the wedge as shown in the figure such that block remains stationary with respect to we...

A piece of ice slides down a rough inclined plane at \(45^{\circ}\) inclination in twice the time that it takes to slide down an identical but frictionless inclined plane. What is the coefficient of friction between ice and incline?

A body of mass 5 kg is suspended by a spring
balance on an inclined plane as shown in
figure.

So, force applied on spring balance is

In the figure, blocks A and B of
masses 2m and m are connected
with a string and system is hanged
vertically with the help of a spring.
Spring has negligible mass. Find
out magnitude of acceleration of
masses 2m and m just after the
instan...

In the figure, mass of a ball is \(\frac{9}{5}\) times mass of the rod. Length of rod is \(1 \mathrm{~m}\). The level of ball is same as rod level. Find out time taken by the ball to reach at upper end of rod.

Assertion Angle of repose is equal to angle
of limiting friction.
Reason When a body is just at the point of
motion, the force of friction of this stage is
called as limiting friction.

The horizontal component of the earth's magnetic field at any place is \(0.36 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^2\). If the angle of dip at that place is \(60^{\circ}\), then the value of vertical component of the earth's magnetic fi...

Assertion The maximum height of projectile
is always 25% of the maximum range.
Reason For maximum range, projectile
should be projected at 90°.

Assertion A body is momentarily at rest at
the instant, if it reverse the direction.
Reason A body cannot have acceleration, if
its velocity is zero at a given instant of time.

A long straight wire, carrying current \(I\) is bent at its mid-point to form an angle of \(45^{\circ}\). Induction of magnetic field (in tesla) at point \(P\), distant \(R\) from point of bending is equal to

An element \(d l=d x \hat{\mathbf{i}}\) (where, \(d x=1 \mathrm{~cm}\) ) is placed at the origin and carries a large current \(i=10 \mathrm{~A}\). What is the magnetic field on the \(Y\)-axis at a distance of \(0.5 \mathrm{~m}\) ?

Consider the following figure, a uniform
magnetic field of 0.2 T is directed along the
positive X-axis. The magnetic flux through
top surface of the figure.

Assertion A magnetic field interacts with a
moving charge and not with a stationary
charge.
Reason A moving charge produce a
magnetic field.

A block of rectangular size of mass \(m\) and area of cross-section \(A\), floats in a liquid of density \(\rho\). If we give a small vertical displacement from equilibrium, it undergoes SHM with time period \(T\), then

Assertion A pendulum is falling freely its
time period becomes zero.
Reason Freely falling body has the
acceleration equal to g.

Assertion Smaller drop of water resist deformation forces better than the larger drops.
Reason Excess pressure inside drop is inversely proportional to its radius.

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of disc. The insect now moves along a diameter of the disc to reach its other end. During the journey...

Assertion The angular momentum of
system always remain constant.
Reason For a system, \(\tau_{\mathrm{ext}}=\frac{d L}{d t}=0\)