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Match List I with List II.

Choose the correct answer from the options given below:

Two identical thin metal plates has charge \( q_1 \) and \( q_2 \) respectively such that \( q_1 > q_2 \). The plates were brought close to each other to form a parallel plate capacitor of capacitance \( C \). The potential difference between them is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below:

A \( 1\,\text{m} \) long wire is broken into two unequal parts \( X \) and \( Y \). The \( X \) part of the wire is stretched into another wire \( W \). Length of \( W \) is twice the length of \( X \) and the resistance of \( W \) is twice that of \( Y \). Find the ratio of length of \( X \) and \( Y \).

A wire \( X \) of length \( 50\,\text{cm} \) carrying a current of \( 2\,\text{A} \) is placed parallel to a long wire \( Y \) of length \( 5\,\text{m} \). The wire \( Y \) carries a current of \( 3\,\text{A} \). The distance between two wires is \( 5\,\text{cm} \) and currents flow in the same direction. The force acting on the wire \( Y \) is

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws \( n \) balls per second, the maximum height the balls can reach is

A circuit element \( X \) when connected to an a.c. supply of peak voltage \( 100\,V \) gives a peak current of \( 5\,A \) which is in phase with the voltage. A second element \( Y \) when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by \( \dfrac{\pi}{2} \). If \( X \) and \( Y \) are connected in series to the same supply, what will be the rms value of the current in ampere?

An unpolarised light beam of intensity \( 2I_{0} \) is passed through a polaroid \( P \) and then through another polaroid \( Q \) which is oriented in such a way that its passing axis makes an angle of \( 30^\circ \) relative to that of \( P \). The intensity of the emergent light is

An \( \alpha \) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.
Choose the correct option from the following options.

An object of mass \( 1\,\text{kg} \) is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, \( g=10\,\text{m s}^{-2} \) and radius of earth \( =6400\,\text{km} \)]

A ball is released from a height \( h \). If \( t_1 \) and \( t_2 \) be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between \( t_1 \) and \( t_2 \).

Two bodies of masses \( m_1 = 5 \, \text{kg} \) and \( m_2 = 3 \, \text{kg} \) are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest.
The force exerted by the inclined plane on the body of mass \( m_1 \) will be: [Take \( g = 10 \, \text{m s}^{-2} \)]
 

If momentum of a body is increased by \( 20\% \), then its kinetic energy increases by

The torque of a force \( 5\hat{i} + 3\hat{j} - 7\hat{k} \) about the origin is \( \tau \). If the force acts on a particle whose position vector \( 2\hat{i} + 2\hat{j} + \hat{k} \), then the value of \( \tau \) will be

A thermodynamic system is taken from an original state \( D \) to an intermediate state \( E \) by the linear process shown in the figure. Its volume is then reduced to the original volume from \( E \) to \( F \) by an isobaric process. The total work done by the gas from \( D \) to \( E \) to \( F \) will be

The vertical component of the earth’s magnetic field is \( 6 \times 10^{-5} \, \text{T} \) at any place where the angle of dip is \( 37^\circ \). The earth’s resultant magnetic field at that place will be (Given \( \tan 37^\circ = \dfrac{3}{4} \) )

The root mean square speed of smoke particles of mass \( 5 \times 10^{-17} \, \text{kg} \) in their Brownian motion in air at NTP is approximately. [Given \( k = 1.38 \times 10^{-23} \, \text{J K}^{-1} \) ]

Light enters from air into a given medium at an angle of \( 45^\circ \) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \( 15^\circ \) from its original direction. The refractive index of the medium is :

A tube of length \( 50 \, \text{cm} \) is filled completely with an incompressible liquid of mass \( 250 \, \text{g} \) and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity \( x\sqrt{F} \) \( \text{rad s}^{-1} \). If \( F \) be the force exerted by the liquid at the other end then the value of \( x \) will be _______.

Nearly \( 10\% \) of the power of a \( 110 \, \text{W} \) light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of \( 1 \, \text{m} \) from the bulb to a distance of \( 5 \, \text{m} \) is \( a \times 10^{-2} \, \text{W} / \text{m}^{2} \). The value of ' \( a \) ' will be ________.

A metal wire of length \( 0.5 \, \text{m} \) and cross-sectional area \( 10^{-4} \, \text{m}^2 \) has breaking stress \( 5 \times 10^{8} \, \text{N m}^{-2} \). A block of \( 10 \, \text{kg} \) is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _______ \( \text{ms}^{-1} \).

The velocity of small ball of mass \( 0.3 \, g \) and density \( 8 \, g/cc \) when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is \( 1.3 \, g/cc \), then the value of viscous force acting on the ball will be \( x \times 10^{-4} \, N \), The value of \( x \) is __________. [use \( g = 10 \, m/s^{2} \) ]

A modulating signal \( 2\sin\left(6.28\times10^6\right)t \) is added to the carrier signal \( 4\sin\left(12.56\times10^9\right)t \) for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will ___ \( \text{MHz} \).

The speed of a transverse wave passing through a string of length \( 50\,\text{cm} \) and mass \( 10\,\text{g} \) is \( 60\,\text{m s}^{-1} \). The area of cross-section of the wire is \( 2.0\,\text{mm}^2 \) and its Young’s modulus is \( 1.2\times10^{11}\,\text{N m}^{-2} \). The extension of the wire over its natural length due to its tension will be \( x\times10^{-5}\,\text{m} \). The value of \( x \) is ______.

The metallic bob of simple pendulum has the relative density \( 5 \). The time period of this pendulum is \( 10\,\text{s} \). If the metallic bob is immersed in water, then the new time period becomes \( 5\sqrt{x}\,\text{s} \). The value of \( x \) will be _____.

A \( 8\,\text{V} \) zener diode along with a series resistance \( R \) is connected across a \( 20\,\text{V} \) supply (as shown in the figure). If the maximum Zener current is \( 25\,\text{mA} \), then the minimum value of \( R \) will be ______ \( \Omega \).

Two radioactive materials \( A \) and \( B \) have decay constant \( 25\lambda \) and \( 16\lambda \) respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of \( B \) to that of \( A \) will be " \( e \) " after a time \( \dfrac{1}{a\lambda} \). The value of \( a \) is ______.

A capacitor of capacitance \( 500\,\mu\text{F} \) is charged completely using a \( dc \) supply of \( 100\,\text{V} \). It is now connected to an inductor of inductance \( 50\,\text{mH} \) to form an \( LC \) circuit. The maximum current in \( LC \) circuit will be ______ \( \text{A} \).