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JEE Mains | PYQ

\( \left(P+\frac{a}{\nu^{2}}\right)(V-b)=RT \) represents the equation of state of some gases. Where \( P \) is the pressure, \( V \) is the volume. \( T \) is the temperature and \( a \), \( b \), \( R \) are the constants. The physical quantity, which has dimensional formula as that of \( \frac{b^{2}}{a} \), will be:

An object moves with speed \( v_{1} \), \( v_{2} \) and \( v_{3} \) along a line segment \( AB \), \( BC \) and \( CD \) respectively as shown in figure. Where \( AB = BC \) and \( AD = 3AB \), then average speed of the object will be:

Let \( \sigma \) be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region \( {E}_{I} \), \({E}_{II} \) and \( {E}_{III} \) are: 

A mercury drop of radius \( 10^{-3} \, \text{m} \) is broken into \( 125 \) equal size droplets. Surface tension of mercury is \( 0.45 \, \text{N m}^{-1} \). The gain in surface energy is:

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of \( \lambda \). An alpha particle having certain kinetic energy has the same de-Broglie wavelength \( \lambda \). The ratio of kinetic energy of proton and that of alpha particle is:

Match List I with List II:

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Which of the following frequencies do not belong to FM broadcast.

A block of mass \( 5 \ \text{kg} \) is placed at rest on a table of rough surface. Now, if a force of \( 30 \ \text{N} \) is applied in the direction parallel to surface of the table, the block slides through a distance of \( 50 \ \text{m} \) in an interval of time \( 10 \ \text{s} \). Coefficient of kinetic friction is: (given \( g = 10 \ \text{m} / \text{s}^{2} \) )

A steel wire with mass per unit length \( 7.0 \times 10^{-3} \ \text{kg} \ \text{m}^{-1} \) is under tension of \( 70 \ \text{N} \). The speed of transverse wave in the wire will be:

The mass of proton, neutron and helium nucleus are respectively \( 1.0073 \ \text{u} \), \( 1.0087 \ \text{u} \) and \( 4.0015 \ \text{u} \). The binding energy of helium nucleus is:

A sample of gas at temperature \( T \) is adiabatically expanded to double its volume. The work done by the gas in the process is: (given, \( \gamma = \frac{3}{2} \))

A child stands on the edge of the cliff \( 10 \, \text{m} \) above the ground and throws a stone horizontally with an initial speed of \( 5 \, \text{m}\,\text{s}^{-1} \). Neglecting the air resistance, the speed with which the stone hits the ground will be ________ \( \text{m}\,\text{s}^{-1} \). (given, \( g = 10 \, \text{m}\,\text{s}^{-2} \))

Match List I with List II:

Choose the correct answer from the options given below:

Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

Match List I with List II:

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‘\( n \)’ polarizing sheets are arranged such that each makes an angle \( 45^\circ \) with the proceeding sheet. An unpolarized light of intensity \( I \) is incident into this arrangement. The output intensity is found to be \( \dfrac{I}{64} \). The value of \( n \) will be:

If earth has a mass nine times and radius twice to that of a planet \( P \). Then \( \frac{v_e}{3}\sqrt{x}\, \text{ms}^{-1} \) will be the minimum velocity required by a rocket to pull out of gravitational force of \( P \), where \( v_e \) is escape velocity on earth. The value of \( x \) is:

The equivalent resistance between \( A \) and \( B \) of the network shown in figure:

Two equal positive point charges are separated by a distance \( 2a \). The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge \( q_0 \) becomes maximum is \( \frac{a}{\sqrt{x}} \). The value of \( x \) is ________.

A light of energy \( 12.75 \, \text{eV} \) is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is \( \frac{x}{\pi}\times 10^{-17}\, \text{eV}\,\text{s} \). The value of \( x \) is _______. (use \( h=4.14\times 10^{-15}\, \text{eV}\,\text{s},\, c=3\times 10^{8}\, \text{m}\,\text{s}^{-1} \)).

In an experiment to find emf of a cell using potentiometer, the length of null point for a cell of emf \( 1.5\,\text{V} \) is found to be \( 60\,\text{cm} \). If this cell is replaced by another cell of emf \( E \), the length of null point increases by \( 40\,\text{cm} \). The value of \( E \) is \( \frac{x}{10}\,\text{V} \). The value of \( x \) is ________.

A thin cylindrical rod of length \( 10\,\text{cm} \) is placed horizontally on the principle axis of a concave mirror of focal length \( 20\,\text{cm} \). The rod is placed in a such a way that mid point of the rod is at \( 40\,\text{cm} \) from the pole of mirror. The length of the image formed by the mirror will be \( \frac{x}{3}\,\text{cm} \). The value of \( x \) is ______.

A small particle moves to position \( 5\hat{i} - 2\hat{j} + \hat{k} \) from its initial position \( 2\hat{i} + 3\hat{j} - 4\hat{k} \) under the action of force \( 5\hat{i} + 2\hat{j} + 7\hat{k} \, \text{N} \). The value of work done will be \( \_\_\_\_\_\_\_ \) \( \text{J} \).

A certain pressure ‘\( P \)’ is applied to \( 1 \, \text{litre} \) of water and \( 2 \, \text{litre} \) of a liquid separately. Water gets compressed to \( 0.01\% \) whereas the liquid gets compressed to \( 0.03\% \). the ratio of Bulk modulus of water to that of the liquid is \( \frac{3}{x} \). The value of \( x \) is \( \_\_\_\_\_\_\_ \).

The series LCR circuit is connected to an ac source of \( 220 \, \text{V} \), \( 50 \, \text{Hz} \). The circuit contain a resistance \( R = 100\Omega \) and an inductor of inductive reactance \( X_L = 79.6\Omega \). The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be \( \_\_\_\_\_ \) \( \mu \text{F} \).

The amplitude of a particle executing SHM is \( 3 \, \text{cm} \). The displacement at which its kinetic energy will be \( 25\% \) more than the potential energy is: \( \_\_\_\_ \) \( \text{cm} \).

A solid cylinder is released from rest from the top of an inclined plane of inclination \( 30^\circ \) and length \( 60 \, \text{cm} \). If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is \( \_\_\_\_\_\_ \) \( \text{ms}^{-1} \). (Given \( g = 10 \, \text{ms}^{-2} \))

A charge particle of \( 2\mu \text{C} \) accelerated by a potential difference of \( 100 \, \text{V} \) enters a region of uniform magnetic field of magnitude \( 4 \, \text{mT} \) at right angle to the direction of field. The charge particle completes semicircle of radius \( 3 \, \text{cm} \) inside magnetic field. The mass of the charge particle is \( \_\_\_\_\_ \times 10^{-18} \) \( \text{kg} \).