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Physics

A thin prism \( P_1 \) with an angle \( 6^\circ \) and made of glass of refractive index \( 1.54 \) is combined with another prism \( P_2 \) made from glass of refractive index \( 1.72 \) to produce dispersion without average deviation. The angle of prism \( P_2 \) is:

2.

A point source of \( 100 \, \mathrm{W} \) emits light with \( 5\% \) efficiency. At a distance of \( 5 \, \mathrm{m} \) from the source, the intensity produced by the electric field component is:

3.

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The nuclear density of nuclides \( {}^{10}_{5}\mathrm{B} \), \( {}^{6}_{3}\mathrm{Li} \), \( {}^{56}_{26}\mathrm{Fe} \), \( {}^{20}_{10}\mathrm{Ne} \) and \( {}^{209}_{83}\mathrm{Bi} \) can be arranged as \( \rho^{N}_{\mathrm{Bi}} > \rho^{N}_{\mathrm{Fe}} > \rho^{N}_{\mathrm{Ne}} > \rho^{N}_{\mathrm{B}} > \rho^{N}_{\mathrm{Li}} \).
Reason R: The radius \( R \) of nucleus is related to its mass number \( A \) as \( R = R_{0} A^{1/3} \), where \( R_0 \) is a constant.
In the light of the above statements, choose the correct answer from the options given below

4.

The output \( Y \) for the inputs \( A \) and \( B \) of circuit is given by:

Truth table of the shown circuit is:

5.

In the given circuit, rms value of current \( (I_{\mathrm{rms}}) \) through the resistor \( R \) is:

6.

An object is allowed to fall from a height \( R \) above the earth, where \( R \) is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be:

7.

A machine gun of mass \( 10 \, \text{kg} \) fires \( 20 \, \text{g} \) bullets at the rate of \( 180 \) bullets per minute with a speed of \( 100 \, \text{m s}^{-1} \) each. The recoil velocity of the gun is :

8.

The equivalent resistance between \( A \) and \( B \) is ___________.

9.

As shown in the figure, a point charge \( Q \) is placed at the centre of conducting spherical shell of inner radius \( a \) and outer radius \( b \). The electric field due to charge \( Q \) in three different regions \( I \), \( II \) and \( III \) is given by: \( ( I : r < a , \, II : a < r < b , \, III : r > b ) \).

10.

A current carrying rectangular loop \( PQRS \) is made of uniform wire. The length \( PR = QS = 5 \, \text{cm} \) and \( PQ = RS = 100 \, \text{cm} \). If ammeter current reading changes from \( I \) to \( 2I \), the ratio of magnetic forces per unit length on the wire \( PQ \) due to wire \( RS \) in the two cases respectively \( ( f_{PQ}^{I} : f_{PQ}^{2I} ) \) is :

11.

For a simple harmonic motion in a mass spring shown, the surface is frictionless. When the mass of the block is \( 1 \, \text{kg} \), the angular frequency is \( \omega_{1} \). When the mass block is \( 2 \, \text{kg} \) the angular frequency is \( \omega_{2} \). The ratio \( \frac{\omega_{1}}{\omega_{2}} \) is :

12.

An electron accelerated through a potential difference \( V_{1} \) has a de-Broglie wavelength of \( \lambda \). When the potential is changed to \( V_{2} \), its de-Broglie wavelength increases by \( 50\% \). The value of \( \left( \frac{V_{1}}{V_{2}} \right) \) is equal to:

13.

Other is labelled as Reason R
Assertion A : Efficiency of a reversible heat engine will be highest at \( -273^\circ \text{C} \) temperature of cold reservoir.
Reason R : The efficiency of Carnot’s engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as \( n = \left( 1 - \frac{T_2}{T_1} \right) \).
In the light of the above statements, choose the correct answer from the options given below :

14.

A vehicle travels \( 4 \, \text{km} \) with speed of \( 3 \, \text{km/h} \) and another \( 4 \, \text{km} \) with speed of \( 5 \, \text{km/h} \), then its average speed is :

15.

A flask contains hydrogen and oxygen in the ratio of \( 2 : 1 \) by mass at temperature \( 27^\circ \text{C} \). The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is :

16.

Match List I and List II :

Choose the correct answer from the options given below :

17.

Match List I and List II :

Choose the correct answer from the options given below :

18.

As shown in the figure, a current of \( 2 \, \text{A} \) flowing in an equilateral triangle of side \( 4\sqrt{3} \, \text{cm} \). The magnetic field at the centroid \( O \) of the triangle is :

(Neglect the effect of earth’s magnetic field)

19.

A block of \( \sqrt{3} \, \text{kg} \) is attached to a string whose other end is attached to the wall. An unknown force \( F \) is applied so that the string makes an angle of \( 30^\circ \) with the wall. The tension \( T \) is: ( Given \( g = 10 \, \text{m s}^{-2} \) )

20.

A force is applied to a steel wire ‘\( A \)’, rigidly clamped at one end. As a result elongation in the wire is \( 0.2 \, \text{mm} \). If same force is applied to another steel wire ‘\( B \)’ of double the length and a diameter \( 2.4 \) times that of the wire ‘\( A \)’, the elongation in the wire ‘\( B \)’ will be (wire having uniform circular cross sections)

21.

A body of mass \( 2 \, \text{kg} \) is initially at rest. It starts moving unidirectionally under the influence of a source of constant power \( P \). Its displacement in \( 4 \, \text{s} \) is \( \dfrac{1}{3} \alpha^{2} \sqrt{P} \, \text{m} \). The value of \( \alpha \) will be _____.

22.

The velocity of a particular executing SHM varies with displacement \( (x) \) as \( 4v^{2} = 50 - x^{2} \). The time period of oscillations is \( \dfrac{x}{7} \, \text{s} \). The value of \( x \) is ____. \( \left( \text{Take } \pi = \dfrac{22}{7} \right) \)

23.

A uniform disc of mass \( 0.5 \, \text{kg} \) and radius \( r \) is projected with velocity \( 18 \, \text{m/s} \) at \( t = 0 \, \text{s} \) on a rough horizontal surface. It starts off with a purely sliding motion at \( t = 0 \, \text{s} \). After \( 2 \, \text{s} \) it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after \( 2 \, \text{s} \) will be _____ \( \text{J} \) (Given, coefficient of friction is \( 0.3 \) and \( g = 10 \, \text{m/s}^{2} \).)

24.

A stone tied to \( 180 \, \text{cm} \) long string at its end is making \( 28 \) revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is \( \dfrac{1936}{x} \, \text{m s}^{-2} \). The value of \( x \) ___. \( \left( \text{Take } \pi = \dfrac{22}{7} \right) \)

25.

In a Young’s double slit experiment, the intensities at two points, for the path differences \( \frac{\lambda}{4} \) and \( \frac{\lambda}{3} \) (\( \lambda \) being the wavelength of light used) are \( I_1 \) and \( I_2 \) respectively. If \( I_0 \) denotes the intensity produced by each one of the individual slits, then \( \frac{I_1 + I_2}{I_0} = \) ________.

26.

A faulty thermometer reads \( 5^{\circ} \text{C} \) in melting ice and \( 95^{\circ} \text{C} \) in stream. The correct temperature on absolute scale will be ________ \( \text{K} \) when the faulty thermometer reads \( 41^{\circ} \text{C} \).

27.

In an ac generator, a rectangular coil of \( 100 \) turns each having area \( 14 \times 10^{-2}\, \text{m}^2 \) is rotated at \( 360 \, \text{rev/min} \) about an axis perpendicular to a uniform magnetic field of magnitude \( 3.0 \, \text{T} \). The maximum value of the emf produced will be ______ \( \text{V} \). (Take \( \pi = \frac{22}{7} \))

28.

If the potential difference between \( B \) and \( D \) is zero, the value of \( x \) is \( \frac{1}{n} \, \Omega \). The value of \( n \) is _______.

29.

A radioactive nucleus decays by two different process. The half life of the first process is \( 5 \, \text{minutes} \) and that of the second process is \( 30 \, \text{s} \). The effective half-life of the nucleus is calculated to be \( \frac{\alpha}{11} \, \text{s} \). The value of \( \alpha \) is __________.

30.

As shown in figure, a cuboid lies in a region with electric field \( {E} = 2x^{2}\hat{i} - 4y\hat{j} + 6\hat{k} \, \frac{\text{N}}{\text{C}} \). The magnitude of charge within the cuboid is \( n \varepsilon_{0} \, \text{C} \). The value of \( n \) is _____. (If dimension of cuboid is \( 1 \times 2 \times 3 \, \text{m}^{3} \))

JEE Main 2023 30th Jan Evening Shift

Physics Chemistry Mathematics

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For a simple harmonic motion in a mass spring shown, the surface is frictionless. When the mass of the block is \( 1 \, \text{kg} \), the angular frequency is \( \omega_{1} \). When the mass block is \( 2 \, \text{kg} \) the angular frequency is \( \omega_{2} \). The ratio \( \frac{\omega_{1}}{\omega_{2}} \) is :

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JEE Mains | PYQ