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Physics

Considering a group of positive charges, which of the following statements is correct?

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by \( 50\% \). The percentage change in voltage sensitivity of the galvanometer will be:

3.

Heat energy of \( 735 \, \text{J} \) is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

4.

The \( H \) amount of thermal energy is developed by a resistor in \( 10 \, \text{s} \) when a current of \( 4 \, \text{A} \) is passed through it. If the current is increased to \( 16 \, \text{A} \), the thermal energy developed by the resistor in \( 10 \, \text{s} \) will be:

5.

Under the same load, wire \( A \) having length \( 5.0 \, \text{m} \) and cross section \( 2.5 \times 10^{-5} \, \text{m}^{2} \) stretches uniformly by the same amount as another wire \( B \) of length \( 6.0 \, \text{m} \) and a cross section of \( 3.0 \times 10^{-5} \, \text{m}^{2} \) stretches. The ratio of the Young’s modulus of wire \( A \) to that of wire \( B \) will be:

6.

A stone of mass \( 1 \, \text{kg} \) is tied to end of a massless string of length \( 1 \, \text{m} \). If the breaking tension of the string is \( 400 \, \text{N} \), then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

7.

A long conducting wire having a current \( I \) flowing through it, is bent into a circular coil of \( N \) turns. Then it is bent into a circular coil of \( n \) turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

8.

Given below are two statements:
Statement I: For transmitting a signal, size of antenna \( (l) \) should be comparable to wavelength of signal (at least \( l = \dfrac{\lambda}{4} \) in dimension)
Statement II: In amplitude modulation, amplitude of carrier wave remains constant (unchanged).
In the light of the above statements, choose the most appropriate answer from the options given below:

9.

A hypothetical gas expands adiabatically such that its volume changes from \( 08 \, \text{litres} \) to \( 27 \, \text{litres} \). If the ratio of final pressure of the gas to initial pressure of the gas is \( \dfrac{16}{81} \). Then the ratio of \( \dfrac{C_P}{C_V} \) will be:

10.

The radius of electron’s second stationary orbit in Bohr’s atom is \( R \). The radius of \( 3^{\text{rd}} \) orbit will be:

11.

A body is moving with constant speed, in a circle of radius \( 10 \, \text{m} \). The body completes one revolution in \( 4 \, \text{s} \). At the end of \( 3^{\text{rd}} \) second, the displacement of body (in \( \text{m} \)) from its starting point is:

12.

If the metals \( A \) and \( B \) are exposed to radiation of wavelength \( 350 \, \text{nm} \). The work functions of metals \( A \) and \( B \) are \( 4.8 \, \text{eV} \) and \( 2.2 \, \text{eV} \). The choose the correct option:

13.

Match List I with List II:

Choose the correct answer from the options given below:

14.

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index \( \frac{5}{3} \) is poured inside the bucket, the microscope have to be raised by \( 30 \, \text{cm} \) to focus the object again. The height of the liquid in the bucket is:

15.

A body weight \( W \), is projected vertically upwards from earths surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

16.

An alternating voltage source \( V = 260 \sin(628 t) \) is connected across a pure inductor of \( 5 \, \text{mH} \). Inductive reactance in the circuit is:

17.

For a solid rod, the Youngs modulus of elasticity is \( 3.2 \times 10^{11} \, \text{N m}^{-2} \) and density is \( 8 \times 10^{3} \, \text{kg m}^{-3} \). The velocity of longitudinal wave in the rod will be:

18.

Given below are two statements:
Statement I: In a typical transistor, all three regions emitter, base and collector have same doping level.
Statement II: In a transistor, collector is the thickest and base is the thinnest segment.
In the light of the above statements, choose the most appropriate answer from the options given below.

19.

A body of mass \(10 \, \text{kg}\) is moving with an initial speed of \(20 \, \text{m/s}\). The body stops after \(5 \, \text{s}\) due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity \(g = 10 \, \text{m s}^{-2}\))

20.

Match List I with List II:

Choose the correct answer from the options given below:

21.

The displacement equations of two interfering waves are given by:
\( y_1 = 10 \sin \left(\omega t + \frac{\pi}{3}\right) \, \text{cm} \), \( y_2 = 5\left[ \sin \omega t + \sqrt{3} \cos \omega t \right] \, \text{cm} \) respectively. The amplitude of the resultant wave is ______ \( \text{cm} \).

22.

Two discs of same mass and different radii are made of different materials such that their thicknesses are \(1 \, \text{cm}\) and \(0.5 \, \text{cm}\) respectively. The densities of materials are in the ratio \(3:5\). The moment of inertia of these discs respectively about their diameters will be in the ratio of \( \dfrac{x}{6} \). The value of \(x\) is ______.

23.

A series LCR circuit consists of \(R = 80\,\Omega\), \(X_L = 100\,\Omega\), and \(X_C = 40\,\Omega\). The input voltage is \(2500 \cos(100\pi t)\, \text{V}\). The amplitude of current, in the circuit, is ______ \( \text{A} \).

24.

If the binding energy of ground state electron in a hydrogen atom is \(13.6 \, \text{eV}\), then the energy required to remove the electron from the second excited state of \(\mathrm{Li}^{2+}\) will be: \( x \times 10^{-1} \, \text{eV} \). The value of \(x\) is ______.

25.

Two bodies are projected from ground with same speeds \( 40 \, \text{m s}^{-1} \) at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of \( 60^\circ \), with horizontal then sum of the maximum heights, attained by the two projectiles, is ______ m.
(Given \( g = 10 \, \text{m s}^{-2} \))

26.

Two light waves of wavelengths \( 800 \, \text{nm} \) and \( 600 \, \text{nm} \) are used in Young’s double slit experiment to obtain interference fringes on a screen placed \( 7 \, \text{m} \) away from plane of slits. If the two slits are separated by \( 0.35 \, \text{mm} \), then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ mm.

27.

Two parallel plate capacitors \( C_{1} \) and \( C_{2} \) each having capacitance of \( 10 \, \mu \text{F} \) are individually charged by a \( 100 \, \text{V} \) D.C. source. Capacitor \( C_{1} \) is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor \( C_{2} \) is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor \( C_{1} \) is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ______ V.

28.

A ball is dropped from a height of \( 20 \, \text{m} \). If the coefficient of restitution for the collision between ball and floor is \( 0.5 \), after hitting the floor, the ball rebounds to a height of ______ m.

29.

A water heater of power \( 2000 \, \text{W} \) is used to heat water. The specific heat capacity of water \( 4200 \, \text{J kg}^{-1}\text{K}^{-1} \). The efficiency of heater is \( 70\% \). Time required to heat \( 2 \, \text{kg} \) of water from \( 10^\circ\text{C} \) to \( 60^\circ\text{C} \) is ______ s. (Assume that the specific heat capacity of water remains constant over the temperature range of the water)

30.

For the given circuit, in the steady state, \( |V_{B}-V_{D}| = \) ______ V.

JEE Main 2023 31st Jan Evening Shift

Physics Chemistry Mathematics

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An alternating voltage source \( V = 260 \sin(628 t) \) is connected across a pure inductor of \( 5 \, \text{mH} \). Inductive reactance in the circuit is:

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JEE Mains | PYQ