JEE MAIN - Physics (2024 - 4th April Evening Shift)

1
Applying the principle of homogeneity of dimensions, determine which one is correct, where $$T$$ is time period, $$G$$ is gravitational constant, $$M$$ is mass, $$r$$ is radius of orbit.
پاسخ دهید
(C)
$$T^2=\frac{4 \pi^2 r^3}{G M}$$
2
A $$2 \mathrm{~kg}$$ brick begins to slide over a surface which is inclined at an angle of $$45^{\circ}$$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:
پاسخ دهید
(A)
1

Match List I with List II

	LIST I
A.	Purely capacitive circuit	I.
B.	Purely inductive circuit	II.
C.	LCR series at resonance	III.
D.	LCR series circuit	IV.

Choose the correct answer from the options given below:

پاسخ دهید

(B)

A-I. B-IV, C-II, D-III

4
Which of the diode circuit shows correct biasing used for the measurement of dynamic resistance of p-n junction diode :
پاسخ دهید
(D)
5
A sample of gas at temperature $$T$$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $$\gamma=3 / 2$$. The work done by the gas in the process is:

$$(\mu=1 \text { mole })$$
پاسخ دهید
(B)
$$R T[2-\sqrt{2}]$$
6
The magnetic moment of a bar magnet is $$0.5 \mathrm{~Am}^2$$. It is suspended in a uniform magnetic field of $$8 \times 10^{-2} \mathrm{~T}$$. The work done in rotating it from its most stable to most unstable position is:
پاسخ دهید
(C)
$$8 \times 10^{-2} \mathrm{~J}$$
7
In simple harmonic motion, the total mechanical energy of given system is $$E$$. If mass of oscillating particle $$P$$ is doubled then the new energy of the system for same amplitude is:

پاسخ دهید
(D)
$$E$$
8
Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason R.

Assertion A: Number of photons increases with increase in frequency of light.

Reason R: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

In the light of the above statements, choose the most appropriate answer from the options given below:
پاسخ دهید
(A)
$$\mathbf{A}$$ is not correct but $$\mathbf{R}$$ is correct.
9
A $$90 \mathrm{~kg}$$ body placed at $$2 \mathrm{R}$$ distance from surface of earth experiences gravitational pull of :

($$\mathrm{R}=$$ Radius of earth, $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$)
پاسخ دهید
(C)
100 N
10
According to Bohr's theory, the moment of momentum of an electron revolving in $$4^{\text {th }}$$ orbit of hydrogen atom is:
پاسخ دهید
(A)
$$2 \frac{h}{\pi}$$
11
A cyclist starts from the point $$P$$ of a circular ground of radius $$2 \mathrm{~km}$$ and travels along its circumference to the point $$\mathrm{S}$$. The displacement of a cyclist is:

پاسخ دهید
(A)
$$\sqrt8$$ km
12
A body of $$m \mathrm{~kg}$$ slides from rest along the curve of vertical circle from point $$A$$ to $$B$$ in friction less path. The velocity of the body at $$B$$ is:

(given, $$R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2$$ and $$\sqrt{2}=1.4$$)
پاسخ دهید
(D)
21.9 m/s
13
The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:
پاسخ دهید
(D)
$$9: 1$$
14
The translational degrees of freedom $$\left(f_t\right)$$ and rotational degrees of freedom $$\left(f_r\right)$$ of $$\mathrm{CH}_4$$ molecule are:
پاسخ دهید
(B)
$$f_t=3$$ and $$f_r=3$$
15
A charge $$q$$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:
پاسخ دهید
(A)
$$\frac{q}{2 \epsilon_0}$$
16
Correct formula for height of a satellite from earths surface is :
پاسخ دهید
(A)
$$\left(\frac{T^2 R^2 g}{4 \pi^2}\right)^{1 / 3}-R$$
17
Given below are two statements :

Statement I : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II : The rise of a liquid in a capillary tube does not depend on the inner radius of the tube.

In the light of the above statements, choose the correct answer from the options given below :
پاسخ دهید
(D)
Statement I is true but Statement II is false.
18
An electric bulb rated $$50 \mathrm{~W}-200 \mathrm{~V}$$ is connected across a $$100 \mathrm{~V}$$ supply. The power dissipation of the bulb is:
پاسخ دهید
(C)
12.5 W
19
Arrange the following in the ascending order of wavelength:

A. Gamma rays $$\left(\lambda_1\right)$$

B. $$x$$ - rays $$\left(\lambda_2\right)$$

C. Infrared waves $$\left(\lambda_3\right)$$

D. Microwaves $$\left(\lambda_4\right)$$

Choose the most appropriate answer from the options given below
پاسخ دهید
(A)
$$\lambda_1<\lambda_2<\lambda_3<\lambda_4$$
20
Identify the logic gate given in the circuit :

پاسخ دهید
(A)
OR gate
21
In a system two particles of masses $$m_1=3 \mathrm{~kg}$$ and $$m_2=2 \mathrm{~kg}$$ are placed at certain distance from each other. The particle of mass $$m_1$$ is moved towards the center of mass of the system through a distance $$2 \mathrm{~cm}$$. In order to keep the center of mass of the system at the original position, the particle of mass $$m_2$$ should move towards the center of mass by the distance _________ $$\mathrm{cm}$$.
پاسخ دهید
3
22
Two parallel long current carrying wire separated by a distance $$2 r$$ are shown in the figure. The ratio of magnetic field at $$A$$ to the magnetic field produced at $$C$$ is $$\frac{x}{7}$$. The value of $$x$$ is __________.

پاسخ دهید
5
23
A bus moving along a straight highway with speed of $$72 \mathrm{~km} / \mathrm{h}$$ is brought to halt within $$4 s$$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ $$m$$.
پاسخ دهید
40
24
A rod of length $$60 \mathrm{~cm}$$ rotates with a uniform angular velocity $$20 \mathrm{~rad} \mathrm{s}^{-1}$$ about its perpendicular bisector, in a uniform magnetic filed $$0.5 T$$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _________ V.
پاسخ دهید
0
25
The disintegration energy $$Q$$ for the nuclear fission of $${ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+n$$ is _______ $$\mathrm{MeV}$$.

Given atomic masses of $${ }^{235} \mathrm{U}: 235.0439 u ;{ }^{140} \mathrm{Ce}: 139.9054 u, { }^{94} \mathrm{Zr}: 93.9063 u ; n: 1.0086 u$$, Value of $$c^2=931 \mathrm{~MeV} / \mathrm{u}$$.
پاسخ دهید
208
26
Mercury is filled in a tube of radius $$2 \mathrm{~cm}$$ up to a height of $$30 \mathrm{~cm}$$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric pressure $$=10^5 \mathrm{~Nm}^{-2}$$, density of mercury $$=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~m} \mathrm{~s}^{-2}, \pi=\frac{22}{7})$$
پاسخ دهید
177
27
A light ray is incident on a glass slab of thickness $$4 \sqrt{3} \mathrm{~cm}$$ and refractive index $$\sqrt{2}$$ The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ $$\mathrm{cm}$$.

(Given $$\sin 15^{\circ}=0.25$$)
پاسخ دهید
2
28
Two wires $$A$$ and $$B$$ are made up of the same material and have the same mass. Wire $$A$$ has radius of $$2.0 \mathrm{~mm}$$ and wire $$B$$ has radius of $$4.0 \mathrm{~mm}$$. The resistance of wire $$B$$ is $$2 \Omega$$. The resistance of wire $$A$$ is ________ $$\Omega$$.
پاسخ دهید
32
29
The displacement of a particle executing SHM is given by $$x=10 \sin \left(w t+\frac{\pi}{3}\right) m$$. The time period of motion is $$3.14 \mathrm{~s}$$. The velocity of the particle at $$t=0$$ is _______ $$\mathrm{m} / \mathrm{s}$$.
پاسخ دهید
10
30
A parallel plate capacitor of capacitance $$12.5 \mathrm{~pF}$$ is charged by a battery connected between its plates to potential difference of $$12.0 \mathrm{~V}$$. The battery is now disconnected and a dielectric slab $$(\epsilon_{\mathrm{r}}=6)$$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ________ $$\times10^{-12} \mathrm{~J}$$.
پاسخ دهید
750