JEE MAIN - Physics (2024 - 31st January Morning Shift)

• 1

  Four identical particles of mass $$m$$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $$\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{L^2}$$, the length of the sides of the square is

  پاسخ دهید

  (A)

  4L
• 2

  Two charges $$q$$ and $$3 q$$ are separated by a distance '$$r$$' in air. At a distance $$x$$ from charge $$q$$, the resultant electric field is zero. The value of $$x$$ is :

  پاسخ دهید

  (C)

  $$\frac{r}{(1+\sqrt{3})}$$
• 3

  The given figure represents two isobaric processes for the same mass of an ideal gas, then

  

  پاسخ دهید

  (B)

  $$P_1>P_2$$
• 4

  In the given arrangement of a doubly inclined plane two blocks of masses $$M$$ and $$m$$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of $$m$$, for which $$M=10 \mathrm{~kg}$$ will move down with an acceleration of $$2 \mathrm{~m} / \mathrm{s}^2$$, is: (take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ and $$\left.\tan 37^{\circ}=3 / 4\right)$$

  

  پاسخ دهید

  (A)

  4.5 kg
• 5

  The relation between time '$$t$$' and distance '$$x$$' is $$t=\alpha x^2+\beta x$$, where $$\alpha$$ and $$\beta$$ are constants. The relation between acceleration $$(a)$$ and velocity $$(v)$$ is :

  پاسخ دهید

  (C)

  $$a=-2 \alpha v^3$$
• 6

  An artillery piece of mass $$M_1$$ fires a shell of mass $$M_2$$ horizontally. Instantaneously after the firing, the ratio of kinetic energy of the artillery and that of the shell is:

  پاسخ دهید

  (B)

  $$\frac{M_2}{M_1}$$
• 7

  The parameter that remains the same for molecules of all gases at a given temperature is :

  پاسخ دهید

  (A)

  kinetic energy
• 8

  A rigid wire consists of a semicircular portion of radius $$R$$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $$B=B_0 \hat{k}$$ as shown in figure. The magnetic force on the wire if it has a current $$i$$ is:

  

  پاسخ دهید

  (B)

  $$-2 i B R \hat{j}$$
• 9

  When a metal surface is illuminated by light of wavelength $$\lambda$$, the stopping potential is $$8 \mathrm{~V}$$. When the same surface is illuminated by light of wavelength $$3 \lambda$$, stopping potential is $$2 \mathrm{~V}$$. The threshold wavelength for this surface is:

  پاسخ دهید

  (B)

  9$$\lambda$$
• 10

  The refractive index of a prism with apex angle $$A$$ is $$\cot A / 2$$. The angle of minimum deviation is :

  پاسخ دهید

  (C)

  $$\delta_m=180^{\circ}-2 A$$
• 11

  The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $$60 \mathrm{~cm}$$, the length of the closed pipe will be:

  پاسخ دهید

  (A)

  15 cm
• 12

  If the wavelength of the first member of Lyman series of hydrogen is $$\lambda$$. The wavelength of the second member will be

  پاسخ دهید

  (C)

  $$\frac{27}{32} \lambda$$
• 13

  A coil is places perpendicular to a magnetic field of $$5000 \mathrm{~T}$$. When the field is changed to $$3000 \mathrm{~T}$$ in $$2 \mathrm{~s}$$, an induced emf of $$22 \mathrm{~V}$$ is produced in the coil. If the diameter of the coil is $$0.02 \mathrm{~m}$$, then the number of turns in the coil is:

  پاسخ دهید

  (B)

  70
• 14

  A coin is placed on a disc. The coefficient of friction between the coin and the disc is $$\mu$$. If the distance of the coin from the center of the disc is $$r$$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

  پاسخ دهید

  (B)

  $$\sqrt{\frac{\mu g}{r}}$$
• 15

  Two conductors have the same resistances at $$0^{\circ} \mathrm{C}$$ but their temperature coefficients of resistance are $$\alpha_1$$ and $$\alpha_2$$. The respective temperature coefficients for their series and parallel combinations are :

  پاسخ دهید

  (B)

  $$\frac{\alpha_1+\alpha_2}{2}, \frac{\alpha_1+\alpha_2}{2}$$
• 16

  If the percentage errors in measuring the length and the diameter of a wire are $$0.1 \%$$ each. The percentage error in measuring its resistance will be:

  پاسخ دهید

  (D)

  0.3%
• 17

  A small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity time graph for the transit of the ball?

  پاسخ دهید

  (B)

  
• 18

  A force is represented by $$F=a x^2+b t^{\frac{1}{2}}$$

  where $$x=$$ distance and $$t=$$ time. The dimensions of $$b^2 / a$$ are:

  پاسخ دهید

  (B)

  $$\left[\mathrm{ML}^3 \mathrm{~T}^{-3}\right]$$
• 19

  In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $$5 \times 10^{10} \mathrm{~Hz}$$ and an amplitude of $$50 \mathrm{~Vm}^{-1}$$. The total average energy density of the electromagnetic field of the wave is : [Use $$\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$$ ]

  پاسخ دهید

  (D)

  $$1.106 \times 10^{-8} \mathrm{Jm}^{-3}$$
• 20

  Identify the logic operation performed by the given circuit.

  

  پاسخ دهید

  (C)

  OR
• 21

  A solid circular disc of mass $$50 \mathrm{~kg}$$ rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \mathrm{~m} / \mathrm{s}$$. The absolute value of work done on the disc to stop it is ________ J.

  پاسخ دهید

  6
• 22

  An electron moves through a uniform magnetic field $$\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T$$. At a particular instant of time, the velocity of electron is $$\vec{u}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}$$. If the magnetic force acting on electron is $$\vec{F}=5 e \hat{k} N$$, where $$e$$ is the charge of electron, then the value of $$B_0$$ is _________ $$T$$.

  پاسخ دهید

  5
• 23

  A parallel plate capacitor with plate separation $$5 \mathrm{~mm}$$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $$2 \mathrm{~mm}$$, while keeping the battery connections intact, the capacitor draws $$25 \%$$ more charge from the battery than before. The dielectric constant of the sheet is _________.

  پاسخ دهید

  2
• 24

  The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $$0.02 \%$$ is _______ $$m$$.

  (Take density of sea water $$=10^3 \mathrm{kgm}^{-3}$$, Bulk modulus of rubber $$=9 \times 10^8 \mathrm{~Nm}^{-2}$$, and $$g=10 \mathrm{~ms}^{-2}$$)

  پاسخ دهید

  18
• 25

  A body starts falling freely from height $$H$$ hits an inclined plane in its path at height $$h$$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $$\frac{H}{h}$$ for which the body will take the maximum time to reach the ground is __________.

  پاسخ دهید

  2
• 26

  A particle performs simple harmonic motion with amplitude $$A$$. Its speed is increased to three times at an instant when its displacement is $$\frac{2 A}{3}$$. The new amplitude of motion is $$\frac{n A}{3}$$. The value of $$n$$ is ___________.

  پاسخ دهید

  7
• 27

  The mass defect in a particular reaction is $$0.4 \mathrm{~g}$$. The amount of energy liberated is $$n \times 10^7 \mathrm{~kWh}$$, where $$n=$$ __________. (speed of light $$\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)$$

  پاسخ دهید

  1
• 28

  A small square loop of wire of side $$l$$ is placed inside a large square loop of wire of side $$L\left(L=l^2\right)$$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $$\sqrt{x} \times 10^{-7} \mathrm{H}$$, where $$x=$$ _________.

  پاسخ دهید

  128
• 29

  Equivalent resistance of the following network is __________ $$\Omega$$.

  

  پاسخ دهید

  1
• 30

  Two waves of intensity ratio $$1: 9$$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $$I_1$$ (b) Waves are coherent is $$I_2$$ and differ in phase by $$60^{\circ}$$. If $$\frac{I_1}{I_2}=\frac{10}{x}$$ then $$x=$$ _________.

  پاسخ دهید

  13