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If \( Z = \frac{A^2 B^3}{C^4} \), then the relative error in \( Z \) will be:

\( \vec{A} \) is a vector quantity such that \( |\vec{A}| \) = non-zero constant. Which of the following expression is true for \( \vec{A} \)?

Which of the following relations is true for two unit vector \( \vec{A} \) and \( \vec{B} \) making an angle \( \theta \) to each other?

If force \( \vec{F}=3\hat{i}+4\hat{j}-2\hat{k} \) acts on a particle having position vector \(2\hat{i}+\hat{j}+2\hat{k} \) then, the torque about the origin will be:

The height of any point \( P \) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \( P \) will be: (Given \( g \) = acceleration due to gravity at the surface of earth).

The terminal velocity \( (v_t) \) of the spherical rain drop depends on the radius \( (r) \) of the spherical rain drop as:

The relation between root mean square speed \( v_{\mathrm{rms}} \) and most probable speed \( v_p \) for molar mass \( M \) of oxygen gas molecule at the temperature of \( 300 \, \text{K} \) will be:

In the figure, a very large plane sheet of positive charge is shown. \( P_1 \) and \( P_2 \) are two points at distance \( l \) and \( 2l \) from the charge distribution. If \( \sigma \) is the surface charge density, then the magnitude of electric fields \( E_1 \) and \( E_2 \) at \( P_1 \) and \( P_2 \) respectively are:

Match List I with List – II

Choose the CORRECT answer from the options given below:

A long straight wire with a circular cross-section having radius \( R \), is carrying a steady current \( I \). The current \( I \) is uniformly distributed across this cross-section. Then the variation of magnetic field due to current \( I \) with distance \( r \) (\( r<R \)) from its centre will be:

If wattless current flows in the AC circuit, then the circuit is:

The electric field in an electromagnetic wave is given by \( E = 56.5 \sin \omega (t - x/c) \, \mathrm{N\,C^{-1}} \). Find the intensity of the wave if it is propagating along \( x \)-axis in the free space.
(Given \( \varepsilon_0 = 8.85 \times 10^{-12} \, \mathrm{C^2 N^{-1} m^{-2}} \))

The two light beams having intensities \( I \) and \( 9I \) interfere to produce a fringe pattern on a screen. The phase difference between the beams \( \frac{\pi}{2} \) at point P and \( \pi \) at point Q. Then the difference between the resultant intensities at P and Q will be:

A light wave travelling linearly in a medium of dielectric constant \( 4 \), incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:

Given below are two statements :

In the light of the above statements choose the correct answer from the option given below :

The ratio for the speed of the electron in the \( 3\text{rd} \) orbit of \( \text{He}^+ \) to the speed of the electron in the \( 3^{rd} \) orbit of hydrogen atom will be:

The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :

A signal of \( 100 \, \text{THz} \) frequency can be transmitted with maximum efficiency by :

The difference of speed of light in the two media A and \( (v_A - v_B) \) is \( 2.6 \times 10^7 \, \text{m /s}^{} \). If the refractive index of medium B is \( 1.47 \), then the ratio of refractive index of medium B to medium A is: (Given : speed of light in vacuum \( c = 3 \times 10^8 \, \text{m s}^{-1} \) )

A teacher in his physics laboratory allotted an experiment to determine the resistance \( (G) \) of a galvanometer. Students took the observations for \( \frac{1}{3} \) deflection in the galvanometer. Which of the below is true for measuring value of \( G \)?

A uniform chain of \( 6 \, \text{m} \) length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is \( 0.5 \), the maximum length of the chain hanging from the table is ________ \( \text{m} \).

A \( 0.5 \, \text{kg} \) block moving at a speed of \( 12 \, \text{m s}^{-1} \) compresses a spring through a distance \( 30 \, \text{cm} \) when its speed is halved. The spring constant of the spring will be ________ \( \text{N m}^{-1} \).

The velocity of upper layer of water in a river is \( 36 \, \text{km h}^{-1} \). Shearing stress between horizontal layers of water is \( 10^{-3} \, \text{N m}^{-2} \). Depth of the river is __________ \( \text{m} \). (Co-efficient of viscosity of water is \( 10^{-2} \, \text{Pa s} \) )

A steam engine intakes \( 50 \, \text{g} \) of steam at \( 100^\circ \text{C} \) per minute and cools it down to \( 20^\circ \text{C} \). If latent heat of vaporization of steam is \( 540 \, \text{cal g}^{-1} \), then the heat rejected by the steam engine per minute is ________ \( \times 10^{3} \, \text{cal} \).
(Given : specific heat capacity of water : \( 1 \, \text{cal g}^{-1} \, {}^\circ\text{C}^{-1} \) )

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is \( 20 \, \text{cm} \). The length of the open organ pipe is _______ \( \text{cm} \).

The equivalent capacitance between points \( A \) and \( B \) is below shown figure will be________ \( \mu \text{F} \).

A resistor develops \( 300 \, \text{J} \) of thermal energy in \( 15 \, \text{s} \), when a current of \( 2 \, \text{A} \) is passed through it. If the current increases to \( 3 \, \text{A} \), the energy developed in \( 10 \, \text{s} \) is __________ \( \text{J} \).

The total current supplied to the circuit as shown in figure by the \( 5 \, \text{V} \) battery is ______ \( \text{A} \).

The current in a coil of self inductance \( 2.0 \, \text{H} \) is increasing according to \( I = 2 \sin(t^2) \, \text{A} \). The amount of energy spent during the period when current changes from \( 0 \) to \( 2 \, \text{A} \) is __________ \( \text{J} \).

A force on an object of mass \( 100 \, \text{g} \) is \( (10\hat{i} + 5\hat{j}) \, \text{N} \). The position of that object at \( t = 2 \, \text{s} \) is \( (a\hat{i} + b\hat{j}) \, \text{m} \) after starting from rest. The value of \( \frac{a}{b} \) will be __________________.

JEE Main 2022 25th June Morning Shift

Physics Chemistry Mathematics

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If force \( \vec{F}=3\hat{i}+4\hat{j}-2\hat{k} \) acts on a particle having position vector \(2\hat{i}+\hat{j}+2\hat{k} \) then, the torque about the origin will be: