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Physics

Given below are two statements: One is labelled a Assertion A and the other is labelled as Reason R.

Assertion A: Product of Pressure ($P$) and time ($t$) has the same dimension at that of coefficient of viscosity.
Reason R: $\text{Coefficient of viscosity} = \frac{\text{Force}}{\text{Velocity gradient}}$.

Choose the correct answer from the options given below:

2.

A particle of mass $ m $ is moving in a circular path of constant radius $ r $ such that its centripetal acceleration $ a $ is varying with time $ t $ as $ a = k^{2} r t^{2} $, where $ k $ is a constant. The power delivered to the particle by the force acting on it is given as:

3.

Motion of a particle in $ x-y $ plane is described by a set of following equations $ x=4\sin\left(\frac{\pi}{2}-\omega t\right)\, \text{m} $ and $ y=4\sin(\omega t)\, \text{m} $. The path of the particle will be:

4.

Match List-I with List-II

Choose the correct answer from the options given below:

5.

Two planets $ A $ and $ B $ of equal mass are having their period of revolutions $ T_{A} $ and $ T_{B} $ such that $ T_{A}=2T_{B} $. These planets are revolving in the circular orbits of radii $ r_{A} $ and $ r_{B} $ respectively. Which out of the following would be the correct relationship of their orbits?

6.

A water drop of diameter $ 2 \, \text{cm} $ is broken into $ 64 $ equal droplets. The surface tension of water is $ 0.075 \, \text{N/m} $. In this process the gain in surface energy will be:

7.

Given below are two statements:
Statement-I: When $ \mu $ amount of an ideal gas undergoes adiabatic change from state $ (P_{1}, V_{1}, T_{1}) $ to state $ (P_{2}, V_{2}, T_{2}) $, then work done is $ W = \dfrac{\mu R (T_{2}-T_{1})}{1-\gamma} $, where $ \gamma = \dfrac{C_{p}}{C_{v}} $, and $ R $ = universal gas constant.
Statement-II: In the above case, when work is done on the gas, the temperature of the gas would rise.
Choose the correct answer from the options given below:

8.

Given below are two statements:
Statement-I: A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.
Statement-II: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.
Choose the correct answer from the options given below:

9.

The three charges $ \dfrac{q}{2} $, $ q $ and $ \dfrac{q}{2} $ are placed at the corners $ A $, $ B $ and $ C $ of a square of side $ a $ as shown in figure. The magnitude of electric field $ (E) $ at the corner $ D $ of the square, is:

10.

An infinitely long hollow conducting cylinder with radius $ R $ carries a uniform current along its surface. Choose the correct representation of magnetic field $ (B) $ as a function of radial distance $ (r) $ from the axis of cylinder.

11.

A radar sends an electromagnetic signal of electric field $ (E_{0}) = 2.25 \, \text{V/m} $ and magnetic field $ (B_{0}) = 1.5 \times 10^{-8} \, \text{T} $ which strikes a target on line of sight at a distance of $ 3 \, \text{km} $ in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal as transmitted at time $ t = 0 $ from radar, then after how much time echo will reach to the transmitted at time $ t = 0 $ from radar, then after how much time echo will echo to the radar?

12.

The refracting angle of a prism is $ A $ and refractive index of the material of the prism is $ \cot(A/2) $. Then the angle of minimum deviation will be:

13.

The aperture of the objective is $ 24.4 \, \text{cm} $. The resolving power of this telescope, if a light of wavelength 2440 Å is used to see the object will be:

14.

The de Broglie wavelengths for an electron and a photon are $ \lambda_e $ and $ \lambda_p $ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

15.

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, $ K_p $ are related as:

16.

In the following circuit, the correct relation between output ($ Y $) and inputs $ A $ and $ B $ will be:

17.

For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode:

18.

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: $ n\text{-}p\text{-}n $ transistor permits more current than a $ p\text{-}n\text{-}p $ transistor.
Reason R: Electrons have greater mobility as a charge carrier.
Choose the correct answer from the options given below:

19.

Match List-I with List-II

Choose the correct answer from the options given below:

20.

The velocity of sound in a gas, in which two wavelengths $ 4.08 \, \text{m} $ and $ 4.16 \, \text{m} $ produce $ 40 $ beats in $ 12 \, \text{s} $, will be:

21.

A pendulum is suspended by a string of length $ 250 \, \text{cm} $. The mass of the bob of the pendulum is $ 200 \, \text{g} $. The bob is pulled aside until the string is at $ 60^\circ $ with Vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ________ $ \text{m s}^{-1} $. (if $ g = 10 \, \text{m /s}^{2} $)

22.

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $ R $ using a given resistor of $ 15 \, \Omega $. The galvanometer ($ G $) shows null deflection when tapping key is at $ 43 \, \text{cm} $ mark from end A. If the end correction for end A is $ 2 \, \text{cm} $, then the determined value of $ R $ will be ________ $ \Omega $.

23.

Current measured by the ammeter $ A $ in the reported circuit when no current flows through $ 10 \, \Omega $ resistance, will be ________ $ \text{A} $.

24.

An AC source is connected to an inductance of $ 100 \, \text{mH} $, a capacitance of $ 100 \, \mu \text{F} $ and a resistance of $ 120 \, \Omega $ as shown in figure. The time in which the resistance having a thermal capacity $ 2 \, \text{J}/^\circ\text{C} $ will get heated by $ 16^\circ \text{C} $ is ______ $ \text{s} $.

25.

The position vector of $ 1 \, \text{kg} $ object is $ \vec{r} = (3\hat{i} - \hat{j}) \, \text{m} $ and its velocity $ \vec{v} = (3\hat{j} + \hat{k}) \, \text{m}\,\text{s}^{-1} $. The magnitude of its angular momentum is $ \sqrt{x} \, \text{N}\,\text{m} $ where $ x $ is _______.

26.

A man of $ 60 \, \text{kg} $ is running on the road and suddenly jumps into a stationary trolly car of mass $ 120 \, \text{kg} $. Then, the trolly car starts moving with velocity $ 2 \, \text{m}\,\text{s}^{-1} $. The velocity of the running man was ________ $ \text{m}\,\text{s}^{-1} $, when he jumps into the car.

27.

A hanging mass $ M $ is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by $ 2 \, Mg $ force. In this situation, tension in the string is $ \dfrac{x}{5} \, Mg $ for $ x = $ ______. Neglect mass of the string and friction of the block (bigger mass) with ice slab.
(Given $ g = $ acceleration due to gravity)

28.

The total internal energy of two mole monoatomic ideal gas at temperature $ T = 300 \, \text{K} $ will be ______ $ \text{J} $. (Given $ R = 8.31 \, \text{J/mol}\,\text{K} $)

29.

A single ionized magnesium atom $ (A = 20) $ ion is accelerated to kinetic energy $ 5 \, \text{keV} $, and is projected perpendicularly into a magnetic field $ B $ of the magnitude $ 0.5 \, \text{T} $. The radius of path formed will be _____ $ \text{cm} $.

30.

A telegraph line of length $ 100 \, \mathrm{km} $ has a capacity of $ 0.01 \, \mu \mathrm{F}/\mathrm{km} $ and it carries an alternating current at $ 0.5 $ kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ________ $ \mathrm{mH} $. (if $ \pi = \sqrt{10} $ ).

JEE Main 2022 28th June Morning Shift

Physics Chemistry Mathematics

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A man of $ 60 \, \text{kg} $ is running on the road and suddenly jumps into a stationary trolly car of mass $ 120 \, \text{kg} $. Then, the trolly car starts moving with velocity $ 2 \, \text{m}\,\text{s}^{-1} $. The velocity of the running man was ________ $ \text{m}\,\text{s}^{-1} $, when he jumps into the car.

JEE MainsJEE AdvanceBITSATJEE Mains | PYQ

JEE Mains JEE Advance BITSAT
JEE Mains | PYQ