NTA JEE Main 24th January 2023 Shift 2 - Physics

If two vectors $$\vec{P} = \hat{i} + 2m\hat{j} + m\hat{k}$$ and $$\vec{Q} = 4\hat{i} - 2\hat{j} + m\hat{k}$$ are perpendicular to each other. Then, the value of $$m$$ will be

The frequency ($$\nu$$) of an oscillating liquid drop may depend upon radius ($$r$$) of the drop, density ($$\rho$$) of liquid and the surface tension ($$s$$) of the liquid as: $$\nu = r^a \rho^b s^c$$. The values of $$a$$, $$b$$ and $$c$$ respectively are

The velocity-time graph of a body moving in a straight line is shown in figure.

The ratio of displacement and distance travelled by the body in time 0 to 10 s is

A body of mass 200 g is tied to a spring of spring constant 12.5 N m$$^{-1}$$, while the other end of spring is fixed at point $$O$$. If the body moves about $$O$$ in a circular path on a smooth horizontal surface with constant angular speed 5 rad s$$^{-1}$$, then the ratio of extension in the spring to its natural length will be:

Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if $$h = d$$.
In the light of above statements, choose the most appropriate answer form the options given below

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion $$A$$: A pendulum clock when taken to Mount Everest becomes fast.
Reason $$R$$: The value of g (acceleration due to gravity) is less at Mount Everest than its value on the surface of earth.
In the light of the above statements, choose the most appropriate answer from the options given below

If the distance of the earth from Sun is $$1.5 \times 10^6$$ km, then the distance of an imaginary planet from Sun, if its period of revolution is 2.83 years is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion (A): Steel is used in the construction of buildings and bridges.
Reason (R): Steel is more elastic and its elastic limit is high.
In the light of above statements, choose the most appropriate answer from the options given below

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $$T_3 > T_2 > T_1$$ as:

Let $$\gamma_1$$ be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and $$\gamma_2$$ be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio $$\frac{\gamma_1}{\gamma_2}$$ is:

The electric potential at the centre of two concentric half rings of radii $$R_1$$ and $$R_2$$, having same linear charge density $$\lambda$$ is

A cell of emf 90 V is connected across series combination of two resistors each of 100 $$\Omega$$ resistance. A voltmeter of resistance 400 $$\Omega$$ is used to measure the potential difference across each resistor. The reading of the voltmeter will be:

A long solenoid is formed by winding 70 turns cm$$^{-1}$$. If 2.0 A current flows, then the magnetic field produced inside the solenoid is _____.
($$\mu_0 = 4\pi \times 10^{-7}$$ T m A$$^{-1}$$)

A metallic rod of length $$L$$ is rotated with an angular speed of $$\omega$$ normal to a uniform magnetic field $$B$$ about an axis passing through one end of rod as shown in figure. The induced emf will be:

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
$$E_x = E_0 \sin(kz - \omega t)$$
$$B_y = B_0 \sin(kz - \omega t)$$
Then the correct relation between $$E_0$$ and $$B_0$$ is given by

When a beam of white light is allowed to pass through convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called:

An $$\alpha$$ particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength:

A photon is emitted in transition from $$n = 4$$ to $$n = 1$$ level in hydrogen atom. The corresponding wavelength for this transition is (given, $$h = 4 \times 10^{-15}$$ eV s)

The logic gate equivalent to the given circuit diagram is:

Match List I with List II
LIST I                                           LIST II
A. AM Broadcast                         I. 88 - 108 MHz
B. FM Broadcast                          II. 540 - 1600 kHz
C. Television                               III. 3.7 - 4.2 GHz
D. Satellite Communication       IV. 54 MHz - 590 MHz
Choose the correct answer from the options given below:

A body of mass 1 kg begins to move under the action of a time dependent force $$\vec{F} = (t\hat{i} + 3t^2\hat{j})$$ N, where $$\hat{i}$$ and $$\hat{j}$$ are the unit vectors along $$x$$ and $$y$$ axis. The power developed by above force, at the time $$t = 2$$ s, will be _____ W.

A uniform solid cylinder with radius $$R$$ and length $$L$$ has moment of inertia $$I_1$$, about the axis of cylinder. A concentric solid cylinder of radius $$R' = \frac{R}{2}$$ and length $$L' = \frac{L}{2}$$ is carved out of the original cylinder. If $$I_2$$ is the moment of inertia of the carved out portion of the cylinder then $$\frac{I_1}{I_2} =$$ _____.

A spherical ball of radius 1 mm and density 10.5 g cc$$^{-1}$$ is dropped in glycerine of coefficient of viscosity 9.8 poise and density 1.5 g cc$$^{-1}$$. Viscous force on the ball when it attains constant velocity is $$3696 \times 10^{-x}$$ N. The value of $$x$$ is
(Given, $$g = 9.8$$ m s$$^{-2}$$ and $$\pi = \frac{22}{7}$$)

A mass $$m$$ attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass $$m$$ is _____ kg.

A parallel plate capacitor with air between the plate has a capacitance of 15 pF. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant 3.5. Then the capacitance becomes $$\frac{x}{4}$$ pF. The value of $$x$$ is _____.

If a copper wire is stretched to increase its length by 20%. The percentage increase in resistance of the wire is _____%.

A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be $$\frac{x}{130}$$ N. The value of $$x$$ is _____.

Three identical resistors with resistance $$R = 12$$ $$\Omega$$ and two identical inductors with self inductance $$L = 5$$ mH are connected to an ideal battery with emf of 12 V as shown in figure. The current through the battery long after the switch has been closed will be _____ A.

A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be _____ cm.
(Given refractive index of water = $$\frac{4}{3}$$)

The energy released per fission of nucleus of $$^{240}$$X is 200 MeV. The energy released if all the atoms in 120 g of pure $$^{240}$$X undergo fission is _____ $$\times 10^{25}$$ MeV.
(Given $$N_A = 6 \times 10^{23}$$)