NTA JEE Mains 27th Jan 2024 Shift 1 - Physics

Given below are two statements: 

Statement (I) : Planck's constant and angular momentum have the same dimensions.

Statement (II) : Linear momentum and moment of force have the same dimensions. In light of the above statements, choose the correct answer from the options given below :

Position of an ant (S in metres) moving in $$Y - Z$$ plane is given by $$S = 2t^2 \hat{j} + 5\hat{k}$$ (where $$t$$ is in second). The magnitude and direction of velocity of the ant at $$t = 1$$ s will be :

A train is moving with a speed of $$12 \text{ m s}^{-1}$$ on rails which are $$1.5$$ m apart. To negotiate a curve radius $$400$$ m, the height by which the outer rail should be raised with respect to the inner rail is (Given, $$g = 10 \text{ m s}^{-2}$$):

Two bodies of mass $$4$$ g and $$25$$ g are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

A body of mass $$1000$$ kg is moving horizontally with a velocity $$6 \text{ m s}^{-1}$$. If $$200$$ kg extra mass is added, the final velocity (in $$\text{m s}^{-1}$$) is:

The acceleration due to gravity on the surface of earth is $$g$$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

Given below are two statements : 

Statement (I) : Viscosity of gases is greater than that of liquids. 

Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

$$0.08$$ kg air is heated at constant volume through $$5°C$$. The specific heat of air at constant volume is $$0.17 \text{ kcal kg}^{-1} \text{ °C}^{-1}$$ and $$1 \text{ J} = 4.18 \text{ joule cal}^{-1}$$. The change in its internal energy is approximately.

The average kinetic energy of a monatomic molecule is $$0.414$$ eV at temperature: (Use $$K_B = 1.38 \times 10^{-23} \text{ J mol}^{-1} \text{ K}^{-1}$$)

An electric charge $$10^{-6}$$ $$\mu$$C is placed at origin $$(0, 0)$$ m of $$X - Y$$ co-ordinate system. Two points $$P$$ and $$Q$$ are situated at $$(\sqrt{3}, \sqrt{3})$$ m and $$(\sqrt{6}, 0)$$ m respectively. The potential difference between the points $$P$$ and $$Q$$ will be :

A wire of resistance $$R$$ and length $$L$$ is cut into $$5$$ equal parts. If these parts are joined parallely, then resultant resistance will be :

A wire of length $$10$$ cm and radius $$\sqrt{7} \times 10^{-4}$$ m connected across the right gap of a meter bridge. When a resistance of $$4.5 \; \Omega$$ is connected on the left gap by using a resistance box, the balance length is found to be at $$60$$ cm from the left end. If the resistivity of the wire is $$R \times 10^{-7} \; \Omega$$ m, then value of $$R$$ is :

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $$\vec{E}$$ and $$\vec{B}$$ represent the electric and magnetic fields respectively, then the region of space may have : 

(A) $$E = 0, B = 0$$; (B) $$E = 0, B \neq 0$$; (C) $$E \neq 0, B = 0$$; (D) $$E \neq 0, B \neq 0$$. Choose the most appropriate answer from the options given below :

A rectangular loop of length $$2.5$$ m and width $$2$$ m is placed at $$60°$$ to a magnetic field of $$4$$ T. The loop is removed from the field in $$10$$ sec. The average emf induced in the loop during this time is

A plane electromagnetic wave propagating in $$x$$-direction is described by $$E_y = (200 \text{ V m}^{-1}) \sin[1.5 \times 10^7 t - 0.05x]$$. The intensity of the wave is : (Use $$\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}$$)

If the refractive index of the material of a prism is $$\cot\left(\frac{A}{2}\right)$$, where $$A$$ is the angle of prism then the angle of minimum deviation will be

A convex lens of focal length $$40$$ cm forms an image of an extended source of light on a photoelectric cell. A current $$I$$ is produced. The lens is replaced by another convex lens having the same diameter but focal length $$20$$ cm. The photoelectric current now is

The radius of third stationary orbit of electron for Bohr's atom is $$R$$. The radius of fourth stationary orbit will be:

Which of the following circuits is reverse-biased?

Identify the physical quantity that cannot be measured using spherometer :

A particle starts from origin at $$t = 0$$ with a velocity $$5\hat{i} \text{ m s}^{-1}$$ and moves in $$x - y$$ plane under action of a force which produces a constant acceleration of $$(3\hat{i} + 2\hat{j}) \text{ m s}^{-2}$$. If the $$x$$-coordinate of the particle at that instant is $$84$$ m, then the speed of the particle at this time is $$\sqrt{\alpha} \text{ m s}^{-1}$$. The value of $$\alpha$$ is _______.

Four particles, each of mass $$1$$ kg are placed at four corners of a square of side $$2$$ m. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______ kg m$$^2$$.

If average depth of an ocean is $$4000$$ m and the bulk modulus of water is $$2 \times 10^9 \text{ N m}^{-2}$$, then fractional compression $$\frac{\Delta V}{V}$$ of water at the bottom of ocean is $$\alpha \times 10^{-2}$$. The value of $$\alpha$$ is _______, (Given, $$g = 10 \text{ m s}^{-2}, \rho = 1000 \text{ kg m}^{-3}$$)

A particle executes simple harmonic motion with an amplitude of $$4$$ cm. At the mean position, velocity of the particle is $$10 \text{ cm s}^{-1}$$. The distance of the particle from the mean position when its speed becomes $$5 \text{ cm s}^{-1}$$ is $$\sqrt{\alpha}$$ cm, where $$\alpha =$$ ______.

A thin metallic wire having cross sectional area of $$10^{-4} \text{ m}^2$$ is used to make a ring of radius $$30$$ cm. A positive charge of $$2\pi$$ C is uniformly distributed over the ring, while another positive charge of $$30$$ pC is kept at the centre of the ring. The tension in the ring is _______ N; provided that the ring does not get deformed (neglect the influence of gravity). (Given, $$\frac{1}{4\pi\epsilon_0} = 9 \times 10^9$$ SI units)

The charge accumulated on the capacitor connected in the following circuit is ______ $$\mu$$C. (Given $$C = 150 \; \mu$$F)

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $$5.0$$ cm. The magnitude of the magnetic field at a point P midway between the wires is ______ $$\mu$$T. (Given: $$\mu_0 = 4\pi \times 10^{-7} \text{ T m A}^{-1}$$)

Two coils have mutual inductance $$0.002$$ H. The current changes in the first coil according to the relation $$i = i_0 \sin \omega t$$, where $$i_0 = 5$$ A and $$\omega = 50\pi \text{ rad s}^{-1}$$. The maximum value of emf in the second coil is $$\frac{\pi}{\alpha}$$ V. The value of $$\alpha$$ is

Two immiscible liquids of refractive indices $$\frac{8}{5}$$ and $$\frac{3}{2}$$ respectively are put in a beaker as shown in the figure. The height of each column is $$6$$ cm. A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is $$\frac{\alpha}{4}$$ cm. The value of $$\alpha$$ is _______.

In a nuclear fission process, a high mass nuclide $$(A \approx 236)$$ with binding energy $$7.6$$ MeV/Nucleon dissociated into two middle mass nuclides $$(A \approx 118)$$, having binding energy of $$8.6$$ MeV/Nucleon. The energy released in the process would be _______ MeV.