JEE Main Exam January 2024
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Questions and Answers

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: ______

4g

A train is moving with a speed of 12 m/s 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 m/s²).

5.4 cm

Which of the following circuits is reverse-biased?

  • +2 V ~~~ +4 V
  • -5 V ~~~ +2 V (correct)
  • +2 V ~~~ -10 V
  • +2 V ~~~ -10 V
  • Identify the physical quantity that cannot be measured using spherometer:

    <p>Specific rotation of liquids</p> Signup and view all the answers

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

    <p>2:5</p> Signup and view all the answers

    0.08 kg air is heated at constant volume through 5°C. The specific heat of air at constant volume is 0.17 kcal/kg°C and J = 4.18 joule/cal. The change in its internal energy is approximately.

    <p>284 J</p> Signup and view all the answers

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

    <p>R/9</p> Signup and view all the answers

    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

    <p>1V</p> Signup and view all the answers

    An electric charge 10µC is placed at origin (0, 0) m of X-Y coordinate system. Two points P and Q are situated at (√3, √3)m and (√6, 0)m respectively. The potential difference between the points P and Q will be:

    <p>0 V</p> Signup and view all the answers

    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:

    <p>I</p> Signup and view all the answers

    A body of mass 1000 kg is moving horizontally with a velocity 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:

    <p>5</p> Signup and view all the answers

    A plane electromagnetic wave propagating in x-direction is described by Ey = (200 Vm-1) sin[1.5 × 107t – 0.05 x]; The intensity of the wave is: (Use ∈0 = 8.85 × 10-12 C2N-1m-2)

    <p>53.1 W/m²</p> Signup and view all the answers

    Given below are two statements: Statement (I): Planck's constant and angular momentum have same dimensions. Statement (II): Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below:

    <p>Statement I is true but Statement II is false</p> Signup and view all the answers

    A wire of length 10 cm and radius √7×10-4 m connected across the right gap of a meter bridge. When a resistance of 4.5 Ω 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 × 10-7 Ωm, then the value of R is :

    <p>66</p> Signup and view all the answers

    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:

    <p>R/25</p> Signup and view all the answers

    The average kinetic energy of a monatomic molecule is 0.414 eV at temperature: (Use kB = 1.38 × 10⁻²³ J/mol-K)

    <p>3200 K</p> Signup and view all the answers

    A particle starts from origin at t = 0 with a velocity 5i m/s and moves in x-y plane under action of a force which produces a constant acceleration of (3i+2j)m/s². If the x-coordinate of the particle at that instant is 84 m, then the speed of the particle at this time is √am/s. The value of a is

    <p>673</p> Signup and view all the answers

    A thin metallic wire having cross sectional area of 10-4 m² is used to make a ring of radius 30 cm. A positive charge of 2π 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, 1/(4πε0)=9 × 10^9 SI units)

    <p>3</p> Signup and view all the answers

    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 μT (Given : μo = 4π*10^-7 TmA-¹)

    <p>160</p> Signup and view all the answers

    The charge accumulated on the capacitor connected in the following circuit is μC (Given C = 150 μF)

    <p>400</p> Signup and view all the answers

    Two coils have mutual inductance 0.002 H. The current changes in the first coil according to the relation i = i₀ sin ωt, where i₀ = 5A and ω = 50π rad/s. The maximum value of emf in the second coil is V. The value of α is

    <p>2</p> Signup and view all the answers

    Two immiscible liquids of refractive indices 3/2 and 8/5 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 α cm. The value of α is

    <p>31</p> Signup and view all the answers

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

    <p>236</p> Signup and view all the answers

    Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is kgm².

    <p>16</p> Signup and view all the answers

    A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position, velocity of the particle is 10 cm/s. The distance of the particle from the mean position when its speed becomes 5 cm/s is √a cm, where a =

    <p>12</p> Signup and view all the answers

    Study Notes

    JEE Main Examination - January 2024

    • Held on: Saturday, 27th January, 2024
    • Time: 9:00 AM to 12:00 NOON

    Mathematics Section-A

    • Question 1: 2√2 < k ≤ 3√2 is the solution.
    • Question 2: The distance from (7, -2, 11) to the line x-6/1 = y-4/0 = z-8/3 is 14
    • Question 3: x(t)=y(t) occurs at t=log42
    • Question 4: Orthocentre (2, 2) is the solution for (a,b).
    • Question 5: A=8, B=4, A=B^3 is the solution.

    Physics Section-A

    • Question 31: Velocity of ant at t=1s is 4 m/s in the y-direction
    • Question 32: Viscosity of gases is less than that of liquids. Surface tension of a liquid decreases due to the presence of insoluble impurities. Statement I is incorrect, Statement II is correct.
    • Question 33: Angle of minimum deviation is π-2A/2
    • Question 34: E=0, B=0 is a possible condition.
    • Question 35: Acceleration due to gravity would be 4g.

    Chemistry Section-A

    • Question 61: Phosphodiester linkage joins two nucleotides.
    • Question 62: The compound with highest enol content is the one with the most resonance structures.
    • Question 63: Fluorine does not display variable oxidation states.
    • Question 64: The strongest Bronsted base is NH2−.
    • Question 65: [Ar] 3d7 will have the highest magnetic moment.

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    Prepare for the JEE Main Examination with this comprehensive quiz covering Mathematics, Physics, and Chemistry sections. Each section comprises challenging questions that focus on key concepts and problem-solving skills. Test your knowledge and readiness for the upcoming exam on January 27, 2024.

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