IIT JAM 2024 Question Paper PDF with Solutions

IIT JAM 2024 Questions

• 1.

  The divergence of a 3-dimensional vector \(\frac{𝑟̂}{𝑟^3}\) (𝑟̂ is the unit radial vector) is:

  • \(\text{Zero}\)

  • \(-\frac{1}{r^4}\)

  • \(\frac{1}{r^3}\)
  • \(-\frac{3}{r^4}\)
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• 2.

  The plane 𝑧=0 separates two linear dielectric media with relative permittivities 𝜀_𝑟1=4 and 𝜀_𝑟2=3, respectively. There is no free charge at the interface. If the electric field in the medium 1 is 𝐸⃗ ₁=3𝑥̂+2𝑦̂ +4𝑧̂, then the displacement vector \(\overrightarrow{D_2}\) in medium 2 is: (𝜀₀ is the permittivity of free space)

  • (3𝑥̂ + 4𝑦̂ + 6𝑧̂)𝜀₀
  • (3𝑥̂ + 6𝑦̂ + 8𝑧̂)𝜀₀
  • (9𝑥̂ + 6𝑦̂ + 16𝑧̂)𝜀₀
  • (4𝑥̂ + 2𝑦̂ + 3𝑧̂)𝜀₀
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• 3.

  In the following OP-AMP circuit, 𝑣_𝑖𝑛 and 𝑣_𝑜𝑢𝑡 represent the input and output signals, respectively.
  
  Choose the correct statement(s):

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• 4.

  In the x-y plane, a vector is given by
  \(\overrightarrow𝐹 (𝑥, 𝑦) = \frac{−𝑦𝑥̂ + 𝑥𝑦̂}{𝑥^ 2 + 𝑦^2} . \)
  The magnitude of the flux of \(\overrightarrow∇ ×\overrightarrow 𝐹\) , through a circular loop of radius 2, centered at the origin, is:

  • π
  • 2π
  • 4π
  • 0
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• 5.

  Consider a thick biconvex lens (thickness t=4cm and refractive index n=1.5) whose magnitudes of the radii of curvature R1 and R2, of the first and second surfaces are 30cm and 20cm, respectively. Surface 2 is silvered to act as a mirror. A point object is placed at point A on the axis (OA= 60cm) as shown in the figure. If its image is formed at point Q, the distance d between O and Q is_____ cm. (Rounded off to two decimal places)
  

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