Mathematical Methods

JKPSC Assistant Professor (Physics) · Physics · 58 practice questions with answers and explanations: 5 Easy, 53 Medium, 0 Hard.

Sample questions

Sample Easy question 1

The Lorentz transformation for length contraction gives a moving rod's length as:

  1. L₀√(1 − v²/c²)
  2. L₀(1 + v²/c²)
  3. L₀(1 − v²/c²)
  4. L₀/√(1 − v²/c²)
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Answer: A. Lengths contract along the motion.

Sample Easy question 2

The Laplace transform of a unit step function is:

  1. s
  2. 1/s
  3. e⁻ˢ
  4. 1/s²
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Answer: B. L{u(t)} = 1/s.

Sample Easy question 3

The eigenvalues of the Pauli matrix σz are:

  1. 0 and 1
  2. +i and −i
  3. +1 and −1
  4. 1 and 2
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Answer: C. σz = diag(1, −1).

Sample Medium question 4

A second-rank tensor in three dimensions has how many components?

  1. 27
  2. 3
  3. 9
  4. 6
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Answer: C. It has two indices.

Sample Medium question 5

The Kronecker delta δᵢⱼ equals:

  1. 1 if i = j, else 0
  2. 1 always
  3. i + j
  4. 0 always
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Answer: A. It is the identity tensor.

Sample Medium question 6

The Levi-Civita symbol εᵢⱼₖ is:

  1. Zero
  2. Diagonal
  3. Symmetric
  4. Totally antisymmetric
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Answer: D. ε₁₂₃ = 1.

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