Computational Methods

JKPSC Assistant Professor (Physics) · Physics · 49 practice questions with answers and explanations: 2 Easy, 45 Medium, 2 Hard.

Sample questions

Sample Easy question 1

Which numerical method finds a root by repeatedly halving an interval?

  1. Euler's method
  2. Newton–Raphson
  3. Bisection
  4. Simpson's rule
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Answer: C. It keeps the half in which the sign of the function changes.

Sample Easy question 2

The Python data type for a number such as 3.14 is:

  1. int
  2. float
  3. str
  4. bool
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Answer: B. An int holds whole numbers.

Sample Medium question 3

The Verlet algorithm integrates:

  1. Newton's equations in molecular dynamics
  2. Heat equation
  3. Laplace equation
  4. Schrödinger equation
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Answer: A. It conserves energy well.

Sample Medium question 4

The Jacobi iteration method for linear systems converges when the matrix is:

  1. Strictly diagonally dominant
  2. Triangular
  3. Singular
  4. Zero
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Answer: A. The Gauss–Seidel method converges faster.

Sample Medium question 5

An ordinary differential equation of second order can be solved numerically by converting it into:

  1. Two first-order equations
  2. One third-order equation
  3. An algebraic equation
  4. An integral only
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Answer: A. The RK method can then be used.

Sample Hard question 6

Solving n linear equations by Gaussian elimination takes about how many operations?

  1. O(n)
  2. O(log n)
  3. O(n²)
  4. O(n³)
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Answer: D. The elimination step dominates.

Sample Hard question 7

The trapezoidal rule with step h = 0.5 gives, for ∫₀¹ x dx, the value:

  1. 0.5
  2. 1
  3. 0.75
  4. 0.25
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Answer: A. The rule is exact for straight lines.

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