Sample questions
You've seen the pattern — here are a few of the actual PYQs.
ESE2026
Consider the following statements regarding cancellation laws : Let A, B, C be n×n matrices, then
- if rank A = n and AB = AC, then B = C
- if rank A = n, then AB = 0 implies B = 0. Hence if AB = 0, but A ≠ 0 as well as B ≠ 0, then rank A < n and rank B < n
Which of the above statements is/are correct ?
- A 1 only
- B Both 1 and 2
- C 2 only
- D Neither 1 nor 2
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2026
Which one of the following statements is correct in the context of quadratic forms V = x^T Ax, where x = [x1, x2 ... xn]^T ?
- A V < 0 for all vectors x except x = 0, if and only if all the eigenvalues of A are positive
- B V ≤ 0 for all vectors x and V = 0 for at least one vector x = 0, if and only if all the eigenvalues of A are non-negative or non-zero but at least one of the eigenvalues is zero
- C V is negative-definite if −V is positive-definite, with a corresponding condition on the eigenvalues of A
- D V is negative-semi definite if −V is positive-semi definite, with a corresponding condition on the eigenvalues of −A
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
ESE2025
Consider the following matrix: A = [[-2, 2, -3], [2, 1, -6], [-1, -2, 0]] The Eigen values are
- A -3, -3 and 5
- B -3, 3 and -5
- C 3, 3 and -5
- D 3, -3 and 5
Answer key not yet available (pending official release)
Engineering › Engineering Mathematics & General
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