IIM B UG (B.Sc-Hons.)- Sample Paper 2026 · Quant & DI · Question 26

IIM B UG (B.Sc-Hons.)- Sample Paper 2026 question on Determinants, with the answer and a step-by-step solution.

DeterminantsAlgebraMultiple choiceHard

For which real value of k does the following system have no solution?

kx + y + z = 1, x + ky + z = 1, x + y + kz ={k}^{2}

  1. A
    0 only
  2. B
    −2 only
  3. C
    Both 1 and −2
  4. D
    1 only
Pick an option, then check.
Answer & solution

Answer: Option B

The coefficient determinant of the system factorises as (k − 1)²(k + 2).

It vanishes only at k = 1 and k = −2, so those are the only values that can give no solution or infinitely many.

Test k = 1: all three equations become x + y + z = 1, so the system is consistent with infinitely many solutions. This is not the case wanted.

Test k = −2: adding the three equations gives (k + 2)(x + y + z) = 2 + k².

At k = −2 the left side is 0 while the right side is 2 + 4 = 6, which is impossible.

So the system is inconsistent and has no solution only at k = −2.

Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.

Practice timed →