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JEE Main 202225 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
25 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2022 · 25 June · Evening Shift · Mathematics · Determinants

The system of equations - kx + 3y - 14z = 25 - 15x + 4y - kz = 3 -...

The system of equations
−kx+3y−14z=25- kx + 3y - 14z = 25

−15x+4y−kz=3- 15x + 4y - kz = 3

−4x+y+3z=4- 4x + y + 3z = 4

Question: is consistent for all kk in the set

Options

  1. ARR
  2. BR−{−11,13}R - \left\{- 11, 13\right\}
  3. CR−{−13}R - \left\{- 13\right\}
  4. DR−{−11,11}R - \left\{- 11, 11\right\}

Correct answer

D. R−{−11,11}R - \left\{- 11, 11\right\}

Step-by-step solution

For consistent solutions ∆≠0∆ \ne 0

⇒ \left|\begin{cases}- k & 3 & - 14 \\ - 15 & 4 & - k \\ - 4 & 1 & 3\end{cases}\right| \ne 0

⇒−k(12+k)−3(−45−4k)−14(−15+16)≠0⇒ - k\left(12 + k\right) - 3\left(- 45 - 4k\right) - 14\left(- 15 + 16\right) \ne 0

⇒−12k−k2+135+12k−14≠0⇒ - 12k - {k}^{2} + 135 + 12k - 14 \ne 0

⇒k2≠121⇒ {k}^{2} \ne 121

⇒k≠11,−11⇒ k \ne 11, - 11

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