Verified Solution • 2025–26 Session moderate

QJEEM20Ma7dde: JEE Main 2020 Mathematics - Class 12 JEEM20Ma7dde Solution: For which of the following ordered pairs ( , ), the system of…

For which of the following ordered pairs ( μ\mu , δ\delta ), the system of linear equations
x + 2y + 3z = 1
3x + 4y + 5z = μ\mu
4x + 4y + 4z = δ\delta
is inconsistent ?

Multiple Choice Options

  • A (1, 0)
  • B (4, 3)
  • C (4, 6)
  • D (3, 4)

Step-by-Step Verified Solution

For inconsistent system we need

Δ\Delta = 0 and atleast one of Δ\Delta x, Δ\Delta y, Δ\Delta z ≠\ne 0

∴\therefore Δ\Delta = |123345444| = 0

Δ\Delta x = |123μ45δ44|

= (-4) - 2( μ\mu - 5 δ\delta ) + 3(4 μ\mu - 4 δ\delta )

⇒\Rightarrow 2 μ\mu ≠\ne δ\delta + 2 ....(1)

Only ( μ\mu , δ\delta ) = (4, 3) does satisfy the equation (1).

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring