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JEE Advanced 2016Paper 2
Exam
JEE Advanced
Year
2016
Paper
Paper 2
Subject
Mathematics
Chapter
Determinants

JEE Advanced 2016 · Paper 2 · Mathematics · Determinants

Let a, λ, u ∈ ℝ . Consider the system of linear equations ax + 2y =...

Let a,λ,u∈Ra, \lambda, u \in \mathbb{R} . Consider the system of linear equations
ax+2y=λax + 2y = \lambda
3x−2y=μ3x - 2y = \mu
Which of the following statement(s) is (are) correct ?

Options

  1. AIf a=−3,a = - 3, then the system has infinitely many solutions for all values of λ\lambda and μ\mu
  2. BIf a≠−3,a \ne - 3, then the system has a unique solution for all values of λ\lambda and μ\mu
  3. CIf λ+μ=0,\lambda + \mu = 0, then the system has infinitely many solutions for a=−3a = - 3
  4. DIf λ+μ≠0,\lambda + \mu \ne 0, then the system has no solution for a=−3a = - 3

Correct answer

B. If a≠−3,a \ne - 3, then the system has a unique solution for all values of λ\lambda and μ\mu

Step-by-step solution

ax+2y=λax + 2y = \lambda
3x−2y=μ3x - 2y = \mu
If a=−3a = - 3 lines will be parallel or coincident, parallel for λ+μ≠0\lambda + \mu \ne 0 and coincident if λ+μ=0\lambda + \mu = 0 and if a≠−3a \ne - 3 lines are intersecting ⇒⇒ unique solution.
If parallel then no solution & If coincident then infinite solution

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