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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
For how many diff erent values of $a$ does the following system have at least two distinct solutions?

$a x+y=0$

$x+(a+10) y=0$

  • A
    $0$
  • B
    $1$
  • ✓
    $2$
  • D
    Infinitely many
✓

Answer

Correct option: C.
$2$
c
(c)

We have, $a x+y=0$

$x+(a+10) y=0$

From Eqs.$(i)$ and $(ii)$, we get

$\frac{a}{1}=\frac{1}{a+10} \Rightarrow a^2+10 a-1=0$

$a=\frac{-10 \pm \sqrt{104}}{2}$

$\therefore$ Two values of $a$ for systems has at least two distinct solution.

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