Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Value of λ for Which the Lines 3x + 4y = 5, 5x + 4y = 4 and λX + 4y = 6 Meet at a Point is - Mathematics

MCQ

The value of λ for which the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point is

• 2

• 1

• 4

• 3

• 0

#### Solution

1

It is given that the lines 3x + 4y = 5, 5x + 4y = 4 and λx + 4y = 6 meet at a point.
In other words, the given lines are concurrent.

$\begin{vmatrix}3 & 4 & - 5 \\ 5 & 4 & - 4 \\ \lambda & 4 & - 6\end{vmatrix} = 0$

$\Rightarrow 3\left( - 24 + 16 \right) - 4\left( - 30 + 4\lambda \right) - 5\left( 20 - 4\lambda \right) = 0$

$\Rightarrow - 24 + 120 - 16\lambda - 100 + 20\lambda = 0$

$\Rightarrow 4\lambda = 4$

$\Rightarrow \lambda = 1$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Q 25 | Page 134