Statement-I If the lines $x + 2 y - 3 = 0$ and $2 x + k y + 10 = 0$ are parallel, then the value of $‘ k ’ is ‘ 4 ’$ .
Statement-II The lines $3 x + 4 y - 3 = 0$ and $4 x + 3 y - 10 = 0$ are perpendicular

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Statement I is False, Statement II is False

Statement I is False, Statement II is True

Statement I is True, Statement II is True

Statement I is True, Statement II is False

answer is C.

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Detailed Solution

Statement (I) : Slope of line

x + 2 y - 3 = 0

- \frac{1}{2}

Slope of the line $2 x + k y + 10 = 0$ is $\frac{- 2}{k}$

Since, given lines are parallel

Slope are equal

$- \frac{1}{2} = - \frac{2}{k}$

$k = 4$

Statement (II) : Slope of line $3 x + 4 y - 3 = 0$ is $m_{1} = \frac{- 3}{4}$

Slope of line $4 x + 3 y - 10 = 0$ is $m_{2} = \frac{- 4}{3}$

$m_{1} \times m_{2} = \frac{- 3}{4} \times \frac{- 4}{3} = 1 \neq - 1$

$∴$ Given lines are not perpendicular

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