MCQ
Choose the correct answer from the given four options: If the lines given by $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, then the value of $k$ is :
- A$\frac{-5}{4}$
- B$\frac{2}{5}$
- ✓$\frac{15}{4}$
- D$\frac{3}{2}$
✓
Answer
Correct option: C.
$\frac{15}{4}$
Condition for parallel lines is
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
Given lines $3x + 2ky - 2 = 0$
and $2x + 5y - 1 = 0$
Here, $a_1=3, b_1=2 k, c_1=-2$
and $a_2=2, b_2=5, c_2=-1$
From Eq. $(i), \frac{3}{2}=\frac{2\text{k}}{5}$
$\therefore\ \text{k}=\frac{15}{4}$
$\frac{\text{a}_1}{\text{a}_2}=\frac{\text{b}_1}{\text{b}_2}\neq\frac{\text{c}_1}{\text{c}_2}$
Given lines $3x + 2ky - 2 = 0$
and $2x + 5y - 1 = 0$
Here, $a_1=3, b_1=2 k, c_1=-2$
and $a_2=2, b_2=5, c_2=-1$
From Eq. $(i), \frac{3}{2}=\frac{2\text{k}}{5}$
$\therefore\ \text{k}=\frac{15}{4}$
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