Question

Question 7
If the lines given by 3x + 2ky = 2 and 3x + 5y = 1 are parallel, then the value of k is
(a) $-\frac{5}{4}$
(b) $\frac{1}{2}$
(c) $\frac{15}{4}$
(d) $\frac{3}{2}$

Answer 1

Answer - C

Condition for parallel lines is
$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
Given 3x + 2ky – 2 = 0
And 2x + 5y – 1 = 0
Here, $a1=3,b1=2k,c1=-2$
and $a_2=2,b_2=5,c_2=-1$

From Eq (i), $\frac{3}{2}=\frac{2k}{5}$
$\therefore k=\frac{15}{4}$

Also, $\frac{c_1}{c_2}=\frac{-2}{-1}=2$

Thus, $\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$