A) \[-\frac{5}{4}\]
B) \[\frac{2}{5}\]
C) \[\frac{15}{4}\]
D) \[\frac{3}{2}\]
Correct Answer: C
Solution :
| Condition for parallel lines is |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] (i) |
| Given lines, \[3x+2ky-2=0\] |
| and \[2x+5y-1=0\] |
| Here, \[{{a}_{1}}=3,\,{{b}_{1}}=2k,\,{{c}_{1}}=-2\] |
| and \[{{a}_{2}}=2,\,{{b}_{2}}=5,\,{{c}_{2}}=-1\] |
| From Eq. (i), \[\frac{3}{2}=\frac{2k}{5}\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,k=\frac{15}{4}\] |
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