| Column - I | Column - II | ||
| A. | \[2x+3y=40\] \[6x+5y=10\] | 1. | Coincident lines |
| B. | \[2x+3y=40\] \[6x+9y=50\] | 2. | Intersecting lines |
| C. | \[2x+3y=10\] \[4x+6y=20\] | 3. | Parallel lines |
A) A-R, B-P, C-Q
B) A-P, B-R, C-Q
C) A-R, B-Q, C-P
D) None of these
Correct Answer: C
Solution :
| [A] \[{{a}_{1}}=2,\,{{b}_{1}}=3,\,{{c}_{1}}=40\] |
| \[{{a}_{2}}=6,\,{{b}_{2}}=5,\,{{c}_{2}}=10\] |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{6}=\frac{1}{3},\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{3}{5},\,\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{40}{10}=\frac{4}{1}\] |
| Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}\ne \frac{{{b}_{1}}}{{{b}_{2}}}\]so intersecting line |
| [B] \[{{a}_{1}}=2,\,{{b}_{1}}=3,\,{{c}_{1}}=40\] |
| \[{{a}_{2}}=6,\,{{b}_{2}}=9,\,{{c}_{2}}=50\] |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{6}=\frac{1}{3},\,\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{3}{9}=\frac{1}{3},\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{40}{50}=\frac{4}{5}\] |
| Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\] so parallel lines |
| [C] \[{{a}_{1}}=2,\,{{b}_{1}}=3,\,{{c}_{1}}=10\] |
| \[{{a}_{2}}=4,\,{{b}_{2}}=6,\,{{c}_{2}}=20\] |
| \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{2}{4}=\frac{1}{2},\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{3}{6}=\frac{1}{2},\] |
| \[\frac{{{c}_{1}}}{{{c}_{2}}}=\frac{10}{20}=\frac{1}{2}\] |
| Here, \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}\ne \frac{{{c}_{1}}}{{{c}_{2}}}\]so coincident line. |
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