question_answer

                Let \[{{\theta }_{1}}\]be the angle between two lines \[2x+3y+{{\operatorname{c}}_{1}}=0\]and \[-x+5y+{{c}_{2}}=0,\]and\[{{\theta }_{2}}\] be the angle between two lines \[2x+3y+{{c}_{1}}=0\],  and\[-x+5y+{{c}_{3}}=0,\]where, \[{{c}_{1}},{{c}_{2}},\,\,{{c}_{3}}\]are any real numbers :                 Statement 1: If \[{{c}_{2}}\] and \[{{c}_{3}}\] are proportional, then \[{{\theta }_{1}}={{\theta }_{2}}\]                 Statement 2: \[{{\theta }_{1}}={{\theta }_{2}}\] for all \[{{\operatorname{c}}_{2}}\] and \[{{\operatorname{c}}_{3}}\]     JEE Main Online Paper ( Held On 23  April 2013 )

A)                   Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.

B)                                          Statement 1 is true; Statement 2 is true; Statement 2 is not correct explanation for Statement 1.

C)                                          Statement 1 is false; Statement 2 is true.

D)                                          Statement 1 is true; Statement 2 is false.