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JEE Mains · Maths · STD 11 - 9. straight line
Let \(\theta_1\) be the angle between two lines \(2x + 3y + c_1\, = 0\) 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 \(c_2\) and \(c_3\)
- A Statement \(- 1\) is true, Statement \(-2\) is true;
Statement \(-2\) is a correct explanation of Statement \(-1\) - B Statement \(- 1\) is true, Statement \(-2\) is true;
Statement \(-2\) is not a correct explanation of Statement \(-1\) . - C Statement \(- 1\) is false; Statement \(-2\) is true.
- D Statement \(- 1\) is true; Staternent \(-2\) is false .
Answer & Solution
Correct Answer
(A) Statement \(- 1\) is true, Statement \(-2\) is true;
Statement \(-2\) is a correct explanation of Statement \(-1\)
Step-by-step Solution
Detailed explanation
Two lines \(-x + 5y + c_2\, = 0\) and \(-x + 5y+c_3\, = 0\) are parallel to each other . Hence statement \(- 1\) is true, statement \(-2\) is true and statement \(-2\) is the correct explanation of statement \(-1\)
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