Question

Assertion :The straight line $(\sin \theta +\sqrt{3}\cos \theta )x+(\sqrt{3}\sin \theta -\cos \theta )y+(5\sin \theta -7\cos \theta )=0$ passes through the point of intersection of the lines $x+\sqrt{3}y+5=0$ and $\sqrt{3}x-y-7=0$ for all values of $\theta$ except $\theta =\frac{n\pi }{2}$, where $n$ is an integer. Reason: $L_1+\lambda L_2=0$ represents the equation of a line through the points of intersection of the lines $L_1=0$ and $L_2=0$ for all non-zero finite values of $\lambda$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Reason is true (from theory)
Assertion
Equation in assertion is
$x+\sqrt{3}y+5+\cot \theta (\sqrt{3}x-y-7)=0$
Where $\cot \theta$ is non zero finite real number
As $\theta \ne \frac{n\pi }{2}$
From reason assertion is true.