10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

If the pair of equations \[x+y=\sqrt{2}\] and \[x\,\,\sin \theta +y\,\,\cos \theta =1\] has infinitely many solutions, then \[\theta =\]

A) \[30{}^\circ \]

B) \[45{}^\circ \]

C) \[60{}^\circ \]

D) \[90{}^\circ \]

Correct Answer: B

Solution :

[b] \[\frac{\sin \theta }{1}=\frac{\cos \theta }{1}=\frac{1}{\sqrt{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\sin \theta =\frac{1}{\sqrt{2}},\,\,\cos \theta =\frac{1}{\sqrt{2}}\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\theta =45{}^\circ \]