Set Theory and types of Sets MCQ Quiz in मराठी - Objective Question with Answer for Set Theory and types of Sets - मोफत PDF डाउनलोड करा
Last updated on Mar 10, 2025
Latest Set Theory and types of Sets MCQ Objective Questions
Set Theory and types of Sets Question 1:
समजा, \(P = \left \{\theta : \sin \theta - \cos \theta = \sqrt {2} \cos \theta \right \}\) आणि \(Q = \left \{\theta : \sin \theta + \cos \theta = \sqrt {2}\sin \theta \right \}\) असे दोन संच आहेत. तर:
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 1 Detailed Solution
\(\Rightarrow \sin \theta = \cos \theta + \sqrt {2} \cos \theta\)
\(= (\sqrt {2} + 1)\cos \theta = \left (\dfrac {2 - 1}{\sqrt {2} - 1}\right ) \cos \theta\)
\(\Rightarrow (\sqrt {2} - 1)\sin\theta = \cos \theta \)
\(\Rightarrow \sin \theta + \cos \theta = \sqrt {2}\sin \theta\)
\(\therefore P = Q\)
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Set Theory and types of Sets Question 2:
समजा, \(P = \left \{\theta : \sin \theta - \cos \theta = \sqrt {2} \cos \theta \right \}\) आणि \(Q = \left \{\theta : \sin \theta + \cos \theta = \sqrt {2}\sin \theta \right \}\) असे दोन संच आहेत. तर:
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 2 Detailed Solution
\(\Rightarrow \sin \theta = \cos \theta + \sqrt {2} \cos \theta\)
\(= (\sqrt {2} + 1)\cos \theta = \left (\dfrac {2 - 1}{\sqrt {2} - 1}\right ) \cos \theta\)
\(\Rightarrow (\sqrt {2} - 1)\sin\theta = \cos \theta \)
\(\Rightarrow \sin \theta + \cos \theta = \sqrt {2}\sin \theta\)
\(\therefore P = Q\)