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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    The number of values of \[\theta \]satisfying \[4\,\cos \theta +3\sin \theta =5\]as well as\[3\,\cos \theta +4\,\sin \theta =5\]is

    A)  one                                      

    B)  two

    C)  zero                     

    D)  none of these

    Correct Answer: C

    Solution :

     Adding both the given equations, we get \[7\,(\cos \theta +\sin \theta )=10\] or \[\cos \theta +\sin \theta =10\text{/}7\] But maximum value of\[\cos \theta +\sin \theta \]is  \[\sqrt{{{1}^{2}}+{{1}^{2}}}=\sqrt{2}<\frac{10}{7}\] So, no\[\theta \]is possible.


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