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JEE Main & Advanced Sample Paper JEE Main Sample Paper-22

  • question_answer
    A triangle has sides of length 13, 30 and 37. If the radius of the inscribed circle is \[\frac{p}{q}\] (where p and q are coprime), then the value of \[{{q}^{p+3}}\] is

    A)  2048                           

    B)  4096

    C)  1024                           

    D)  512

    Correct Answer: B

    Solution :

    \[r=\frac{\Delta }{s}\]                             ? \[s=\,\frac{13+30+37}{2}=40\] \[\Delta \sqrt{s(s-a)\,(s-b)\,(s-c)}\] \[=\sqrt{40.27.10.3}\,=20.9\,=180\] \[\therefore \,\,r=\frac{180}{40}=\frac{9}{2}\Rightarrow \,p=9\] and \[q=2\] Hence \[{{q}^{p+3}}\,={{2}^{12}}\,=4096\]


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