Xavier Aptitude Test 2011 Paper

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Question : 30 of 101

Marks: +1, -0

What is the maximum possible value of

(21 \Sin \ X + 72 \ Cos\ X )

?

21
57
63
75
None of the above

Solution:

(d)

y=21 \sin x+72 \cos x \ ...(1)

{d y}/{d x}=21 \cos x-72 \sin x=0

\tan x=\ {21}/{72}=\ {7}/{24}

\sin x=\ {7}/{\√{7^{2}+24^{2}}}, \cos x= {24}/{\√{7^{2}+24^{2}}}

Put these value in

(1)

y_{\max } =21 ×{7}/{\√{7^{2}+24^{2}}}+72 \×{24}/{\√{7^{2}+24^{2}}} \

=\ {21 × 7+72 \×24}/{ (√{7^{2}+24^{2}}\ )} \

=

\ {1875}/{25}=75 \

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