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The number of integers in the range of `3 sin^(2)x+3sin x cos x+7cos^(2)x` is
A. 3
B. 4
C. 5
D. 6

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Correct Answer - C
`3 sin^(2)x+3 sin x.cos x+7 cos^(2)x`
`=(3(1-cos 2x))/(2)+(3sin 2x)/(2)+(7(1+cos 2x))/(2)`
`=(3 sin 2x 2x + 4 cos 2x)/(2)+5`
Now `-5 le 3 sin 2x + 4 cos 2x le 5`
`therefore (3 sin 2x + 4 cos 2x)/(2)+5 in [(5)/(2),(15)/(2)]`

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