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Q.

a≤5cosθ+3cos(θ−π3)+8≤b then

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a

a=1,b=15

b

a=2,b=14

c

a=3,b=13

d

a=4,b=12

answer is C.

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Detailed Solution

5cosθ+3cosθ−π3+8=5cosθ+312cosθ+32sinθ+8=132cosθ+332sinθ+8 minimum and maximum is8±169+274  ∴a=8−7=1,b=8+7=15
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