match the following .List - I List – II1) 2 tan x + 32 cot x≥ a) 242) 3sec2x+27cos2x≥ b) 163)16sin2x+9cosec2x≥ c) 18

ax+bx≥2abi)2tanx+32cotx≥22×32=16ii)3sec2x+27cos2x≥23×27=18iii)16sin2x+9cosec2x≥216×9=24

match the following .List - I List – II1) 2 tan x + 32 cot x≥ a) 242) 3sec2x+27cos2x≥ b) 163)16sin2x+9cosec2x≥ c) 18

ax+bx≥2abi)2tanx+32cotx≥22×32=16ii)3sec2x+27cos2x≥23×27=18iii)16sin2x+9cosec2x≥216×9=24

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match the following .
List - I                                            List – II
1) 2 tan x + 32 cot x $\geq$                    a) 24
2) $3 \sec^{2} x + 27 \cos^{2} x \geq$                    b) 16
3) $16 \sin^{2} x + 9 \cos e c^{2} x \geq$                c) 18

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1-a , 2 - b , 3 - c

1- c , 2 - a , 3 – b

1 - b , 2 - c , 3 - a

1 - c , 2 - b , 3 - a

answer is C.

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Detailed Solution

$\begin{matrix} a x + \frac{b}{x} \geq 2 \sqrt{a b} \\ i) 2 \tan x + 32 \cot x \geq 2 \sqrt{2 \times 32} = 16 \\ i i) 3 \sec^{2} x + 27 \cos^{2} x \geq 2 \sqrt{3 \times 27} = 18 \\ i i i) 16 \sin^{2} x + 9 \cos e c^{2} x \geq 2 \sqrt{16 \times 9} = 24 \end{matrix}$