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Question

# Match of the following :List - I List - II1. Max. value of 3sinx+4cosx a.242. Min. positive value of sinx+cosecx b.53. Min. value of 9sin2x+16cosec2x c.24. Max. value of sin4x+cos4x d.1

A
1b,2c,3a,4d
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B
1d,2a,3b,4c
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C
1c,2d,3a,4b
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D
1c,2b,3d,4a
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Solution

## The correct option is A 1−b,2−c,3−a,4−d1. f(x)=3sinx+4cosx we know, max value of asinx±bcosx is +√a2+b2 ∴ max. value of 3sinx+4cosx is 5 2. sinx+cosecx=sinx+1sinx put sinx=4⇒f(y)=y+1y f′(y)=1−1y2=0 y=1 at sinx=1,f(x)=1+11=2. at sinx=−1,f(x)=−2 at sinx=0,f(x)=∞ min. positive value of sinx+cosecx=2. 3. f(x)=9sin2x+16sin2x put y=sinx,yϵ[−1,1] f(y)=9y2+16y2 f′(y)=18y−32y2=0 ⇒y2=43 ∴9×43+16×34 f(x)=24f(n)ϵ(24,∞) 4. f(x)=sin4x+cos4x=1−(sin2x)22 f(x)ϵ[12,1]

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