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99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

The minimum value of (1+ 1 ^n ) (1+ 1 ^n ) is

Options

  1. A1
  2. B2
  3. C(1+2^n )^2
  4. D(1+2^ n / 2 )^2

Correct answer

D. (1+2^ n / 2 )^2

Step-by-step solution

Let f(x)= (1+ 1 ^n x ) (1+ 1 ^n x )= (1+ cosec ^n x ) (1+ ^n x ) aligned & f ( x )= [- n cosec ^ n -1 x - cosec n x ] dx & (1+ ^ n x )+ (1+ cosec ^ n x ) & nsec ^ n x x x =0 aligned x = 4 Now, f ( 4 )= [1+(2)^ n / 2 ]^2

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