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JEE Main20203 Sep 2020Morning ShiftMathematicsDifferentiationActual

If y 2 + log e cos 2 x = y , x ∈ - π 2 , π 2 then :

Options

  1. Ay ' ' ( 0 ) = 0
  2. By ' ( 0 ) + y " ( 0 ) = 1
  3. Cy " ( 0 ) = 2
  4. Dy ' ( 0 ) + y " ( 0 ) = 3

Correct answer

C. y " ( 0 ) = 2

Step-by-step solution

Putting, x = 0 in y 2 + log e cos 2 x = y we get y = 0 , 1 2 y · y ' + 1 cos 2 x · 2 cos x - sin x = y ' ⇒ 2 y · y ' - 2 tan x = y ' … … 1 y ' 0 = 0 for y = 0 & y = 1 . Differentiating 1 , 2 y · y ' ' + 2 y ' 2 - 2 s e c 2 x = y ' ' , y ' ' 0 = - 2 for y = 0 y ' ' 0 = 2 , for y = 1 ∴ y ' ' 0 = 2

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