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If u = x 2 + y 2 and x = s + 3 t ,   y = 2 s - t , then d 2 u d s 2 is equal to (where t is a constant)

Options

  1. A12
  2. B32
  3. C36
  4. D10

Correct answer

D. 10

Step-by-step solution

Given, u = x 2 + y 2 , x = s + 3 t ,   y = 2 s - t Now , d x d s = 1 , d y d s = 2 … ( i ) d 2 x d s 2 = 0 , d 2 y d s 2 = 0 … ( i i ) Now, u = x 2 + y 2 d u d s = 2 x d x d s + 2 y d y d s d 2 u d s 2 = 2 d x d s 2 + 2 x d 2 x d s 2 + 2 d y d s 2 + 2 y d 2 y d s 2 ⇒ d 2 u d s 2 = 2 1 2 + 2 x 0 + 2 2 2 + 2 y 0     ( from   ( i )   and   ( i i ) ) = 2 + 8 = 10

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