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JEE Main202624 January 2026Evening ShiftMathematicsContinuity and DifferentiabilityActual

Let [t] denote the greatest integer less than or equal to t . If the function f(x)= array cl b² ( 2 [ 2 ( x+ x) x ] ), & x 0 a &, x=0 array . is continuous at x=0 , then a²+b² is equal to

Options

  1. A5 8
  2. B1 2
  3. C9 16
  4. D3 4

Correct answer

D. 3 4

Step-by-step solution

For x > 0 : x - 1 2 2x = x(1 - x) . _ x 0^+ x(1- x) x^3 = _ x 0^+ x x 1- x x^2 = 1 1 2 = 1 2 . So a = 1 2 . For x f(x) = b^2 ( 2 1 ) = b^2 . For continuity: b^2 = a = 1 2 . a^2 + b^2 = 1 4 + 1 2 = 3 4 .

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