Question
Let [t] denote the greatest integer less than or equal to t. If the function f(x)= \ array cl b^ 2 ( 2 [ 2 ( x+ x) x ] ), & x 0 \\ a &, x=0 array . is continuous at x=0, then a^ 2 +b^ 2 is equal to
JEE Main
Mathematics
Continuity and Differentiability
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 5 8
- B. 1 2
- C. 9 16
- D. 3 4
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 .
Related: Mathematics — Continuity and Differentiability · All PYQ Banks