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Jee Main 2025Medium JEE math MCQ

If the function $f(x) = \begin{cases} \frac{2}{x} \sin (k_1 x + k_2 - 1) x, & x < 0 \\ 4, & x = 0 \\ \frac{2}{x} \log_e (\frac{2 + k_2 x}{2 + k_2 x}), & x > 0 \end{cases}$ is continuous at $x = 0$, then $k_1^2 + k_2^2$ is equal to
  1. A. 20 -
  2. B. 5 -
  3. C. 8 -
  4. D. 10

Solution

The correct option is **D**. (D. 10)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
If the function f(x)={2xsin(k1x+k21)x,x<04,x=02xloge(2+k2x2+k2x),x>0f(x) = \begin{cases} \frac{2}{x} \sin (k_1 x + k_2 - 1) x, & x < 0 \\ 4, & x = 0 \\ \frac{2}{x} \log_e (\frac{2 + k_2 x}{2 + k_2 x}), & x > 0 \end{cases} is continuous at x=0x = 0, then k12+k22k_1^2 + k_2^2 is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep