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Jee Main 2025 — Hard JEE math MCQ

For some \(a, b\), let \(f(x) = \frac{a + \sin x}{x} \begin{vmatrix} 1 & 1 & b \\ a & 1 + \sin x & b \\ a & 1 & b + \sin x \end{vmatrix}, x \neq 0, \lim_{x \to 0} f(x) = \lambda + \mu a + \nu b\). Then \((\lambda + \mu + \nu)^2\) is equal to
  1. A. 16
  2. B. 25
  3. C. 9
  4. D. 36

Solution

The correct option is **A**. (A. 16)

MATH

hard • PYQ Reworded
Question
Read carefully, then pick the best option.
For some a,ba, b, let f(x)=a+sin⁡xx∣11ba1+sin⁡xba1b+sin⁡x∣,x≠0,lim⁡x→0f(x)=λ+μa+νbf(x) = \frac{a + \sin x}{x} \begin{vmatrix} 1 & 1 & b \\ a & 1 + \sin x & b \\ a & 1 & b + \sin x \end{vmatrix}, x \neq 0, \lim_{x \to 0} f(x) = \lambda + \mu a + \nu b. Then (λ+μ+ν)2(\lambda + \mu + \nu)^2 is equal to
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