JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumMatrices and Determinants245× since 2002For some aaa, bbb, let f(x)=∣a+sinxx1ba1+sinxxba1b+sinxx∣f(x) = \left| \begin{array}{ccc} a + \frac{\sin x}{x} & 1 & b \\ a & 1 + \frac{\sin x}{x} & b \\ a & 1 & b + \frac{\sin x}{x} \end{array} \right|f(x)=a+xsinxaa11+xsinx1bbb+xsinx, x≠0x \neq 0x=0, limx→0f(x)=λ+μa+νb\lim_{x \to 0} f(x) = \lambda + \mu a + \nu blimx→0f(x)=λ+μa+νb. Then (λ+μ+ν)2(\lambda + \mu + \nu)^2(λ+μ+ν)2 is equal to:AOption A. 16BOption B. 25COption C. 9DOption D. 36CheckSkip · show solution
