If $\lim _{x\to 0}\frac{{e}^{(a−1)x}+2\cos bx+(c−2){e}^{−x}}{x\cos x−{\log }_{e}(1+x)}=2,$ then ${a}^{2}+{b}^{2}+{c}^{2}$ is equal to: [JEE Main 2026, 22 Jan (Shift 2)]

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If \(\lim _{x\to 0}\frac{{e}^{(a−1)x}+2\cos bx+(c−2){e}^{−x}}{x\cos x−{\log }_{e}(1+x)}=2,\) then \({a}^{2}+{b}^{2}+{c}^…

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