Differential Calculus jee mains questions | JEE Main Maths Quadratic Equations Previous Year Question

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Q 41 :

If $\lim_{x \to 0} \frac{e^{(a - 1) x} + 2 \cos b x + (c - 2) e^{- x}}{x \cos x - \log_{e} (1 + x)} = 2,$ then $a^{2} + b^{2} + c^{2}$ is equal to: [2026]

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(1)

Q 42 :

The value of $\lim_{x \to 0} \frac{\log_{e} ((\sec (e x) \cdot \sec ((e^{2} x)) \dots \sec ((e^{10} x))))}{e^{2} - e^{2 \cos x}}$ is equal to [2026]

$\frac{(e^{10} - 1)}{2 e^{2} (e^{2} - 1)}$
$\frac{(e^{20} - 1)}{2 e^{2} (e^{2} - 1)}$
$\frac{(e^{10} - 1)}{2 (e^{2} - 1)}$
$\frac{(e^{20} - 1)}{2 (e^{2} - 1)}$

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(4)

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