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MathsJEE Main 28 Jan 2026, Shift 1·Q14·MCQ·Moderate

Limits, Continuity & Differentiability · Limits using standard expansions

The value of lim⁡x→0log⁡e(sec⁡(ex)⋅sec⁡(e2x)⋅…⋅sec⁡(e10x))e2−e2cos⁡x\lim_{x\to0}\frac{\log_e\left(\sec(ex)\cdot\sec\left(e^2x\right)\cdot\ldots\cdot\sec\left(e^{10}x\right)\right)}{e^2 - e^{2\cos x}} is equal to
  1. (1)(e10−1)2e2(e2−1)\dfrac{(e^{10} - 1)}{2e^2(e^2 - 1)}
  2. (2)(e20−1)2e2(e2−1)\dfrac{(e^{20} - 1)}{2e^2(e^2 - 1)}
  3. (3)(e20−1)2(e2−1)\dfrac{(e^{20} - 1)}{2(e^2 - 1)}
  4. (4)(e10−1)2(e2−1)\dfrac{(e^{10} - 1)}{2(e^2 - 1)}

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See the full 28 Jan 2026, Shift 1 paper