Given below are two statements: Statement I: lim x → 0 ((tan ⁻¹x + log e ((√(1 + x) - √(1 - x))/x) - 2x)/(x⁵)) = 2/5 Statement II: lim x → 1 (2/(x¹⁻ˣ)) = 1/(e²) In the light of the above statements, choose the correct answer from the options given below:

(D) Both Statement I and Statement II are true

(A) Statement I is false but Statement II is true

(B) Statement I is true but Statement II is false

(C) Both Statement I and Statement II are false

Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

JEE Main 2025 · April, Unspecified (session-level dataset) · Q220

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Given below are two statements: **Statement I:**

\lim_{x \to 0} \left( \frac{\tan^{-1}x + \log_e \left( \frac{\sqrt{1 + x} - \sqrt{1 - x}}{x} \right) - 2x}{x^5} \right) = \frac{2}{5}

**Statement II:**

\lim_{x \to 1} \left( \frac{2}{x^{1 - x}} \right) = \frac{1}{e^2}

In the light of the above statements, choose the correct answer from the options given below:

JEE Main 2025 · April, Unspecified (session-level dataset) · Q220

JEE Main 2025April, Unspecified (session-level dataset)MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Given below are two statements: **Statement I:**

\lim_{x \to 0} \left( \frac{\tan^{-1}x + \log_e \left( \frac{\sqrt{1 + x} - \sqrt{1 - x}}{x} \right) - 2x}{x^5} \right) = \frac{2}{5}

**Statement II:**

\lim_{x \to 1} \left( \frac{2}{x^{1 - x}} \right) = \frac{1}{e^2}

In the light of the above statements, choose the correct answer from the options given below: