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JEE Main 2020 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 8 January 2020, Shift 1, Maths Q57

Question 57 of 75 in this shift, Maths question 7 of 25, Section A.

\lim_{x\to 0}\left(\dfrac{3x^2+2}{7x^2+2}\right)^{1/x^2}

is equal to :

(1) $e$
(2) $e^2$
(3) $\frac{1}{e}$
(4) $\frac{1}{e^2}$ Official answer

Official answer

Option 4

NTA final key (Jan 2020).

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: e-Power Shortcut for 1^infinity Forms

Same idea in other shifts

Asked 2× in all

28 Jul 2022, Shift 1 · Q29 $\lim_{x\to0}\left(\frac{(x+2\cos x)^3+2(x+2\cos x)^2+3\sin(x+2\cos x)}{(x+2)^3+2(x+2)^2+3\sin(x+2)}\right)^{\frac{100}{x}}$ is equal to…HardNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.