JEE Main 2021 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 26 February 2021, Shift 1, Maths Q67

Question 67 of 90 in this shift, Maths question 7 of 30, Section A.

The value of

\lim_{h\to 0} 2\left\{\frac{\sqrt{3}\sin\left(\frac{\pi}{6}+h\right)-\cos\left(\frac{\pi}{6}+h\right)}{\sqrt{3}h\left(\sqrt{3}\cos h-\sin h\right)}\right\}

is :

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

Official answer

Option 2

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Trigonometric Pre-Simplification

Same topic in other shifts

All L'Hopital's Rule questions

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2 Apr 2025, Shift 2 · Q17If $\lim_{x\to0} \frac{\cos(2x) + a\cos(4x) - b}{x^4}$ is finite, then $(a+b)$ is equal to :MediumSingle correct

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 108 of the 174 JEE Main shifts held from 2017 to 2026.