JEE Main 2022 · MathsNumerical answerNumerical valueHardMulti-step

JEE Main 30 June 2022, Shift 1, Maths Q23

Question 23 of 90 in this shift, Maths question 23 of 30, Section B.

Suppose

\lim_{x\to 0} \frac{F(x)}{x^3}

exists and is equal to L, where

F(x) = \begin{vmatrix} a + \sin\frac{x}{2} & -b\cos x & 0 \\ -b\cos x & 0 & a + \sin\frac{x}{2} \\ 0 & a + \sin\frac{x}{2} & -b\cos x \end{vmatrix}

. Then,

-112

L is equal to __________.

Official answer

NTA final key.

Chapter: Determinants
Topic: L'Hopital's Rule
Idea tested: L'Hopital on Determinant Functions

Same topic in other shifts

All L'Hopital's Rule questions

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6 Apr 2026, Shift 1 · Q17The value of $\lim_{x\to 0}\left(\frac{x^2\sin^2 x}{x^2-\sin^2 x}\right)$ is:MediumSingle correct
2 Apr 2025, Shift 1 · Q7For $\alpha, \beta, \gamma\in\mathbf{R}$ , if $\lim_{x\to0}\frac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin2x-\beta x}=3$ , then…MediumSingle correct
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.