JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 25 June 2022, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let

f(x)

be a polynomial function such that

f(x)+f'(x)+f''(x)=x^5+64

. Then, the value of

\lim_{x\to1}\frac{f(x)}{x-1}

is equal to :

(1) $-15$ Official answer
(2) $-60$
(3) $60$
(4) $15$

Official answer

Option 1

NTA final key.

Chapter: Limits and Derivatives
Topic: L'Hopital's Rule
Idea tested: Derivative Limit Existence Condition

Same topic in other shifts

All L'Hopital's Rule questions

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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.