JEE Main 2022 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 27 July 2022, Shift 2, Maths Q5

Question 5 of 90 in this shift, Maths question 5 of 30, Section A.

If for

p \neq q \neq 0

, the function

f(x) = \frac{\sqrt[7]{p(729 + x)} - 3}{\sqrt[3]{729 + qx} - 9}

is continuous at

x = 0

, then :

(1) $7pq\, f(0) - 1 = 0$
(2) $63q\, f(0) - p^2 = 0$ Official answer
(3) $21q\, f(0) - p^2 = 0$
(4) $7pq\, f(0) - 9 = 0$

Official answer

Option 2

NTA final key.

Chapter: Continuity and Differentiability
Topic: Continuity and Differentiability
Idea tested: Continuity at a Point

Same idea in other shifts

Asked 8× in all

4 Apr 2024, Shift 1 · Q6Let $f: \mathbf{R} \to \mathbf{R}$ be a function given by…MediumSingle correct
4 Apr 2024, Shift 2 · Q8If the function $f(x)=\begin{cases}\dfrac{72^x-9^x-8^x+1}{\sqrt2-\sqrt{1+\cos x}}, & x\ne 0\\ a\log_e 2\log_e 3, & x=0\end{cases}$ is…HardSingle correct
30 Jul 2022, Shift 2 · Q69Let…HardSingle correct
26 Aug 2021, Shift 1 · Q82Let a, b $\in$ $\mathbf{R}$ , b $\neq$ 0. Define a function…MediumNumerical value
25 Jul 2021, Shift 1 · Q65Let $f:\mathbf{R}\to\mathbf{R}$ be defined as…MediumSingle correct
9 Jan 2020, Shift 1 · Q58If…MediumSingle correct
2 Sep 2020, Shift 1 · Q59If a function $f(x)$ defined by…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.