Let $f(x) = \begin{cases} \dfrac{\sin(\alpha x + 3x) + \sin x}{x}, & x 0 \end{cases}$ be continuous at $x = 0$. If $(1-k)\, f\left(\frac{7}{18}\right) = \alpha b$ , then $k$ is equal to

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 30 July 2022, Shift 2, Maths Q69

Question 69 of 90 in this shift, Maths question 9 of 30, Section A.

Let

f(x) = \begin{cases} \dfrac{\sin(\alpha x + 3x) + \sin x}{x}, & x < 0 \\ 2, & x = 0 \\ \dfrac{(x + 6bx^2)^{1/3} - x^{1/3}}{3x^{4/3}}, & x > 0 \end{cases}

be continuous at

x = 0

. If

(1-k)\, f\left(\frac{7}{18}\right) = \alpha b

, then

k

is equal to

(1) $-6$
(2)15
(3) $-13$
(4)8Official answer

Official answer

Option 4

NTA final key.

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

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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.