JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 June 2022, Shift 2, Maths Q25

Question 25 of 90 in this shift, Maths question 25 of 30, Section B.

Let

[t]

denote the greatest integer

\leq t

and

\{t\}

denote the fractional part of

t

. The integral value of

\alpha

for which the left hand limit of the function

f(x)=[1+x]+\frac{\alpha^{2[x]+\{x\}}+[x]-1}{2[x]+\{x\}}

x=0

is equal to

\alpha-\frac{4}{3}

, is ___________.

Official answer

NTA final key.

Chapter: Limits and Derivatives
Topic: Continuity and Differentiability
Idea tested: Continuity involving GIF and Fractional Part

Same idea in other shifts

Asked 17× in all

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5 Apr 2024, Shift 2 · Q10Let $f : [-1, 2] \to \mathbf{R}$ be given by $f(x) = 2x^2 + x + [x^2] - [x]$ , where $[t]$ denotes the greatest integer less than or equal…MediumSingle correct
6 Apr 2024, Shift 2 · Q24Let $[t]$ denote the greatest integer less than or equal to $t$ . Let $f:[0,\infty)\to\mathbb{R}$ be a function defined by…MediumNumerical value
27 Jan 2024, Shift 1 · Q8Consider the function.…HardSingle correct
6 Apr 2023, Shift 1 · Q25Let $a\in\mathbb{Z}$ and $[t]$ be the greatest integer $\le t$ . Then the number of points, where the function $f(x)=[a+13\sin x]$ ,…HardNumerical value
11 Apr 2023, Shift 1 · Q7Let $f(x) = [x^2 - x] + |-x + [x]|$ , where $x \in \mathbb{R}$ and $[t]$ denotes the greatest integer less than or equal to $t$ . Then, $f$ isMediumSingle correct
12 Apr 2023, Shift 1 · Q25Let $[x]$ be the greatest integer $\le x$ . Then the number of points in the interval $(-2,1)$ , where the function…MediumNumerical value
29 Jul 2022, Shift 2 · Q26If $[t]$ denotes the greatest integer $\leq t$ , then the number of points, at which the function…HardNumerical value

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.