JEE Main 2025 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 3 April 2025, Shift 1, Maths Q19

Question 19 of 75 in this shift, Maths question 19 of 25, Section A.

Let the domain of the function

f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2)

(a, b)

. If

\int_0^{b-a} [x^2]\,dx = p - \sqrt{q} - \sqrt{r}

p, q, r \in \mathbb{N}

\gcd(p, q, r) = 1

, where

[\cdot]

is the greatest integer function, then

p + q + r

is equal to

(1)8
(2)9
(3)10Official answer
(4)11

Official answer

Option 3

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Greatest Integer Function Integrals

Same idea in other shifts

Asked 29× in all

2 Apr 2026, Shift 1 · Q19Let $[\cdot]$ denote the greatest integer function. Then the value of $\int_0^3\left(\frac{e^x+e^{-x}}{[x]!}\right)dx$ is :MediumSingle correct
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6 Apr 2024, Shift 2 · Q25Let $[t]$ denote the largest integer less than or equal to $t$ . If…HardNumerical value
30 Jan 2024, Shift 1 · Q25The value of $9\int_0^9\left[\sqrt{\frac{10x}{x+1}}\right]dx$ , where $[t]$ denotes the greatest integer less than or equal to $t$ , is…HardNumerical value
8 Apr 2023, Shift 1 · Q24Let $[t]$ denote the greatest integer $\le t$ . Then $\frac{2}{\pi}\int_{\pi/6}^{5\pi/6}(8[\operatorname{cosec}x]-5[\cot x])\,dx$ is equal…HardNumerical value
8 Apr 2023, Shift 2 · Q26Let $[t]$ denote the greatest integer function. If $\int_0^{2.4}[x^2]\,dx = \alpha + \beta\sqrt{2} + \gamma\sqrt{3} + \delta\sqrt{5}$ ,…MediumNumerical value
11 Apr 2023, Shift 2 · Q11Let the function $f : [0, 2] \to \mathbb{R}$ be defined as…HardSingle 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.