JEE Main 2024 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 January 2024, Shift 2, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

Let

f,g:(0,\infty)\to\mathbb{R}

be two functions defined by

f(x)=\int_{-x}^{x}\left(|t|-t^2\right)e^{-t^2}dt

and

g(x)=\int_0^{x^2}t^{1/2}e^{-t}dt

. Then, the value of

9\left(f\left(\sqrt{\log_e 9}\right)+g\left(\sqrt{\log_e 9}\right)\right)

is equal to

(1)8Official answer
(2)6
(3)9
(4)10

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Even and Odd Functions

Same idea in other shifts

Asked 3× in all

6 Apr 2026, Shift 2 · Q20The value of the integral $\int_{-1}^{1}\left(\frac{x^3+|x|+1}{x^2+2|x|+1}\right)dx$ is equal to :MediumSingle correct
18 Mar 2021, Shift 1 · Q82Let $f(x)$ and $g(x)$ be two functions satisfying $f(x^2)+g(4-x)=4x^3$ and $g(4-x)+g(x)=0$ , then the value of $\int_{-4}^{4}f(x^2)\,dx$ is…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 42 of the 174 JEE Main shifts held from 2017 to 2026.