JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 18 March 2021, Shift 2, Maths Q71

Question 71 of 90 in this shift, Maths question 11 of 30, Section A.

Let

g(x)=\int_0^x f(t)\,dt

, where

f

is continuous function in

[0, 3]

such that

\frac{1}{3}\le f(t)\le 1

for all

t\in[0, 1]

and

0\le f(t)\le\frac{1}{2}

for all

t\in(1, 3]

. The largest possible interval in which

g(3)

lies is :

(1) $\left[\frac{1}{3}, 2\right]$ Official answer
(2) $\left[-1, -\frac{1}{2}\right]$
(3) $[1, 3]$
(4) $\left[-\frac{3}{2}, -1\right]$

Official answer

Option 1

NTA final key.

Chapter: Integrals
Topic: Definite Integral Properties
Idea tested: Bounding and Estimation Property

Same idea in other shifts

Asked 4× in all

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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.