JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

(1)9Official answer
(2)10
(3)11
(4)12

Official answer

Option 1

NTA final key (2022 Session 1).

Chapter: Application of Derivatives
Topic: Chain Rule
Idea tested: Chain Rule in Related Rates

Same idea in other shifts

Asked 5× in all

27 Jul 2022, Shift 2 · Q25A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is…MediumNumerical value
25 Jun 2022, Shift 2 · Q11Water is being filled at the rate of $1\ \mathrm{cm}^3 / \mathrm{sec}$ in a right circular conical vessel (vertex downwards) of height 35…MediumSingle correct
9 Jan 2020, Shift 1 · Q59A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of…MediumSingle correct
3 Sep 2020, Shift 2 · Q59If the surface area of a cube is increasing at a rate of 3.6 cm $^2$ /sec, retaining its shape; then the rate of change of its volume (in…EasySingle 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.