JEE Main 2022 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q25

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

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is

\tan^{-1}\frac{3}{4}

. Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is __________.

Official answer

NTA final key.

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

Same idea in other shifts

Asked 5× in all

24 Jun 2022, Shift 1 · Q3The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3…MediumSingle correct
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.