JEE Mains · Maths · STD 12 - 6. Application of derivatives
Water is being filled at the rate of \(1\, cm ^{3} / sec\) in a right circular conical vessel (vertex downwards) of height \(35\, cm\) and diameter \(14 \,cm\). When the height of the water level is \(10\, cm\), the rate (in \(cm ^{2} / sec\) ) at which the wet conical surface area of the vessel increases is
- A \(5\)
- B \(\frac{\sqrt{21}}{5}\)
- C \(\frac{\sqrt{26}}{5}\)
- D \(\frac{\sqrt{26}}{10}\)
Answer & Solution
Correct Answer
(C) \(\frac{\sqrt{26}}{5}\)
Step-by-step Solution
Detailed explanation
Given \(\frac{ dV }{ dt }=1 \Rightarrow \frac{ d }{ dt }\left(\frac{\pi r ^{2} h}{3}\right)=1\) \(\Rightarrow \frac{ d }{ dt }\left(\frac{5 \pi}{3} r ^{3}\right)=1 \Rightarrow r ^{2} \frac{ dr }{ dt }=\frac{1}{5 \pi}\) Let wet conical surface area \(=S\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If the arithmetic mean of two numbers \(a\) and \(b, a>b>0\), is five times their geometric mean, then \(\frac{{a + b}}{{a - b}}\) is equal toJEE Mains 2017 Hard
- If the solution curve of the differential equation \(\left(\left(\tan ^{-1} y\right)-x\right) d y=\left(1+y^{2}\right) d x\) passes through the point \((1,0)\) then the abscissa of the point on the curve whose ordinate is \(\tan \;(1)\) isJEE Mains 2022 Medium
- If all the words (with or without meaning) having five letters, formed using the letters of the word \(SMALL\) and arranged as in a dictionary; then the position of the word \(SMALL\) is :JEE Mains 2016 Hard
- Let \(3,7,11,15, \ldots, 403\) and \(2,5,8,11, \ldots, 404\) be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ...........JEE Mains 2024 Hard
- lf the mean deviation of the numbers \(1, 1 + d, . . . ,1 + 100d\) from their mean is \(255,\) then a value of \(d\) isJEE Mains 2016 Hard
- There are \(15\) players in a cricket team, out of which \(6\) are bowlers, \(7\) are batsmen and \(2\) are wicketkeepers. The number of ways, a team of \(11\) players be selected from them so as to include at least \(4\) bowlers, \(5\) batsmen and \(1\) wicketkeeper, is \(.....\)JEE Mains 2021 Medium
More PYQs from JEE Mains
- The series of positive multiples of \(3\) is divided into sets : \(\{3\},\{6,9,12\},\{15,18,21,24,27\}, \ldots\) Then the sum of the elements in the \(11^{\text {th }}\) set is equal to \(................\)JEE Mains 2022 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(\begin{array}{l} \cos x(3 \sin x+\cos x+3) d y= (1+y \sin x(3 \sin x+\cos x+3)) d x \end{array}\) ; \(0 \leq x \leq \frac{\pi}{2}, y(0)=0 .\) Then \(, y\left(\frac{\pi}{3}\right)\) is equal to ..... .JEE Mains 2021 Hard
- Given below are two statements:
Statement I: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x}{1+|x|}\) is one-one.
Statement II: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x^{2}+4x-30}{x^{2}-8x+18}\) is many-one.
In the light of the above statements, choose the correct answer from the options given below :JEE Mains 2026 Easy - Let the population ofrabbits surviving at time \(t\) be governed by the differential equation \(\frac{{dp\left( t \right)}}{{dt}} = \frac{1}{2}p\left( t \right) - 200\) . If \( p(0)=100 \) ,then \(p(t)\) equals :JEE Mains 2014 Hard
- Let \(S_n\) denote the sum of the first \(n\) terms of an \(A.P\).. If \(S_4 = 16\) and \(S_6 = -48\), then \(S_{10}\) is equal toJEE Mains 2019 Hard
- Let \(A =\{1,2,3,4,5,6,7\}\) and \(B =\{3,6,7,9\}\). Then the number of elements in the set \(\{ C \subseteq A : C \cap B \neq \phi\}\) isJEE Mains 2022 Medium