MHT CET · Maths · Application of Derivatives
20 is divided into two parts so that the product of the cube of one part and the square of the other part is maximum, then these two parts are
- A 15,5
- B 16,4
- C 12,8
- D 14,6
Answer & Solution
Correct Answer
(C) 12,8
Step-by-step Solution
Detailed explanation
Let the parts be \(x\) and \(y\). \(x + y = 20 \Rightarrow y = 20 - x\). Function to maximize: \(P = x^3 y^2 = x^3 (20 - x)^2\).
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
- \(
=1+\sin \frac{\pi}{2}, \quad-\infty < x \leq 1
\)
If the function \(\mathrm{f}(\mathrm{x})=\mathrm{ax}+\mathrm{b}, \quad 1 < \mathrm{x} < 3\) is continuous in
\(
=6 \tan \frac{x \pi}{12}, \quad 3 \leq x < 6
\)
\((-\infty, 6)\), then the values of \(a\) and \(b\) are respectively.MHT CET 2021 Easy - A fair n faced die is rolled repeatedly until a number less than n appears. If the mean of the number of tosses required is \(\frac{\mathrm{n}}{9}\), then \(\mathrm{n}=\) (where \(\mathrm{n} \in \mathbb{N}\) )MHT CET 2025 Medium
- The optimal solution of the L.P.P. Maximize : \(\mathrm{Z}=8 x+3\) y subject to the constraints \(x+y \leq 3,4 x+y \leq 6, x \geq 0, y \geq 0\) isMHT CET 2020 Easy
- If the function \(f(x)=x^3-3(a-2) x^2+3 a x+7\), for some \(a \in R\) is increasing in \((0,1]\) and decreasing in \([0,5)\), then a root of the equation \(\frac{f(x)-14}{(x-1)^2}=0(x \neq 1)\) isMHT CET 2022 Hard
- The area (in sq. units), in the first quadrant bounded by the curve \(y=x^2+2\) and the lines \(y=x+1, x=0\) and \(x=2\), isMHT CET 2024 Easy
- If \(g\) is the inverse of \(f\) and \(f^{\prime}(x)=\frac{1}{1+x^{2}}\), then \(g^{\prime}(x)\) is equal toMHT CET 2010 Easy
More PYQs from MHT CET
- A container consisting mixture of \(28 \mathrm{~g} \mathrm{~N}_2, 8 \mathrm{~g~} \mathrm{He}\) and 40 g Ne at \(25^{\circ} \mathrm{C}\). If the total pressure exerted by the gaseous mixture is 20 bar, What is the partial pressure exerted by \(\mathrm{N}_2\) ?MHT CET 2025 Medium
- Equal volumes of two gases, having their densities in the ratio of \(1: 16\) exert equal pressures on the walls of two containers. The ratio of their rms speeds \(\left(c_1: c_2\right)\) isMHT CET 2021 Easy
- A body of mass 200 gram is tied to a spring of spring constant \(12.5 \mathrm{~N} / \mathrm{m}\), while other end of spring is fixed at point ' \(\mathrm{O}\) '. If the body moves about ' \(\mathrm{O}\) ' in a circular path on a smooth horizontal surface with constant angular speed \(5 \mathrm{rad} / \mathrm{s}\) then the ratio of extension in the spring to its natural length will be
MHT CET 2023 Hard - The conversion of ethyl bromide to ethyl iodide using sodium and dry acetone, this reaction is known asMHT CET 2017 Easy
- Identify product ' \(B\) ' in the following reaction.
Sodium phenoxide \(\xrightarrow[6 \text { atm }]{\mathrm{CO}_2, 398 \mathrm{~K}} \mathrm{~A} \xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}} \mathrm{B}\)MHT CET 2024 Hard - \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) are three parallel conductors of equal lengths and carry currents I, I and 2I respectively as shown in figure. Distance \(A B\) and \(B C\) is same as ' \(d\) '. If ' \(F_1\) ' is the force exerted by \(\mathrm{B}\) on \(\mathrm{A}\) and \(\mathrm{F}_2\) is the force exerted by \(\mathrm{C}\) on \(\mathrm{A}\), then
MHT CET 2023 Hard