AP EAMCET · Maths · Application of Derivatives
If a running track of 500 ft . is to be laid out enclosing a playground, the shape of which is a rectangle with a semicircle at each end, then the length of the rectangular portion such that the area of the rectangular portion is to be maximum is (in feet).
- A 100
- B 125
- C 150
- D 200
Answer & Solution
Correct Answer
(B) 125
Step-by-step Solution
Detailed explanation
Perimeter of track \(=500 \mathrm{ft}\). \(\Rightarrow 500=2 x+2 \pi r\) So, area of rectangular portion \(=x \times 2 r=2 r(250-\pi \mathrm{r})\)…
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 \((-2, 6)\) is the image of the point \((4, 2)\) with respect to the line \(L = 0\), then \(L\) is equal toAP EAMCET 2002 Easy
- The lines \(3 x^2+8 x y-3 y^2+2 x-4 y-1=0\) and \(4 x-3 y-2=0\)AP EAMCET 2017 Medium
- A family of curves has the differential equation \(x y \frac{d y}{d x}=2 y^2-x^2\). Then, the family of curves isAP EAMCET 2010 Medium
- If and are positive integers such that thenAP EAMCET 2018 Easy
- In \(\triangle A B C\) the mid points of the sides \(A B, B C\) and \(C A\) are respectively \((l, 0,0),(0, m, 0)\) and \((0,0, n)\). Then, \(\frac{A B^2+B C^2+C A^2}{l^2+m^2+n^2}\) is equal toAP EAMCET 2008 Hard
- Out of 8 students in a classroom, 4 of them are chosen and they are arranged around a table. If the remaining 4 are arranged in a row, then the total number of arrangements that can be made with those 8 students isAP EAMCET 2025 Medium
More PYQs from AP EAMCET
- \(\sum_{k=1}^n k(k+1)(k+2) \ldots(k+r-1)=\)AP EAMCET 2025 Medium
- At \(27^{\circ} \mathrm{C}, 1 \mathrm{~L}\) of \(\mathrm{H}_2\) with a pressure of 1 bar is mixed with 2 L of \(\mathrm{O}_2\) with a pressure of 2 bar in a 10 L flask. What is the pressure exerted by gaseous mixture in bar ? (Assume \(\mathrm{H}_2\) and \(\mathrm{O}_2\) as ideal gases)AP EAMCET 2025 Medium
- If the position vectors of the points \(A\) and \(B\) are \(2 \hat{i}+3 \hat{j}-\hat{k}\) and \(\hat{i}-\hat{j}+2 \hat{k}\) respectively, then the unit vector along \(\overrightarrow{\mathrm{BA}}\) and in the direction of \(\overrightarrow{\mathrm{AB}}\) isAP EAMCET 2023 Easy
- In Young's double slit experiment, red light of wavelength \(6000 Å\) is used and the \(n\)th bright fringe is obtained at a point \(P\) on the screen. Keeping the same setting, the source of light is replaced by green light of wavelength \(5000 Å\) and now \((n+1)\) th bright fringe is obtained at the point \(P\) on the screen. The value of \(n\) isAP EAMCET 2016 Hard
- The polynomial equation of degree 4 having real coefficients with three of its roots as \(2 \pm \sqrt{3}\) and \(1+2 i\), isAP EAMCET 2019 Medium
- Which of the following is not an example of allylic halide?AP EAMCET 2024 Medium