JEE Mains · Maths · STD 12 - 6. Application of derivatives
The triangle of maximum area that can be inscribed in a given circle of radius \('r'\) is ...... .
- A An isosceles triangle with base equal to \(2 r\).
- B An equilateral triangle of height \(\frac{2 r }{3}\).
- C An equilateral triangle having each of its side of length \(\sqrt{3} r\).
- D A right angle triangle having two of its sides of length \(2 r\) and \(r\).
Answer & Solution
Correct Answer
(C) An equilateral triangle having each of its side of length \(\sqrt{3} r\).
Step-by-step Solution
Detailed explanation
\(h = rsin \theta+ r\) base \(= BC =2 r \cos \theta\) \(\theta \in\left[0, \frac{\pi}{2}\right)\) Area of \(\Delta ABC =\frac{1}{2}( BC ) \cdot h\) \(\Delta=\frac{1}{2}(2 r \cos \theta) \cdot(r \sin \theta+r)\) \(= r ^{2}(\cos \theta) \cdot(1+\sin \theta)\)…
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
- Let \(S _{1}, S _{2}\) and \(S _{3}\) be three sets defined as \(S _{1}=\{ z \in C :| z -1| \leq \sqrt{2}\}\) ; \(S _{2}=\{ z \in C : \operatorname{Re}((1- i ) z ) \geq 1\}\) ; \(S _{3}=\{ z \in C : \operatorname{Im}( z ) \leq 1\}\) Then the set \(S _{1} \cap S _{2} \cap S _{3}\)JEE Mains 2021 Hard
- The coefficients \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) in the quadratic equation \(a x^2+b x+c=0\) are chosen from the set \(\{1,2,3,4,5,6,7,8\}\). The probability of this equation having repeated roots is :JEE Mains 2024 Hard
- If the value of the integral \(\int \limits_{0}^{\frac{1}{2}} \frac{x^{2}}{\left(1-x^{2}\right)^{3 / 2}} d x\) is \(\frac{ k }{6},\) then \(k\) is equal toJEE Mains 2020 Medium
- Five numbers \(x _{1}, x _{2}, x _{3}, x _{4}, x _{5}\) are randomly selected from the numbers \(1,2,3, \ldots \ldots, 18\) and are arranged in the increasing order \(\left( x _{1}< x _{2}< x _{3}< x _{4}< x _{5}\right)\). The probability that \(x_{2}=7\) and \(x_{4}=11\) isJEE Mains 2022 Hard
- The minimum value of the twice differentiable function \(f(x)=\int_{0}^{x} e^{x-t} f^{\prime}(t) d t-\left(x^{2}-x+1\right) e^{x}, x \in R\), is.JEE Mains 2022 Hard
- The value of \(\int_{-1 / \sqrt{2}}^{1 / \sqrt{2}}\left(\left(\frac{x+1}{x-1}\right)^{2}+\left(\frac{x-1}{x+1}\right)^{2}-2\right)^{1 / 2} d x\) is:JEE Mains 2021 Hard
More PYQs from JEE Mains
- The number of terms in an \(A .P.\) is even ; the sum of the odd terms in it is \(24\) and that the even terms is \(30\). If the last term exceeds the first term by \(10\frac{1}{2}\) , then the number of terms in the \(A.P.\) isJEE Mains 2014 Hard
- The value of \( \frac{\sqrt{3}\text{cosec } 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ}\cos 40^{\circ}\cos 60^{\circ}\cos 80^{\circ}} \) is equal toJEE Mains 2026 Easy
- If the line \(y =4+ kx , k >0\), is the tangent to the parabola \(y = x - x ^{2}\) at the point \(P\) and \(V\) is the vertex of the parabola, then the slope of the line through \(P\) and \(V\) isJEE Mains 2022 Hard
- Let \({a_1},{a_2},.......,{a_{30}}\) be an \(A.P.\), \(S = \sum\limits_{i = 1}^{30} {{a_i}} \) and \(T = \sum\limits_{i = 1}^{15} {{a_{2i - 1}}} \).If \({a_5} = 27\) and \(S - 2T = 75\) , then \(a_{10}\) is equal toJEE Mains 2019 Hard
- Let the vertex \(A\) of a triangle \(ABC\) be \((1, 2)\), and the mid-point of the side \(AB\) be \((5, -1)\). If the centroid of this triangle is \((3, 4)\) and its circumcenter is \((\alpha, \beta)\), then \(21(\alpha + \beta)\) is equal to:JEE Mains 2026 Medium
- An angle between the plane, \(x + y + z = 5\) and the line of intersection of the planes, \(3x + 4y + z- 1 = 0\) and \(5x + 8y + 2z+ 14 = 0\) , isJEE Mains 2018 Hard