AP EAMCET · Maths · Application of Derivatives
The radius of a circular plate is increasing at the rate of \(0.01 \mathrm{~cm} / \mathrm{s}\) when the radius is \(12 \mathrm{~cm}\). Then, the rate at which the area increases, is
- A \(0.24 \pi \mathrm{sq} \mathrm{cm} / \mathrm{s}\)
- B \(60 \pi \mathrm{sq} \mathrm{cm} / \mathrm{s}\)
- C \(24 \pi \mathrm{sq} \mathrm{cm} / \mathrm{s}\)
- D \(1.2 \pi \mathrm{sq} \mathrm{cm} / \mathrm{s}\)
Answer & Solution
Correct Answer
(A) \(0.24 \pi \mathrm{sq} \mathrm{cm} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
The area of circular plate is \(A=\pi r^2\) On differentiating w.r.t. \(t\), we get…
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 \(f\) is integrable on \([0, a]\), then the function \(h\) defined on \([0, a]\) as \(h(x)=\ldots . . \forall x \in[0, a]\) is integrable on \([0, a]\)AP EAMCET 2020 Easy
- \(\int \frac{5 x^2+3}{x^2\left(x^2-2\right)} d x=\)AP EAMCET 2017 Medium
- If the line is one of the bisectors of then value ofAP EAMCET 2020 Medium
- The length of the latus rectum of a parabola whose focal chord \(P S Q\) is such that \(P S=3\) and \(Q S=2\) isAP EAMCET 2020 Easy
- \(E_1\) and \(E_2\) are two independent events of a random experiment such that \(P\left(E_1\right)=\frac{1}{2}\) and \(P\left(E_1 \cup E_2\right)=\frac{2}{3}\).
Then match the items of List-I with the items of List-II.
The correct match isAP EAMCET 2024 Easy - \(\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=\)AP EAMCET 2018 Hard
More PYQs from AP EAMCET
- The ratio of de-Broglie wavelength of two particles \(A\) and \(B\) is \(2: 1\). If the velocities of \(A\) and \(B\) are \(0.05 \mathrm{~ms}^{-1}\) and \(0.02 \mathrm{~ms}^{-1}\), respectively, then the ratio of their masses \(m_A: m_B\) must beAP EAMCET 2021 Medium
- Match the following.
AP EAMCET 2015 Medium - Let \(\pi\) be the plane that passes through the point \((-2,1,-1)\) and parallel to the plane \(2 x-y+2 z=0\). Then the foot of perpendicular drawn from the point \((1,2,1)\) to the plane \(\pi\) isAP EAMCET 2024 Medium
- A small block of mass \(20 \mathrm{~g}\) and charge \(4 \mathrm{mC}\) is released on a long smooth inclined plane of inclination angle of \(45^{\circ}\), A uniform horizontal magnetic field of \(1 \mathrm{~T}\) is acting parallel to the surface, as shown in the figure. The time from the start when the block loses contact with the surface of the plane is
AP EAMCET 2019 Hard - If \(-\frac{2}{3} < x < \frac{2}{3}\), then the value of the \(5^{\text {th }}\) term in the expansion of \(\frac{1}{\sqrt[3]{2-3 x}}\) when \(x=\frac{1}{2}\) isAP EAMCET 2025 Medium
- \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin (x-[x]) d x=\)AP EAMCET 2025 Medium