AP EAMCET · Maths · Application of Derivatives
If the percentage error in the radius of circle is 3 , then the percentage error in its area is
- A 6
- B \(\frac{3}{2}\)
- C 2
- D 4
Answer & Solution
Correct Answer
(A) 6
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given } \frac{d r}{r}=\frac{3}{100} \\ & A=\pi r^2 \Rightarrow d A=2 \pi r d r \\ & \Rightarrow \frac{d A}{A}=\frac{2 \pi r d r}{\pi r^2}=\frac{2 d r}{r}=\frac{6}{100} \Rightarrow \frac{d A}{A} \times 100=6 \%\end{aligned}\)
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 5 red roses and 5 white roses of different sizes are used in preparing a garland, the probability that red and white roses come alternately isAP EAMCET 2017 Medium
- The general solution of the differential equation \(\left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0\) isAP EAMCET 2024 Medium
- If \(y=\sqrt{2 x+\cos ^2\left(2 x+\frac{\pi}{4}\right)}\), then \(\frac{d y}{d x}\) at \(x=\frac{\pi}{4}\).AP EAMCET 2020 Easy
- Three letters are chosen at random from the letters of the word VARIABLE and all possible three letter words (with or without meaning) are formed with them. Then the probability of getting a three letter word having a consonent as its middle letter isAP EAMCET 2025 Medium
- Let \(A=\{x \in R, x \neq 0,-4 \leq x \leq 4\} \quad\) and \(f: A \rightarrow R\) defined by \(f(x)=\frac{|x|}{x}\) for \(x \in A\). Then, the range of \(f\) isAP EAMCET 2002 Easy
- If the function \(f\) defined by
\[
f(x)=\left\{\begin{array}{llc}
\cos x, & \text { if } & x \leq 0 \\
3 x+\alpha, & \text { if } & 0 < x < 2 \\
\beta x+3, & \text { if } & 2 \leq x \leq 4 \\
11, & \text { if } & x>4
\end{array}\right.
\]
where, \(\alpha\) and \(\beta\) are real constants, is continuous on \(R\), then \(\alpha^2+\beta^2=\)AP EAMCET 2018 Easy
More PYQs from AP EAMCET
- If a team of 4 persons is to be selected out of 4 married couples to play mixed doubles tennis game, then the number of ways of forming a team in which no married couple appears, isAP EAMCET 2025 Medium
- A cylindrical metal box whose flat surface has an area of \(0.01 \mathrm{~m}^2\) rests on liquid of \(0.3 \mathrm{~mm}\) thickness. If upon applying a horizontal force of magnitude \(\frac{1}{3} \mathrm{~N}\), the box slides with a constant speed of \(0.09 \mathrm{~ms}^{-1}\), the coefficient of viscosity of the liquid is nearlyAP EAMCET 2022 Medium
- The coordinates of a point, in the parametric form, on the ellipse whose foci are \((-1,0)\) and \((7,0)\) and eccentricity \(\frac{1}{2}\), areAP EAMCET 2017 Medium
- The value of \(x\) such that \(\sin \left(2 \tan ^{-1} \frac{3}{4}\right)=\cos \left(2 \tan ^{-1} x\right)\) isAP EAMCET 2024 Easy
- A uniform square plate has a side of length \(2 \mathrm{R}\). A circular piece of maximum possible area is cut and removed from one of the quadrants of the plate as shown in the figure. Shift in the centre of mass of the plate is.
AP EAMCET 2017 Hard - If the wavelengths of maximum intensity of radiation emitted by two black bodies \(A\) and \(B\) are \(0.5 \mu \mathrm{~m}\) and 0.1 mm respectively, then ratio of the temperatures of the bodies A and B isAP EAMCET 2025 Easy