TS EAMCET · Maths · Application of Derivatives
In a \(\triangle A B C\), the sides \(b, c\) are fixed. In measuring angle \(A\), if there is an error of \(\delta \mathrm{A}\), then the percentage error in measuring the length of the side \(a\) is
- A \(\frac{2 \Delta \delta A}{R \sin A} \times 100\)
- B \(2 \times \frac{\delta A}{A} \times 100\)
- C \(\frac{\Delta \delta A}{2 R^2 \sin ^2 A} \times 100\)
- D \(\frac{\Delta^2 \delta A}{R \sin A} \times 100\)
Answer & Solution
Correct Answer
(C) \(\frac{\Delta \delta A}{2 R^2 \sin ^2 A} \times 100\)
Step-by-step Solution
Detailed explanation
\(\begin{gathered}\cos \mathrm{A}=\frac{b^2+c^2-a^2}{2 b c} \\ \Rightarrow 2 \mathrm{bc} \cos \mathrm{A}=b^2+c^2-a^2\end{gathered}\) Differentiate both sides w.r.t a \(2 b c \sin A S A=-20 \delta a\) \(\Rightarrow \delta_E=\frac{b c \sin \mathrm{~A} \mathbb{A}}{a}\)..(i) Area…
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
- The acute angle between the two lines whose direction ratios are given by \(l+m-n=0\) and \(l^2+m^2-n^2=0\), isTS EAMCET 2002 Easy
- . \(\int \sec ^5 x d x=\)TS EAMCET 2019 Hard
- If there is an error of \(\pm 0.04 \mathrm{~cm}\) in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is \(10 \mathrm{~cm}\), isTS EAMCET 2014 Hard
- In a \(\triangle A B C\), if \(a+3 b=3 c\), then \(\sin \frac{A}{2}=\)TS EAMCET 2019 Medium
- The point \(P\) denotes the complex number \(z=x+i y\) in the Argand plane. If \(\frac{2 z-i}{z-2}\) is a purely real number, then the equation of the locus of \(P\) isTS EAMCET 2024 Hard
- If \(\frac{x^2}{2 x^4+7 x^2+6}=\frac{A x+B}{x^2+a}+\frac{C x+D}{a x^2+3}\), then \(A+B+C-2 D\)TS EAMCET 2024 Medium
More PYQs from TS EAMCET
-
The decreasing order of the reaction rate with nucleophile is
TS EAMCET 2021 Easy - Identify the incorrect statement from the following.TS EAMCET 2019 Easy
- Let \(\mathrm{S}\) be the focus of the hyperbola \(x^2-2 y^2=1\) lying on the positive \(\mathrm{X}\)-axis. Let \(\mathrm{P}(-1,1)\) be a given point. Then the area of the triangle formed by the line PS with the coordinate axes is (in sq. units)TS EAMCET 2022 Medium
- A force acts on a body of mass \(15 \mathrm{~kg}\), initially at rest. If the instantaneous power due to the force at the end of the third second is \(5 \mathrm{~W}\), then the instantaneous power (in W) at the end of the \(4 \mathrm{~s}\) will beTS EAMCET 2021 Medium
- \(A B\) is an ionic solid. The ionic radii of \(A^{+}\)and \(B^{-}\) are respectively \(r_c\) and \(r_a\). Lattice energy of \(A B\) is proportional to :TS EAMCET 2006 Medium
- Three particles \(A, B\) and \(C\) of masses \(m, 2 m\) and \(3 m\) are moving towards north, south and east respectively. If the velocities of the particles \(A, B\) and \(C\) are \(6 \mathrm{~ms}^{-1}, 12 \mathrm{~ms}^{-1}\) and \(8 \mathrm{~ms}^{-1}\) respectively, then the velocity of the centre of mass of the system of particles isTS EAMCET 2024 Medium