KCET · Maths · Vector Algebra
If \( x=c t \) and \( y=\frac{c}{t} \), find \( \frac{d y}{d t} \) at \( t=2 \)
- A \( \frac{1}{4} \)
- B \( 4 \)
- C \( -\frac{1}{4} \)
- D \( 0 \)
Answer & Solution
Correct Answer
(C) \( -\frac{1}{4} \)
Step-by-step Solution
Detailed explanation
\( x=c t \)
Given that, \( x c=t \) and \( y=\frac{c}{t} \)
Now \( \frac{d x}{d t}=c, \frac{d y}{d t}=\frac{-c}{t^{2}} \)
So, \( \frac{d y}{d x}=\frac{d y}{d t} \times \frac{d t}{d x}=\frac{-c}{c t^{2}}=\frac{-1}{t^{2}} \)
At \( t=2 \), we get
left. \( \left.\frac{d y}{d x}\right|_{t=2}=\frac{-1}{(2)^{2}}=\frac{-1}{4} \)
Given that, \( x c=t \) and \( y=\frac{c}{t} \)
Now \( \frac{d x}{d t}=c, \frac{d y}{d t}=\frac{-c}{t^{2}} \)
So, \( \frac{d y}{d x}=\frac{d y}{d t} \times \frac{d t}{d x}=\frac{-c}{c t^{2}}=\frac{-1}{t^{2}} \)
At \( t=2 \), we get
left. \( \left.\frac{d y}{d x}\right|_{t=2}=\frac{-1}{(2)^{2}}=\frac{-1}{4} \)
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 \(A\) is a square matrix of order 3 and \(|A|=5\), then \(\mid A\) adj. \(A \mid\) isKCET 2020 Medium
- A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no lockdown. The probability that the pandemic will be controlled in one month isKCET 2022 Hard
- The family of curves whose \(x\) and \(y\) intercepts of a tangent at any point are respectively double the \(x\) and \(y\) coordinates of that point isKCET 2024 Hard
- The length of the chord of the circle \(x^{2}+y^{2}+3 x+2 y-8=0\) intercepted by the \(y\)-axis isKCET 2013 Easy
- If \(a_{1} a_{2} a_{3} \ldots a_{9}\) are in \(\mathrm{AP}\), then the value of \(\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ a_{4} & a_{5} & a_{6} \\ a_{7} & a_{8} & a_{9}\end{array}\right|\) isKCET 2020 Medium
- The equation of a hyperbola whose asymptotes are \(3 x \pm 5 y=0\) and vertices are \((\pm 5,0)\) isKCET 2011 Medium
More PYQs from KCET
- A particle is projected with a velocity \( v \) so that its horizontal range twice the greatest height
attained. The horizontal range isKCET 2015 Hard - The constant term in the expansion of \( \left|\begin{array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3 x+1 & 4 x-1\end{array}\right| \) isKCET 2019 Hard
- Primary endosperm nucleus is formed by fusion ofKCET 2023 Hard
- A multi meter reads a voltage of a certain A.C. source as \( 100 \mathrm{~V} \). What is the peak value of
voltage of A.C. source ?KCET 2014 Hard - Match the reactant in Column - \( 1 \) with the reaction in Column - II
\begin{array}{|l|l|}
\hline I & II \\
\hline (i) Acetic acid & (a) Stephen \\
\hline (ii) Sodium phenate & (b) Friedel-Crafts \\
\hline (iii) Methyl cyanide & (c) HVZ \\
\hline (iv) Toluen & (d) Kolbe's \\
\hline
\end{array}KCET 2014 Easy - Which of the following electrolytes will have maximum coagulating value for \( \mathrm{Agl} / \mathrm{Ag}^{+} \mathrm{sol} \) ?KCET 2018 Easy