AP EAMCET · Maths · Differentiation
If \(u(x, y)=y \log x+x \log y\), then \(u_x u_y-u_x \log x-u_y \log y+\log x \log y\) is equal to :
- A 0
- B -1
- C 1
- D 2
Answer & Solution
Correct Answer
(C) 1
Step-by-step Solution
Detailed explanation
We have, \(u(x, y)=y \log x+x \log y\) On differentiating partially w.r.t. \(x\) and \(y\) respectively, \(u_x=\frac{y}{x}+\log y, u_y=\log x+\frac{x}{y}\) Now, \(u_x u_y-u_x \log x-u_y \log y+\log x \log y\)…
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 equation of an ellipse in its standard form, given the distance between its foci is 2 units and the length of its latusrectum is \(\frac{15}{2}\) units, isAP EAMCET 2021 Easy
- If \(y=a \cos (\log x)+b \sin (\log x)\), where \(a, b\) are parameters, then \(x^2 y^{\prime \prime}+x y^{\prime}\) is equal toAP EAMCET 2002 Hard
- In a \(\triangle A B C\) if \(r_1=2 r_2=3 r_3\) then \(a: b\) isAP EAMCET 2025 Medium
- If \(\mathrm{Q}(h, k)\) is the inverse point of the point \(\mathrm{P}(1,2)\) with respect to the circle \(x^2+y^2-4 x+1-0\), then \(2 h+k=\)AP EAMCET 2024 Easy
- The value of the determinant \(\left|\begin{array}{lll}b^2-a b & b-c & b c-a c \\ a b-a^2 & a-b & b^2-a b \\ b c-a c & c-a & a b-a^2\end{array}\right|\) isAP EAMCET 2015 Easy
- By the definition of the definite integral, the value of
\[
\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^2-1}}+\frac{1}{\sqrt{n^2-2^2}}+\ldots+\frac{1}{\sqrt{n^2-(n-1)^2}}\right)
\]
is equal toAP EAMCET 2016 Easy
More PYQs from AP EAMCET
- The net electric flux due to a uniform electric field of \(3 \times 10^3 \hat{1} \mathrm{NC}^{-1}\) through a cube of side \(20 \mathrm{~cm}\) oriented such that its faces are parallel to the coordinate planes isAP EAMCET 2023 Easy
- The products formed in the reaction of phenol with \(\mathrm{Br}_2\) dissolved in \(\mathrm{CS}_2\) at \(0^{\circ} \mathrm{C}\) areAP EAMCET 2013 Easy
- Match the following
\(\begin{array}{ll}
\text{List - I} & \text{List - II} \\
\text{i) Isothermal process} & \text{a)} 0 \\
\text{ii) Isobaric process} & \text{b)} \frac{1}{\gamma-1}\left[\mathrm{P}_2 \mathrm{~V}_2-\mathrm{P}_1 \mathrm{~V}_1\right] \\
\text{iii) Isochoric process} & \text{c)} \mu \mathrm{RT} \ln \left(\frac{V_2}{V_1}\right) \\
\text{iv) Adiabatic process} & \text{d)} \mathrm{P}\left(\mathrm{V}_2-\mathrm{V}_1\right) \\
\end{array}\)
The correct answer isAP EAMCET 2017 Easy - In a vehicles lifter, the enclosed gas exerts a force \(F\) on a small piston of \(8 \mathrm{~cm}\) diameter.
The pressure is transmitted to a second piston of diameter \(24 \mathrm{~cm}\). If the mass of the vehicle to be lifted is \(1400 \mathrm{~kg}\), then \(F\) must at least be \(\left(g=10 \mathrm{~ms}^{-2}\right)\)AP EAMCET 2021 Medium - The numbers \(a_n=6^n-5 n\) for \(n=1,2,3, \ldots\) when divided by 25 leave the remainderAP EAMCET 2010 Medium
- \(\frac{x-1}{3 x+4} < \frac{x-3}{3 x-2}\) holds, for all \(\mathrm{x}\) in the intervalAP EAMCET 2017 Easy