If $u = x y^2 \tan^{-1}\left(\frac{y}{x}\right)$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to

Data Entry - Physics

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of $45^{\circ}$ at the major segment of the circle,then the value of $m$ is:

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 :

Two strings $A$ and $B$ of lengths $L_A = 80 \ cm$ and $L_B = x \ cm$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency,the value of $x$ is:

In which of the following does aluminum become passive?