If $\frac{x^3 - 6x^2 + 10x - 2}{x^2 - 5x + 6} = f(x) + \frac{A}{(x - 2)} + \frac{B}{(x - 3)}$,then $f(x) =$ ?

$A$ flask of volume $10^3 \text{ cc}$ is completely filled with mercury at $0 \ ^\circ\text{C}$. The coefficient of cubical expansion of mercury is $180 \times 10^{-6} / ^\circ\text{C}$ and that of glass is $40 \times 10^{-6} / ^\circ\text{C}$. If the flask is now placed in boiling water at $100 \ ^\circ\text{C}$,how much mercury (in $\text{cc}$) will overflow?

Observe the following statements:
$I$. If $dy + 2xy dx = 2e^{-x^2} dx$, then $ye^{x^2} = 2x + c$.
$II$. If $ye^{-x^2} - 2x = c$, then $dx = (2e^{-x^2} - 2xy) dy$.
Which of the following is a correct statement?

The equation of a stationary wave along a stretched string is given by $y = 5 \sin \frac{2\pi}{3}x \cos 40\pi t$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is ..... $cm$.

The circles $x^2 + y^2 - 2x - 4y = 0$ and $x^2 + y^2 - 8y - 4 = 0$:

The area (in square units) of the triangle formed by the lines $x=0$,$y=0$ and $3x+4y=12$ is: