An aqueous solution of potash alum gives:

The solution of $\frac{dy}{dx} = (\frac{x}{y})^{-1/3}$ is

The equation of the normal to the circle $x^2 + y^2 = 9$ at the point $\left( \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}} \right)$ is:

Two point white dots are $1 \, mm$ apart on black paper. They are viewed by an eye with a pupil diameter of $3 \, mm$. Approximately,what is the maximum distance at which these dots can be resolved by the eye? (Take $\lambda = 500 \, nm$)

Let $f(x)=e^x$,$g(x)=\sin ^{-1} x$ and $h(x)=f(g(x))$,then $\frac{h^{\prime}(x)}{h(x)}$ is equal to

The centroid of the triangle formed by the pair of straight lines $12x^2 - 20xy + 7y^2 = 0$ and the line $2x - 3y + 4 = 0$ is: