What are $X$ and $Y$ in the following reactions?

The magnifying power of a telescope with tube length $60 \ cm$ is $5$. Then the focal length of its eyepiece is: (in $cm$)

If the decimal $0.d25d25d25\ldots$ is expressible in the form $n/27$,then $d+n$ must be

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$,crosses the layer,and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$,the value of $\theta$ is

If $y = \sin(m \sin^{-1} x)$,then $(1 - x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

If $\frac{{}^{n+2} C_6}{{}^{n-2} C_2} = 11$,then $n$ satisfies the equation