If we use pyrene $(CCl_4)$ in the Riemer-Tiemann reaction in place of chloroform,the product formed is

$ \cos^4 \frac{\pi}{8} + \cos^4 \frac{3\pi}{8} + \cos^4 \frac{5\pi}{8} + \cos^4 \frac{7\pi}{8} = $

If $f(x)$ is a polynomial of degree $n$ with rational coefficients and $1+2i, 2-\sqrt{3},$ and $5$ are three roots of $f(x)=0$,then the least value of $n$ is

The major product of the following reaction is

The compound prepared by a substitution reaction of benzene is

In a compound microscope,the focal lengths of two lenses are $1.5 \, cm$ and $6.25 \, cm$. An object is placed at $2 \, cm$ from the objective lens and the final image is formed at $25 \, cm$ from the eye lens. The distance between the two lenses is.....$cm$