Which one of the following is more readily hydrolysed by $S_{N}1$ mechanism?

The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

$(a)$ Show that for every natural number $n$ relatively prime to $10$,there exists a natural number $m$ consisting only of digits $1$ such that $n$ divides $m$.
$(b)$ Hence or otherwise,show that every positive rational number can be expressed in the form $\frac{a}{10^b(10^c-1)}$ for some natural numbers $a, b, c$.

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then the value of $\lambda$ is

$A$ ray of light passes through four transparent media with refractive indices $\mu_1$,$\mu_2$,$\mu_3$,and $\mu_4$ as shown in the figure. The surfaces of all media are parallel. If the emergent ray $CD$ is parallel to the incident ray $AB$,we must have

The image formed by a convex mirror of focal length $30 \ cm$ is a quarter of the size of the object. The distance of the object from the mirror is $... \ cm$.