What is the formula of Carborundum?

$(a)$ 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 $a, b, c$.

Assertion $(A)$: $-NH_2$ group of aniline is ortho,para directing in electrophilic substitutions.
Reason $(R)$: $-NH_2$ group stabilises the arenium ion formed by the ortho,para attack of the electrophile.
The correct answer is

The point on the curve $y^{2}=2(x-3)$ at which the normal is parallel to the line $y-2x+1=0$ is

If $\tan A$ and $\tan B$ are the roots of the quadratic equation $x^2-px+q=0$,then $\sin^2(A+B)$ is equal to

Which of the following has the longest $C-O$ bond length? (Free $C-O$ bond length in $CO$ is $1.128 \ \mathring{A}$)