In the $lac$ operon model,lactose molecules function as:

Statement $-1$ : $\sim (p \leftrightarrow \sim q)$ is equivalent to $p \leftrightarrow q$.
Statement $-2$ : $\sim (p \leftrightarrow \sim q)$ is a tautology.

Two identical balls $A$ and $B$ are released from the positions shown in the figure. They collide elastically on the horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after the collision will be: (neglect friction)

If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$ $(H^2>A B)$ forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)$ is equal to :

If $\frac{x^3 - 6x^2 + 10x - 2}{x^2 - 5x + 6} = f(x) + \frac{A}{(x - 2)} + \frac{B}{(x - 3)}$,then $f(x) =$ ?

When iron sulfide is heated in air,a sulfur oxide $A$ is formed. When $A$ is dissolved in water,it produces an acid. What is the basicity of this acid?