The equation $12x^2 + 7xy + ay^2 + 13x - y + 3 = 0$ represents a pair of perpendicular lines. Then the value of $a$ is

If $A, B$ and $C$ are any three sets,then $A - (B \cup C)$ is equal to

The population $p(t)$ at time $t$ of a certain mouse species follows the differential equation $\frac{d p(t)}{d t}=0.5 p(t)-450$. If $p(0)=850$, then the time at which the population becomes zero is

In the environment,ozone is known for its

Check whether the following pair of statements are negations of each other. Give reasons for your answer.
$I$: $x+y=y+x$ is true for every real number $x$ and $y$.
$II$: There exists real numbers $x$ and $y$ for which $x+y \neq y+x$.

$y+x^2=\frac{dy}{dx}$ has the solution