If the circles $x^2 + y^2 = 16$ and $x^2 + y^2 + 2ax + 4y + 4 = 0$ touch each other internally then $a =$

If the line $3x + 4y + k = 0$ touches the ellipse $9x^2 + 16y^2 = 144$, then the value of k is.

Which of the following statements is/are False?
$S_1 : \exists\, n \in N$, such that $n^2 + n + 2$ is divisible by 4.
$S_2 : \exists\, x \in N$, such that $x - 17 < 20$.
$S_3 : \forall\, n \in N, \quad x^2 + 3x - 10 = 0$.
$S_4 : \forall\, n \in N, \quad n^2 \geq 1$.

The negation of $(p \wedge q) \rightarrow ((p \vee r) \rightarrow\, \sim q)$ is equivalent to ...