The angle between the tangents drawn from the origin to the circle $(x-7)^2 + (y+1)^2 = 25$ is

The equation of the common tangent touching the circle $(x-3)^2 + y^2 = 9$ and the parabola $y^2 = 4x$ above the X-axis is

If $\lim\limits_{x \to \infty} \dfrac{(2x-1)^{19} \cdot (3x+2)^{11}}{(6x-5)^{30}} = 2^a \cdot 3^b$, then $a + b =$

The dual of the statement pattern $(p \wedge \sim q) \longrightarrow (q \wedge \sim p)$ is equivalent to