If log10 2 log₂ 10 + log₁₀(10^x) = 2, then what is the value of x?

Let ABC be a triangle. If cos2A + cos2B + cos2C = -1 then which one of the following is correct?

What is the value of the following determinant?

$\begin{vmatrix} \cos \rm C & \tan \rm A & 0\\ \sin \rm B & 0 & -\tan \rm A\\ 0 & \sin \rm B & \cos \rm C \end{vmatrix}$

Suppose set A consists of first 250 natural numbers that are multiple of 3 and set B consists of first 200 even natural numbers. How many elements does A ∪ B have?