If a_n = n(n!), then what is a₁ + a₂ + a₃ +...+ a₁₀ equal to?

If p and q are the non-zero roots of the equation x² + px + q = 0, then how many possible values can q have?

If $\rm \Delta = \begin{vmatrix} a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}$ then what is $\rm \begin{vmatrix} 3d + 5g & 4a + 7g & 6g\\ 3e + 5h & 4b + 7h & 6h\\ 3f + 5i & 4c + 7i & 6i \end{vmatrix}$ equal to?

$\frac{1}{b+c}, \frac{1}{c+a},\frac{1}{a+b}$ are in HP, then which of the following is/are correct?

1. a, b, c are in AP

2. (b + c)², (c + a)², (a + b)² are in GP. Select the correct answer using the code given below.