Consider two matrices $A = \begin{bmatrix}2 & 1 & 4 \\ 1 & 0 & 3\end{bmatrix}$ and $B = \begin{bmatrix}-1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$.

The determinant of the matrix $AB$ is __________ (in integer).

A 3 m long, horizontal, rigid, uniform beam PQ has negligible mass. The beam is subjected to a 3 kN concentrated vertically downward force at 1 m from P, as shown in the figure. The beam is resting on vertical linear springs at the ends P and Q. For the spring at the end P, the spring constant $K_P$ = 100 kN/m.

If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant $K_Q$ (in kN/m) for the spring at the end Q is

What is the CORRECT match between the air pollutants and treatment techniques given in the table?

Which one of the following products is NOT obtained in anaerobic decomposition of glucose?