$P$ and $Q$ are two positive integers such that $P^2=Q^2+13$.

The product of the numbers $P$ and $Q$ is $\_\_\_\_$

Scores obtained by two students P and Q in seven courses are given in the table below. Based on the information given in the table, which one of the following statements is INCORRECT?

$$ \begin{array}{|l|l|l|l|l|l|l|l|} \hline \mathrm{P} & 22 & 89 & 50 & 45 & 78 & 60 & 39 \\ \hline \mathrm{Q} & 35 & 65 & 60 & 56 & 81 & 45 & 50 \\ \hline \end{array} $$

In the triangle PQR , the lengths of PT and TR are in the ratio of $3: 2$.

ST is parallel to QR. Two semi-circles are drawn with PS and PQ as diameters, as shown in the figure.

Which one of the following statements is true about the shaded area PQS?

Note: The figure shown is representative.

In the following figure,

• CD = 5 cm, BE = 10 cm, AE = 12 cm,
• ∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90°

Points AFCD create a rhombus.

The length of BF (in cm) is