Consider the following database tables of a sports league. player (\( pid \), \( pname \), \( age \)) coach (\( cid \), \( cname \)) team (\( tid \), \( tname \), \( city \), \( cid \)) members (\( pid \), \( tid \)) An instance of the table and an SQL query are given.
Player table

coach table:

team table:

members table:

SQL query: \[ {SELECT MIN(P.age)} \] \[ {FROM player P} \] \[ {WHERE P.pid IN (} \] \[ { SELECT M.pid} \] \[ { FROM team T, coach C, members M} \] \[ { WHERE C.cname = 'Mark'} \] \[ { AND T.cid = C.cid} \] \[ { AND M.tid = T.tid)} \] The value returned by the given SQL query is _________. (Answer in integer)
coach table, we see that "Mark" has cid = 102.team table, the team with cid = 102 is "MI" (with tid = 10).members table, players who belong to team "MI" (tid = 10) are:player table are:A quadratic polynomial \( (x - \alpha)(x - \beta) \) over complex numbers is said to be square invariant if \[ (x - \alpha)(x - \beta) = (x - \alpha^2)(x - \beta^2). \] Suppose from the set of all square invariant quadratic polynomials we choose one at random. The probability that the roots of the chosen polynomial are equal is ___________. (rounded off to one decimal place)
A disk of size 512M bytes is divided into blocks of 64K bytes. A file is stored in the disk using linked allocation. In linked allocation, each data block reserves 4 bytes to store the pointer to the next data block. The link part of the last data block contains a NULL pointer (also of 4 bytes). Suppose a file of 1M bytes needs to be stored in the disk. Assume, 1K = \(2^{10}\) and 1M = \(2^{20}\). The amount of space in bytes that will be wasted due to internal fragmentation is ___________. (Answer in integer)
In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between the point P and the line QR. What is the ratio of the area of the triangle PST to the area of the trapezium SQRT?
Note: The figure shown is representative

Consider the following hierarchical cache system with the following access times:
\[ \begin{array}{|c|c|c|} \hline \textbf{Cache Level} & \textbf{Hit Rate} & \textbf{Access Time} \\ \hline L1 & 90\% & 1 \text{ ns} \\ L2 & 80\% & 10 \text{ ns} \\ L3 & 100\% & 100 \text{ ns} \\ \hline \end{array} \]Find \( T_{avg} \) for hierarchical or simultaneous access.