ISRO 2023 Quiz 2

For the system in the figure the transfer function is equal to

By considering standard notations, the peak value of the magnitude in the resonant peak M_r is

A system has poles at 0.01 Hz, 1 Hz and 80 Hz; zeroes at 5 Hz, 100 Hz and 200 Hz. The approximate phase of the system response at 20 Hz is

In state variable representation, the size of matrix is decided by

A pipe can empty a tank in 40 minutes. A second pipe with diameter twice as much as that of the first is also attached with the tank to empty it. How much time will the two pipes together take to empty the tank?