A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is

Two system $${H_1}\left( z \right)$$ and $${H_2}\left( z \right)$$ are connected in cascade as shown below. The overall output $$y\left( n \right)$$ is the same as the input $$x\left( n \right)$$ with a one unit delay. The transfer function of the second system $${H_2}\left( z \right)$$ is

There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?

Three friends, R, S and T shared toffee from a bowl. R took 1/3^rd of the toffees, but returned four to the bowl. S took 1/4^rd of what was left but returned three toffees to the bowl. T took half of the remainder but returned two back into the bowl. If the bowl had 17 toffees left, how many toffees-were originally there in the bowl?