Assume for simplicity that $$N$$ people, all born in April (a month of $$30$$ days) are collected in a room, consider the event of at least two people in the room being born on the same date of the month (even if in different years e.g. $$1980$$ and $$1985$$). What is the smallest $$N$$ so that the probability of this exceeds $$0.5$$ is ?

Let $$\,{x^2} - 117 = 0.\,\,$$ The iterative steps for the solution using Newton -Raphson's method is given by

Match the switch arrangements on the top row to be steady $$-$$ state $$V$$ - $$I$$ characteristics on the lower row. The steady state operating points are shown by large black dots.

The Current Source Inverter shown in Figure is operated by alternately turning on thyristor pairs $$\left( {{T_1},\,\,{T_2}} \right)$$ and $$\left( {{T_3},\,\,{T_4}} \right).$$ If the load is purely resistive, the theoretical maximum output frequency obtainable will be