$$F\left( {x,y} \right) = \left( {{x^2} + xy} \right)\,\widehat a{}_x + \left( {{y^2} + xy} \right)\,\widehat a{}_y.\,\,$$ Its line integral over the straight line from $$(x, y)=(0,2)$$ to $$(x,y)=(2,0)$$ evaluates to

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

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