GATE EC 2013 Question Paper (10-Feb-2013) (Shift 2)

Let U and V be two independent zero mean Gaussian random variables of variances 1/4 and 1/9 respectively. The probability P(3V ≥ 2U) is

Let A be m × n matrix and b an n × m matrix. It is given that determinant ( I${}_m$ + AB ) = determinant ( Iₙ + BA ), where Iₖ is the k × k matrix. Using the above property, the determinant of the matrix given below is

≤ft[ {*20c 2&1&1&1\\ 1&2&1&1\\ 1&1&2&1\\ 1&1&1&2 } ]

In the circuit shown below, if the source voltage V${}_S$ = 100∠53.13° V then the Thevenin’s equivalent voltage in Volts as seen by the load resistance R${}_L$ is

The open-loop transfer function of a dc motor is given as: $\frac{\omega \left(s\right)}{V_a\left(s\right)}=\frac{10}{1+10s}$ . When connected in feedback as shown below, the approximate value of Kₐ that will reduce the time constant of the closed-loop system by one hundred times as compared to that of the open-loop system is

In the circuit shown below, the knee current of the ideal Zener diode is 10 mA. To maintain 5 V across R${}_L$, the Minimum value of R${}_L$ in Ω and the Maximum power rating of the Zener diode in mW, respectively are