GATE EE 2014 Question Paper (02-Mar-2014) (Shift 1)

The second order dynamic system

$\frac{dx}{dt}=Px+Qu$

y = Rx

has the matrices, P, Q and R as follows:

P = ≤ft[ {*20c - 1&1\\ 0& - 3 } ] Q = ≤ft[ {*20c 0\\ 1 } ] R = ≤ft[ 0 1 ]

The system has the following controllability and observability properties:

Suppose that resistors R1 and R2 are connected in parallel to give an equivalent resistor R. If resistors R1 and R2 have tolerance of 1% each the equivalent resistor R for resistor R1 = 300 Ω and R2 = 200 Ω will have tolerance of

Two ammeters x and y have resistances of 1.2 Ω and 1.5 Ω respectively and they give full scale deflection with 150 mA and 250 mA respectively. The ranges have been extended by connecting shunts so as to give full scale deflection with 15 A. The ammeters along with shunts are connected in parallel and then placed in a circuit in which the total current flowing is 15 A. The current in amperes indicated in ammeter x is-

An oscillator circuit using ideal op-amp and diodes is shown in the figure.



The time duration for +ve part of the cycle is Δt₁ and for -ve part is Δt₂. The value of $e^{\frac{\mathrm{\Delta }{t}_1-\mathrm{\Delta }{t}_2}{RC}}$ will be______

The SOP (sum of products) form of a Boolean function is ∑(0,1,3,7,11), where inputs are A, B, C, D (A is MSB, and D is LSB). The equivalent minimized expression of the function is: