GATE EE 2019 Question Paper (09-Feb-2019) (Shift 2)

Consider a state-variable model of a system

≤ft[ {*20c {x_1}\\ {x_2} } ] = ≤ft[ {*20c 0&1\\ - α & - 2β } ]≤ft[ {*20c x_1\\ x_2 } ] + ≤ft[ {*20c 0\\ α } ]r

y = ≤ft[ {*20c 1&0 } ]≤ft[ {*20c x_1\\ x_2 } ]

where y is the output, and r is the input. The damping ratio ξ and the undamped natural frequency ωₙ (rad/sec) of the system are given by

A moving coil instrument having a resistance of 10 Ω, gives a full-scale deflection when the current is 10 mA. What should be the value of the series resistance, so that it can be used as a voltmeter for measuring potential difference up to 100 V?

The enhancement type MOSFET in the circuit below operates according to the square law. μₙCₒₓ = 100 μA/V², the threshold voltage (V${}_T$) is 500 mV. Ignore channel length modulation. The output voltage Vₒᵤₜ is

In the circuit below, the operational amplifier is ideal. If V ₁= 10 mV and V ₂= 50 mV, the output voltage (V ₒᵤₜ) is

The output expression for the Karnaugh map shown below is