GATE 2022 Rapid Revision Weekly Quiz 3

The state equation of LTI system is

State transition matrix Is.

The energy of the signal x(t) = is ____________.

(* denotes convolution)

Two persons P and Q can build a bridge in 24 and 22 days respectively. However, if they work together, they use 250 less stones per day and build the bridge in 12 days. Find the number of stones used in the bridge.

The minimum number of 2 – input NOR gates required to implement

Y = ACE + AFC + ADE + ADF + BCE + BDF + BCF + BDE is ______.

The non-linear device with a transfer characteristic given by i = (20 + 2V_i + 0.4V_i²) mA is supplied with a carrier of 2 V amplitude and sinusoidal signal of 0.5 V amplitude in series. If at the output the frequency component of AM signal is considered, then choose the correct options-

Modulating signal with frequency 25 KHz is sampled at 20% higher than the Nyquist rate and quantized into 32 levels. Resultant signal is transmitted using M. Array PSK with raised cosine pulse (roll-off factor 0.4). Available channel Bandwidth is 200 KHz. Determine the symbol rate.

Two numbers are chosen at random from at a time. The probability that the smaller of the two is less than 4 is ____

Find time ‘t’ __________ (m sec)

When transistor enters saturation

(V_BE(ON) = 0.7V, V_CE(sat) = 0.2V, β large)

Consider the following network.

The maximum power transferred to R_L is _____ W.

Consider the integral  then which of the following is simple closed path C .

A system is described by the state equation, X = AX + BU, The output is given by Y = CX where

Transfer function G(s) of the system is _____

A silicon epitaxial npn (BJT) transistor is fabricated with a base doping of N_B = 3 × 10¹⁶/cm³ and heavily doped collector region with N_C = 5 × 10¹⁷/cm³. The neutral base width is x_B = 0.5 μm. When V_BE = V_BC = 0. The V_BC at punch through is