GATE IN 2022 Question Paper (06-Feb-2022) (Shift 2)

Consider the function 𝑓(𝑧) = $\frac{1}{(\mathrm{z}+1)(\mathrm{z}+2)(\mathrm{z}+3)}$. The residue of f(z) at z = -1, is ________

In the circuit shown, the capacitance C₀ = 10 μF and inductance L₀ = 1 mH and the diode is ideal. The capacitor is initially charged to 10 V and the current in the inductor is initially zero. If the switch is closed at 𝑡 = 0 s, the voltage V${}_c$ (t) (in volts) across the capacitor at 𝑡 = 0.5 s is ______ (round off to one decimal place)

The bridge shown is balanced when R₁= 100 Ω, R₂ = 210 Ω, C₂ = 2.9 μF, and R₄ = 50 Ω. The 2 kHz sine-wave generator supplies a voltage of 10 Vₚ₋ₚ. The value of L₃ (in millihenry) is _______ (round off to two decimal places)

In the circuit shown, the switch is initially closed. It is opened at 𝑡 = 0 s and remains open thereafter. The time (in milliseconds) at which the output voltage Vₒᵤₜ becomes LOW is ________ (round off to three decimal places)

In the Wheatstone bridge circuit shown, R1 = 1.5 kΩ and R2 = R3 = R4 = 1 kΩ. The switch is initially open and the voltage between the points C and D is VCD. Upon closing the switch at 𝑡 = 0, the resistance in the arm AD changes by an amount 𝛿R1 , and the voltage between C and D changes by 𝛿VCD. The sensitivity of the bridge (in volt/kiloohm), defined as $\left|\frac{\delta {\mathrm{V}}_{\mathrm{CD}}}{\delta {\mathrm{R}}_1}\right|$, is _______ (round off to two decimal places)