Instrumentation Engineering
2024 · Paper 1
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Complete GATE IN 2024 Paper 1 overview, original pages and practice · Timed previous-paper practice
Questions 55–57 of 65. Imported answers require review unless explicitly marked reviewed.
Question 55
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Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point s = jα, α > 0, lies on the root locus, the value of α is ________ (rounded off to nearest integer).
Note: The poles are marked with × in the figure.
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A shielded cable with C_stray = 20 pF and R_wire = 10 Ω is used to connect the inductive sensors as shown in the figure. The RMS value of V_out is ____ V (rounded off to two decimal places).
Note: Assume all components are ideal, and sensors are not magnetically coupled.
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In the figure shown, the diode current is given by
. V_D is the diode voltage in volts, T is the absolute temperature in Kelvin, α = 1.16 × 10⁴ K/V, and I_S = 10⁻¹⁵ A is the saturation current. The dc current source, opamp and the resistors are ideal, and are assumed to be temperature independent. The change in the output voltage (V_out) per Kelvin change in temperature is ________ mV (rounded off to one decimal place). 
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