GATE IN 2026 Question Paper (07-Feb-2026) (Shift-1)

In the phase-locked-loop circuit shown below, the output of the VCO is a digital square wave.



If the input is a square wave at $10\text{ kHz}$, the steady state frequency of the output is ________ kHz. (rounded off to the nearest integer)

A digital counter increments its count every $0.1\mu \text{s}$. The counter is used in an instrument to measure frequency. The counter is operated for one period of the input signal to the instrument to measure its frequency. The input signal is approximately at $100\text{ kHz}$. The maximum error in the measured frequency is _____ kHz.

(rounded off to the nearest integer)

A current carrying semiconductor of thickness $0.7\text{ mm}$ is placed in a transverse magnetic field. The measured Hall voltage is $0.9\text{ mV}$ and the current is $6\text{ mA}$. If the Hall coefficient is $4\times 10^{-4}{\text{ m}}^3/\text{C}$, the value of the incident magnetic field is _______ T. (rounded off to two decimal places)

For a fiber Bragg grating-based sensor, the shift in the Bragg wavelength gives information about the value of the measurand. For a Bragg wavelength of $1550\text{ nm}$ and effective index of $1.44$, the grating period is _______ nm.

(rounded off to two decimal places)

A photodiode has a responsivity $0.8\text{ A/W}$. If the input optical power to the photodiode is $2\text{ mW}$, the power delivered to a $50\Omega$ load is _______ $\mu \text{W}$.

(rounded off to the nearest integer)