GATE IN 2016 Question Paper (31-Jan-2016) (Shift 2)

A dc potentiometer, shown in figure below, is made by connecting fifteen 10 Ω resistors and a 10 Ω slide wire of length 1000 mm in series. The potentiometer is standardized with the current Iₚ = 10.0000 mA. Balance for an unknown voltage is obtained when the dial is in position 11(11 numbers of the fixed 10 Ω resistor are included) and the slide wire is on the 234th mm position. The unknown voltage (up to four decimal places) involtis _______.

In the circuit given below, each input terminal of the OPAMP draws a bias current of 10 nA. The effect due to these input bias currents on the output voltage V${}_O$ will be zero, if the value of R chosen in kilo-ohm is _______.

A peizo-electric type pressure sensor has a sensitivity of 1 mV/kPa and a bandwidth of 300 Hz to 300 kHz. For a constant (dc) pressure of 100 kPa, the steady state output of the sensor in mllivolt is ______.

The signal m(t) = cos(ω${}_m$ t) is SSB (single side-band) modulated with a carrier cos(ω${}_c$ t) to get s(t). The signal obtained by passing s(t) through an ideal envelope detector is

Let $s\left(t\right)=rect\left(\frac{t-3}{3}\right)$ be a signal passed through an AWGN (additive white Gaussian noise) channel with noise power spectral density (PSD) $\frac{N_0}{2}$ to get v(t). If v(t) is passed through a matched-filter that is matched to s(t), then output signal-to noise ratio (SNR) of the matched-filter is