GATE EC 2025 Question Paper (15-Feb-2025) (Shift 2)

Which of the following can be used as an n-type dopant for silicon? Select the correct option(s).

The function $y(t)$ satisfies

$t^2{y}^{\prime \prime }(t)-2t{y}^{\prime }(t)+2y(t)=0$,

where $y^{\prime }(t)$ and $y^{\prime \prime }(t)$ denote the first and second derivatives of $y(t)$, respectively.
Given $y^{\prime }(0)=1$ and $y^{\prime }(1)=-1$, the maximum value of $y(t)$ over $[0,1]$ is __________

(rounded off to two decimal places).

The generator matrix of a (6,3) binary linear block code is given by

$G=$ $\left[\begin{array}{cccccc}1& 0& 0& 1& 0& 1\\ 0& 1& 0& 0& 1& 1\\ 0& 0& 1& 1& 1& 0\end{array}\right]$ .

The minimum Hamming distance $d_{min}$ between codewords equals __________ (answer in integer).

All the components in the bandpass filter given below are ideal. The lower -3 dB frequency of the filter is 1 MHz.
The upper -3 dB frequency (in MHz, rounded off to the nearest integer) is ________.

A 4-bit weighted-resistor DAC with inputs $b_3$, $b_2$, $b_1$, and $b_0$ (MSB to LSB) is designed using an ideal opamp, as shown below. The switches are closed when the corresponding input bits are logic '1' and open otherwise. When the input $b_3{b}_2{b}_1{b}_0$ changes from 1110 to 1101, the magnitude of the change in the output voltage $V_O$ (in mV, rounded off to the nearest integer) is ________.