GATE EC question library

Consider the square region $R$ in the $X-Y$ plane as shown with the dark shading in the Figure. The value of $\iint_{R}\left(x^{2}+y^{2}-1\right) d x d y$ is $\_\_\_\_$ .(rounded off to two decimal places)

Consider an ideal OP-AMP circuit as shown in the Figure. The resistances $R_{1}=R_{2}=R_{3}=R_{4}=50 \mathrm{~k} \Omega$. The magnitude of the closed loop gain is $\_\_\_\_$ . (rounded off to two decimal places)

The average bit error rate at the input of a $(7,4,1)$ Hamming decoder is $0.10$. The probability that the decoder will fail to decode a received word correctly is $\_\_\_\_\_$ (rounded off to two decimal places)

Consider that the concentration of electrons in a semiconductor bar varies linearly from $2 \times 10^{17} \mathrm{~cm}^{-3}$ at $x=1 \mu \mathrm{~m}$ to $1 \times 10^{16} \mathrm{~cm}^{-3}$ at $x=4 \mu \mathrm{~m}$ along the $x$-direction. Assume that the concentration of electrons is not varying along other directions (that is along $y$ - and …

Consider the ideal diodes $\text{D1}$ and $\text{D2}$ as shown in the Figure with cut-in voltage $V_{\gamma}=0$ Volt and $v_{i}(t)$ is in Volt. The maximum voltage (Volt) of the output $v_{o}(t)$ is $\_\_\_\_$ . (rounded off to two decimal places)