List of top Questions asked in GATE BM

In the circuit given below, \(V_s = 50\ \text{V}\). Let the circuit reach steady state for the SPDT switch at position 1. Once the circuit is switched to position 2, the energy dissipated in the resistors is \(\underline{\hspace{1cm}}\) J (rounded off to one decimal place). 

In the circuit shown below, the output voltage \(V_{out}\) is \(\underline{\hspace{1cm}}\) V. 

In the circuit shown below, \( R_1 = 2 \, \Omega \), \( R_2 = 1 \, \Omega \), \( L_1 = 2 \, H \), and \( L_2 = 0.5 \, H \). Which of the following describe(s) the characteristics of the circuit? 

A novel biomaterial was tested for its tensile properties. The experiment was conducted using a cylindrical sample of this material, which was 10 cm long with 1 cm diameter. When a tensile force of 50 kN was applied, this cylindrical sample elongated by 4 mm. Based on the experimental results described above and the tensile moduli of different tissues given in the table below, this biomaterial would be a suitable replacement for \(\underline{\hspace{2cm}}\). 
\[\begin{array}{|c|c|} \hline \textbf{Tissue} & \textbf{Tensile modulus} \\ \hline \text{Bone} & \text{5 – 20 GPa} \\ \hline \text{Tendon} & \text{0.5 – 1 GPa} \\ \hline \text{Ligament} & \text{20 – 400 MPa} \\ \hline \text{Articular cartilage} & \text{3 – 10 MPa} \\ \hline \end{array}\]

Match the following organs with their functions: 

Match the following in the context of biomaterial characterization: 

As shown in the circuit below, a constant voltage source is connected to two ideal resistors. 
The voltage drop across a resistor is measured using two different voltmeters V1 and V2 at five different time instances and the following values are recorded from V1 and V2. 

In the circuit diagram shown below, NMOS is in saturation region, \( \mu_n C_{\text{ox}} = 200 \, \mu \text{A/V}^2 \), width \( W = 40 \, \mu \text{m} \), length \( L = 1 \, \mu \text{m} \), the threshold voltage is 0.4 V, and the ratio of body-effect transconductance (\( g_m b \)) to transconductance (\( g_m \)) is 0.1. A small input voltage \( v_{\text{in}} \) is applied at the bulk-terminal to produce a small change in the output voltage \( v_{\text{out}} \). The dc gain for \( v_{\text{out}} / v_{\text{in}} \) is \(\underline{\hspace{2cm}}\). (Neglect channel-length modulation for NMOS and all intrinsic capacitors.) 

In the circuit diagram shown below, all OPAMPs are ideal with infinite gain and bandwidth. \(\frac{V_{OUT}}{V_{IN}}\) for this circuit is \(\underline{\hspace{2cm}}\). 

In the block diagram shown below, an infinite tap FIR filter with transfer function \( H(z) = \frac{Y(z)}{X(z)} \) is realized. If \[ H(z) = \frac{1}{1 - 0.5z^{-1}}, \] the value of \( \alpha \) is \(\underline{\hspace{2cm}}\) 

In the circuit shown below, $V_5 = 100 V$, $R_1 = 30 \Omega$, $R_2 = 60 \Omega$, $R_3 = 90 \Omega$, $R_4 = 45 \Omega$, and $R_5 = 30 \Omega$. The current flowing through resistor $R_3$ is \(\underline{\hspace{1cm}}\) A. (rounded off to two decimal places)

$x[n]$ is convolved with $h[n]$ to give $y[n]$. If $y[2] = 1$ and $y[3] = 0$, then $h[0] = \underline{\hspace{1cm}}.$ (Graphs are not uniformly scaled) 

A unit step input is applied to a system with impulse response \( H(s) = \dfrac{1-s/\omega_z}{1+s/\omega_p} \) at \( t = 0 \). The output of the system \( y(t) \) at \( t = 0^+ \) is
 

A continuous time transfer function \( H(s) = \dfrac{1 + s/10^6}{s} \) is converted to a discrete time transfer function \( H(z) \) using a bilinear transform at a sampling rate of 100 MHz. The pole of \( H(z) \) is located at \( z = \) \(\underline{\hspace{2cm}}\).

In the block diagram shown below, an analog signal, \( V_{IN} = \sin(2\pi \cdot 10^6 t) \) is quantized by a 10-bit Nyquist ADC. Later, 4 LSBs are dropped and 6 MSBs are converted to an analog signal \( V_{OUT} \) while using a 6-bit DAC. Assume uniform distribution for the quantization noise. The peak SQNR at the output of DAC is \(\underline{\hspace{2cm}}\) dB. 

In the circuit shown below, Y is a 2-bit (Y\(_1\)Y\(_0\)) output of the combinational logic. What is the maximum value of Y for any given digital inputs, A\(_1\)A\(_0\) and B\(_1\)B\(_0\)? 

Let $X(j\omega)$ denote the Fourier transform of $x(t)$. If $X(j\omega) = 10 e^{-j\pi f} \left( \frac{\sin(\pi f)}{\pi f} \right)$, then $ \frac{1}{2\pi} \int_{-\infty}^{\infty} X(j\omega) d\omega = \underline{\hspace{1cm}}. $ (where $\omega = 2\pi f$)

Three resistive loads are connected to ideal voltage and current sources as shown in the circuit below. The voltage $V_{AB}$ across the terminals A and B is equal to \(\underline{\hspace{1cm}}\) V.