List of top Biomedical Engineering Questions asked in GATE Biomedical Engineering

A continuous time, band limited signal \(x(t)\) has its Fourier transform described by \( X(f)= \begin{cases} 1-\dfrac{|f|}{200}, & |f|\le 200\text{ Hz}\\[4pt] 0, & |f|>200\text{ Hz} \end{cases} \). The signal is uniformly sampled at a sampling rate of \(600\) Hz. The Fourier transform of the sampled signal is \(X_s(f)\). What is the value of \(\dfrac{X_s(600)}{X_s(500)}\)? (Round off the answer to one decimal place.)

The continuous time signal \(x(t)\) is described by \[ x(t) = \begin{cases} 1, & 0 \leq t \leq 1 \\ 0, & \text{elsewhere} \end{cases} \] If \(y(t)\) represents \(x(t)\) convolved with itself, which of the following statements is/are TRUE?

A stone is thrown from an elevation of 2 m above ground level, at an angle of \(30^\circ\) to the horizontal axis. If the stone hits the ground at a horizontal distance of 6 m from the point of release, at what speed (in m/s) was the stone thrown? Use \(g = 10\ \text{m/s}^2\) and assume that there is no air resistance. (Round off your answer to one decimal place.)

Consider the total hip joint prosthesis as shown in the figure. The geometric parameters of the prosthesis are such that \(L_1=40\) mm, \(L_2=60\) mm, \(\theta_1=45^\circ\), \(\theta_2=90^\circ\). Assume that, when standing symmetrically on both feet, a joint reaction force of \(400~\text{N}\) is acting vertically at the femoral head (point A) due to the body weight of the subject. Calculate the magnitude of the moment (in Nm) about point C. (Round off the answer to one decimal place.)

A Wheatstone bridge strain gauge transducer is constructed on a diaphragm in such a way that when a force is applied on the diaphragm, the resistors \(R_1\) and \(R_4\) will be in compression, and the resistors \(R_2\) and \(R_3\) will be in tension. The bridge excitation voltage \((E_{\text{in}})\) is \(10\ \text{V}\). If all the resistors have a resistance of \(200\ \Omega\) in the absence of any force, and each resistance changes by \(20\ \Omega\) upon application of a force, what is the output voltage \(V_{\text{out}}\) (in Volts) from the Wheatstone bridge? (Round off your answer to the nearest integer.)

A metallic strain gauge with negligible piezoresistive effect is subjected to a strain of \(50\times10^{-6}\). For the metal, Young’s Modulus \(=80\) GPa and Poisson’s ratio \(=0.42\). What is the change in resistance (in m\(\Omega\)), if the unstrained resistance is \(200~\Omega\)? (Round off the answer to one decimal place.)

A normally incident X-ray of energy 140 keV passes through a tissue phantom and is detected by the detector as shown. The phantom consists of tissue \(P\) with an absorption coefficient of \(1~\mathrm{cm^{-1}}\) and a thickness of \(1~\mathrm{cm}\), and tissue \(Q\) with an absorption coefficient of \(10~\mathrm{cm^{-1}}\) and a thickness of \(2~\mathrm{cm}\). Calculate the intensity (in \(\mu\mathrm{eV}\)) detected by the detector. (Round off the answer to one decimal place.)

A two-dimensional square plate (20 mm sides) contains a homogeneous circular inclusion of 5 mm diameter in it. A parallel beam of X-rays (beam width 30 mm) is used in a tomography system to determine the location of the inclusion. What is the minimum number of views required to approximately determine the location of the inclusion?

The resistance of a thermistor is 1 k\(\Omega\) at \(25^\circ\mathrm{C}\) and 500 \(\Omega\) at \(50^\circ\mathrm{C}\). Find the temperature coefficient of resistance (in units of \(^{\circ}\mathrm{C}^{-1}\)) at \(35^\circ\mathrm{C}\). (Round off the answer to three decimal places.)

In a cell viability experiment, 10{,000 cells were cultured in the absence and presence of a compound \(Q\) for 24 h. The absorbance of a dye associated with cellular metabolic activity was measured at a wavelength of 570 nm at 24 h. The measured absorbances were \(0.8\) a.u. in the absence of \(Q\), and \(0.5\) a.u. in its presence. If the dye gives an absorbance (at 570 nm) of \(0.1\) a.u. in the absence of cells, what is the percentage cell growth inhibition caused by the compound \(Q\)? (Round off the answer to one decimal place.)}

The volume percentage of oxygen in inspired air is \(20%\) and that of expired air is \(16%\). A person is breathing at a rate of 12 breaths per minute. Each breath is 500 ml in volume. The cardiac output is 5 liters per minute. Assuming ideal, healthy lung and cardiac conditions, what is the change in percentage of oxygen in blood over 1 minute? (Round off the answer to one decimal place.)

The intracellular and extracellular concentrations (in mM) of three important ions are given. The relative permeability of the cell membrane to each ion is provided. Universal gas constant \(R=8.31~\mathrm{J/(mol\cdot K)\) and Faraday’s constant \(F=96500~\mathrm{C/mol}\). What is the \emph{absolute value} of the resting membrane potential (in mV) across the cell membrane at \(27^\circ\mathrm{C}\)? (Round off the answer to one decimal place.)}

A system is described by the following differential equation \[ 0.01 \frac{d^2y(t)}{dt^2} + 0.2 \frac{dy(t)}{dt} + y(t) = 6x(t), \] where time \((t)\) is in seconds. If \(x(t)\) is the unit step input applied at \(t=0\) s to this system, the magnitude of the output at \(t=1\) s is ________. (Round off the answer to two decimal places.)

Assuming the operational amplifier in the circuit shown below to be ideal, which of the following properties hold(s) TRUE for the circuit?

Two sequences \(x_1[n]\) and \(x_2[n]\) are described as follows: \[ x_1[0] = x_2[0] = 1, x_1[1] = x_2[2] = 2, x_1[2] = x_2[1] = 1 \] \[ x_1[n] = x_2[n] = 0 \text{for all } n<0 \text{ and } n>2 \] If \(x[n]\) is obtained by convolving \(x_1[n]\) with \(x_2[n]\), which of the following equations is/are TRUE?

In the circuit given below, what should be the value of the resistance \(R\) for maximum dissipation of power in \(R\)?

In the circuit shown below, the input voltage is sinusoidal and \(2.5~\text{V}\) peak-to-peak. The capacitors are \(20~\mu\text{F}\) each. Assume ideal diodes (zero knee voltage) and \(R_L\) is very large (almost infinite). Which one of the following options is \emph{closest to the peak-to-peak voltage across \(R_L\), after a large number of cycles?}

In the circuit shown below, it is observed that the amplitude of the voltage across the resistor is the same as the amplitude of the source voltage. What is the angular frequency \(\omega_0\) (in rad/s)?

In the circuit below, the two DC voltage sources have voltages of value \(V_1\) and \(V_2\). The expression for the power dissipated in the \(60\,\text{k}\Omega\) resistor is proportional to ____________________.