GATE 2023 Biomedical Engineering Question Paper PDF is available here for download. IIT Kanpur conducted GATE 2023 Biomedical Engineering exam on February 5, 2023 in the Afternoon Session from 02:30 PM to 05:30 PM. Students have to answer 65 questions in GATE 2023 Biomedical Engineering Question Paper carrying a total weightage of 100 marks. 10 questions are from the General Aptitude section and 55 questions are from Engineering Mathematics and Core Discipline.
GATE 2023 Biomedical Engineering Question Paper Solution PDF
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“I cannot support this proposal. My ______ will not permit it.”
Courts : _____ : : Parliament : Legislature (By word meaning)
What is the smallest number with distinct digits whose digits add up to 45?
In a class of 100 students,
How many rectangles are present in the given figure?
Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.
Based only on the information provided above, which one of the following options can be logically inferred with certainty?
Which one of the following options represents the given graph?
Which one of the following options can be inferred from the given passage alone?
When I was a kid, I was partial to stories about other worlds and interplanetary travel. I used to imagine that I could just gaze off into space and be whisked to another planet.
[Excerpt from The Truth about Stories by T. King]
Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:
(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.(ii) Mix the samples within each set and test the mixed sample for covid.
(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.
(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.
Given this strategy, no more than _____ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.
A \(100 cm \times 32 cm\) rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions \(100 cm \times 1 cm\).
The total number of creases visible when the sheet is unfolded is _____.
What is the magnitude of the difference between the mean and the median of the dataset \(\{1,2,3,4,6,8\}\)?
For a Binomial random variable \(X\), \(\mathrm{E}(X)\) and \(\mathrm{Var}(X)\) are the expectation and variance, respectively. Which one of the following statements CANNOT be true?
is a \(2\times2\) matrix. Which one of the following statements is TRUE?
Which one of the following vectors is an eigenvector corresponding to the eigenvalue \(=1\) for the matrix 
?
For the function \(f(x,y)=e^{x}\cos(y)\), what is the value of \(\dfrac{\partial^{2}f}{\partial x\,\partial y}\) at \((x=0,y=\pi/2)\)?
For the circuit given below, choose the angular frequency \(\omega_0\) (in rad/s) at which the voltage across the capacitor has maximum amplitude?
A finite impulse response (FIR) filter has only two non-zero samples in its impulse response \(h[n]\), namely \(h[0]=h[1]=1\). The Discrete Time Fourier Transform (DTFT) of \(h[n]\) equals \(H(e^{j\omega})\), as a function of the normalized angular frequency \(\omega\). For the range \(|\omega|\leq \pi\), \(|H(e^{j\omega})|\) is equal to _________.
An 8 bit successive approximation Analog to Digital Converter (ADC) has a clock frequency of 1 MHz. Assume that the start conversion and end conversion signals occupy one clock cycle each. Among the following options, what is the maximum frequency that this ADC can sample without aliasing?
In the following circuit with an ideal operational amplifier, the capacitance of the parallel plate capacitor \(C\) is given by the expression \(C=\left(\dfrac{\varepsilon A}{x}\right)\), where \(\varepsilon\) is the dielectric constant of the medium between the capacitor plates, and \(A\) is the cross-sectional area. In the above relation, \(x\) is the separation between the two parallel plates, given by \(x=x_0+kt\), where \(t\) is time; \(x_0\) and \(k\) are positive non-zero constants. If the input voltage \(v_i\) is constant, then the output voltage \(v_0\) is given by _________.
Which one of the following techniques makes use of Korotkoff sounds?
The pulmonary artery and pulmonary vein ____________.
Which one of the following bridges CANNOT be used for measuring inductance?
A polychromatic beam of X-Rays has an energy spectrum as shown in Figure P below. Which of the following graphs (in the options A to D) depicts the energy spectrum after passing through a human body? In each figure, the horizontal axis represents Energy in keV and the vertical axis represents Relative X-ray Intensity.
- (A)
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- (B)
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- (C)
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- (D)
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\(M, L, T\) correspond to dimensions representing mass, length and time, respectively. What is the dimension of viscosity?
Choose the option that has the biomaterials arranged in order of decreasing tensile strength. (PMMA : poly-methyl-methacrylate)
A causal, discrete time system is described by the difference equation \[ y[n] = 0.5 \, y[n-1] + x[n], \quad for all n, \]
where \(y[n]\) denotes the output sequence and \(x[n]\) denotes the input sequence. Which of the following statements is/are TRUE?
Which of the following constituents is/are NOT normally found in serum obtained from human blood?
\(Q, R, S\) are Boolean variables and \(\oplus\) is the XOR operator. Select the CORRECT option(s).
In the human pancreas, which cell types secrete insulin and glucagon?
In the following circuit, the switch \(S\) is open for \(t<0\) and closed for \(t\ge 0\). What is the steady state voltage (in Volts) across the capacitor when the switch is closed? (Round off the answer to one decimal place.)
For a tissue with Young’s modulus of \(3.6\ kPa\) and Poisson’s ratio of \(0.2\), what is the value of its shear modulus (in kPa)? (Round off the answer to one decimal place.)
In the circuit shown below, the amplitudes of the voltage across the resistor and the capacitor are equal. What is the value of the angular frequency \(\omega_0\) (in rad/s)? (Round off the answer to one decimal place.)
A continuous time, band limited signal \(x(t)\) has its Fourier transform described by 
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.)
At time \(t\), the cardiac dipole is oriented at \(-45^\circ\) (minus forty five degrees) to the horizontal axis. The magnitude of the dipole is \(3\) mV. Assuming Einthoven frontal plane configuration, what is the magnitude (in mV) of the electrical signal in lead II? (Round off the answer to two decimal places.)
A 5 MHz ultrasound transducer is being used to measure the velocity of blood. When the transducer is placed at an angle of \(45^\circ\) to the direction of blood flow, a frequency shift of 200 Hz is observed in the echo. Assume that the velocity of sound is \(1500\ m/s\). What is the velocity (in cm/s) of the blood flow? (Round off the answer to one decimal place.)
The time-dependent growth of a bacterial population is governed by the equation \[ \frac{dx}{dt}=x\left(1-\frac{x}{200}\right), \]
where \(x\) is the population size at time \(t\). The initial population size is \(x_0=100\) at \(t=0\). As \(t\to\infty\), the population size of bacteria asymptotically approaches ____________.
A 20 mV DC signal has been superimposed with a 10 mV RMS band-limited Gaussian noise with a flat spectrum up to 5 kHz. If an integrating voltmeter is used to measure this DC signal, what is the minimum averaging time (in seconds) required to yield a 99% accurate result with 95% certainty?
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 \(60\,k\Omega\) resistor is proportional to __________.
The Laplace transform of \(x_{1}(t)=e^{-t}u(t)\) is \(X_{1}(s)\), where \(u(t)\) is the unit step function. The Laplace transform of \(x_{2}(t)=e^{t}u(-t)\) is \(X_{2}(s)\). Which one of the following statements is TRUE?
A circular disc of radius \(R\) (in cm) has a uniform absorption coefficient of \(1\ cm^{-1}\). Consider a single ray passing through the disc in the plane of the disc. The shortest distance from the center of the disc to the ray is \(t\) (in cm). If \(I_i\) is the intensity of the incident ray and \(I_o\) is the intensity of the transmitted ray, then \(\log\!\left(\dfrac{I_i}{I_o}\right)\) is given by __________.
The free induction decay (FID) in the MRI of an object can be approximated as \[ s(t)=\iint m(x,y)\,e^{-j2\pi\,(K_x(t)x+K_y(t)y)}\,dx\,dy, \]
where \(K_x(t)=\int_0^t G_x(\tau)\,d\tau\) and \(K_y(t)=\int_0^t G_y(\tau)\,d\tau\).
Here \(G_x\) and \(G_y\) are pulses of identical period and are in–phase. By changing the amplitude of the pulses, one can obtain the two–dimensional Fourier transform of the object _________.
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 a biomaterial, formation of hydrogen bonds on alcoholic groups will lead to a ____________________.
In the circuit shown below, the input voltage is sinusoidal and \(2.5~V\) peak-to-peak. The capacitors are \(20~\mu F\) each. Assume ideal diodes (zero knee voltage) and \(R_L\) is very large (almost infinite). Which one of the following options is closest to the peak-to-peak voltage across \(R_L\), after a large number of cycles?
An ultrasound plane wave of amplitude \(P_0\) hits the semi-infinite boundary of two media having acoustic impedances \(Z_1\) and \(Z_2\). The sum of the amplitudes of the reflected and the incident waves at the boundary is equal to _________.
In the circuit given below, what should be the value of the resistance \(R\) for maximum dissipation of power in \(R\)?
Two sequences \(x_1[n]\) and \(x_2[n]\) are described as follows:
\[ x_1[0] = x_2[0] = 1, \quad x_1[1] = x_2[2] = 2, \quad x_1[2] = x_2[1] = 1 \]
\[ x_1[n] = x_2[n] = 0 \quad for all n < 0 and n > 2 \]
If \(x[n]\) is obtained by convolving \(x_1[n]\) with \(x_2[n]\), which of the following equations is/are TRUE?
The function \( f(Z)=\dfrac{1}{Z-1} \) of a complex variable \(Z\) is integrated on a closed contour in an anti-clockwise direction. For which of the following contours, does this integral have a non-zero value?
The continuous time signal \(x(t)\) is described by
If \(y(t)\) represents \(x(t)\) convolved with itself, which of the following statements is/are TRUE?
Which of the following relations is/are CORRECT in terms of various lung volume measurements?
Assuming the operational amplifier in the circuit shown below to be ideal, which of the following properties hold(s) TRUE for the circuit?
A water insoluble polymeric biomaterial can become water soluble in vivo by which of the following mechanisms?
For the function \(f(x) = x^4 - x^2\), which of the following statements is/are TRUE?
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.)
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.)
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?
Calculate the reciprocal of the coefficient of \(z^3\) in the Taylor series expansion of the function \(f(z)=\sin(z)\) around \(z=0\). (Provide the answer as an integer.)
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 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 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.)
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 \(400~N\) 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 \((E_{in})\) is \(10\ V\). 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 \(V_{out}\) (in Volts) from the Wheatstone bridge? (Round off your answer to the nearest integer.)
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 \(g = 10\ m/s^2\) and assume that there is no air resistance. (Round off your answer to one decimal place.)
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