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Engineering Mathematics(10)Biomedical Engineering Core(45)General Aptitude(10)

Engineering Mathematics

10 Questions

GATE→2023→Engineering Mathematics→Probability and Statistics

Q1

MCQ[1 Mark]

What is the magnitude of the difference between the mean and the median of the dataset $\{1, 2, 3, 4, 6, 8\}$?

(A)

0

(B)

1

(C)

0.5

(D)

0.25

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q2

MCQ[1 Mark]

For a Binomial random variable $X$, $E(X)$ and $\text{Var}(X)$ are the expectation and variance, respectively. Which one of the following statements CANNOT be true?

(A)

$E(X) = 20$ and $\text{Var}(X) = 16$

(B)

$E(X) = 6$ and $\text{Var}(X) = 5.4$

(C)

$E(X) = 10$ and $\text{Var}(X) = 15$

(D)

$E(X) = 64$ and $\text{Var}(X) = 12.8$

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q3

MCQ[1 Mark]

$Q = \begin{bmatrix} 1 & -2 \\ 2 & 1 \end{bmatrix}$ is a $2 \times 2$ matrix. Which one of the following statements is TRUE?

(A)

$Q$ is equal to its transpose.

(B)

$Q$ is equal to its inverse.

(C)

$Q$ is of full rank.

(D)

$Q$ has linearly dependent columns.

Explanation

GATE→2023→Engineering Mathematics→Linear Algebra

Q4

MCQ[1 Mark]

Which one of the following vectors is an eigenvector corresponding to the eigenvalue $= 1$ for the matrix $A$? $$A = \begin{bmatrix} 1 & 1 & 0 \\ 1 & -1 & 0 \\ 1 & -1 & 1 \end{bmatrix}$$

(A)

$\begin{bmatrix} 1 & 0 & 1 \end{bmatrix}^T$

(B)

$\begin{bmatrix} 1 & 1 & 0 \end{bmatrix}^T$

(C)

$\begin{bmatrix} 0 & 1 & 0 \end{bmatrix}^T$

(D)

$\begin{bmatrix} 0 & 0 & 1 \end{bmatrix}^T$

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q5

MCQ[1 Mark]

For the function $f(x,y) = e^x \cos(y)$, what is the value of $\frac{\partial^2 f}{\partial x \partial y}$ at $(x = 0, y = \pi/2)$?

(A)

0

(B)

1

(C)

$-1$

(D)

$e^{\pi/2}$

Explanation

GATE→2023→Engineering Mathematics→Differential Equations

Q6

MCQ[2 Marks]

The time-dependent growth of a bacterial population is governed by the equation $$\frac{dx}{dt} = x\left(1 - \frac{x}{200}\right),$$\nwhere $x$ 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)

150

(B)

200

(C)

300

(D)

500

Explanation

GATE→2023→Engineering Mathematics→Probability and Statistics

Q7

MCQ[2 Marks]

A $20\text{ mV}$ DC signal has been superimposed with a $10\text{ mV}$ RMS band-limited Gaussian noise with a flat spectrum up to $5\text{ kHz}$. 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?

(A)

0.1

(B)

1.0

(C)

5.0

(D)

10.0

Explanation

GATE→2023→Engineering Mathematics→Analysis of Complex Variables

Q8

MSQ[2 Marks]

The function $f(Z) = \frac{1}{Z - 1}$ 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?

(A)

$|Z - 2| = 0.01$

(B)

$|Z - 1| = 0.1$

(C)

$|Z - 3| = 5$

(D)

$|Z| = 2$

Explanation

GATE→2023→Engineering Mathematics→Calculus

Q9

MSQ[2 Marks]

For the function $f(x) = x^4 - x^2$, which of the following statements is/are TRUE?

(A)

The function is symmetric about $x = 0$.

(B)

The minimum value of the function is $-0.5$.

(C)

The function has two minima.

(D)

The function is an odd function.

Explanation

GATE→2023→Engineering Mathematics→Analysis of Complex Variables

Q10

NAT[2 Marks]

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.)

Explanation

Biomedical Engineering Core

45 Questions

GATE→2023→Biomedical Engineering Core→Electrical Circuits

Q11

MCQ[1 Mark]

For the circuit given below, choose the angular frequency $\omega_0$ (in $\text{rad/s}$) at which the voltage across the capacitor has maximum amplitude?

(A)

1000

(B)

100

(C)

1

(D)

0

Explanation

GATE→2023→Biomedical Engineering Core→Signals and Systems

Q12

MCQ[1 Mark]

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 $|\omega| \le \pi$, $|H(e^{j\omega})|$ is equal to ________.

(A)

$2|\cos(\omega)|$

(B)

$2|\sin(\omega)|$

(C)

$2|\cos(\omega/2)|$

(D)

$2|\sin(\omega/2)|$

Explanation

GATE→2023→Biomedical Engineering Core→Analog and Digital Electronics

Q13

MCQ[1 Mark]

An $8\text{ bit}$ successive approximation Analog to Digital Converter (ADC) has a clock frequency of $1\text{ MHz}$. 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?

(A)

0.9 kHz

(B)

9.9 kHz

(C)

49.9 kHz

(D)

99.9 kHz

Explanation

GATE→2023→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q14

MCQ[1 Mark]

In the following circuit with an ideal operational amplifier, the capacitance of the parallel plate capacitor $C$ is given by the expression $C = \left(\frac{\epsilon A}{x}\right)$, where $\epsilon$ 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 $v_o$ is given by ________.

(A)

$\frac{R v_i C k}{x}$

(B)

$\frac{R v_i C}{kx}$

(C)

$\frac{v_i k}{R C x}$

(D)

$0$

Explanation

GATE→2023→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q15

MCQ[1 Mark]

Which one of the following techniques makes use of Korotkoff sounds?

(A)

Sphygmomanometry

(B)

Audiometry

(C)

Spirometry

(D)

Tonometry

Explanation

GATE→2023→Biomedical Engineering Core→Human Anatomy and Physiology

Q16

MCQ[1 Mark]

The pulmonary artery and pulmonary vein ________.

(A)

carry deoxygenated blood and oxygenated blood, respectively

(B)

carry oxygenated blood and deoxygenated blood, respectively

(C)

both carry oxygenated blood

(D)

both carry deoxygenated blood

Explanation

GATE→2023→Biomedical Engineering Core→Measurements and Control Systems

Q17

MCQ[1 Mark]

Which one of the following bridges CANNOT be used for measuring inductance?

(A)

Schering Bridge

(B)

Maxwell Wien Bridge

(C)

Hay Bridge

(D)

Series Owen Bridge

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q18

MCQ[1 Mark]

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)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2023→Biomedical Engineering Core→Biomechanics

Q19

MCQ[1 Mark]

$M, L$ and $T$ correspond to dimensions representing mass, length and time, respectively. What is the dimension of viscosity?

(A)

$M^1 L^{-2} T^{-1}$

(B)

$M^1 L^{-1} T^{-1}$

(C)

$M^1 L^{-1} T^1$

(D)

$M^1 L^{-2} T^{-2}$

Explanation

GATE→2023→Biomedical Engineering Core→Biomaterials

Q20

MCQ[1 Mark]

Choose the option that has the biomaterials arranged in order of decreasing tensile strength. (PMMA: poly-methyl-methacrylate)

(A)

Human compact bone > PMMA bone cement > Polymer foams > Graphite-epoxy

(B)

Human compact bone > Graphite-epoxy > PMMA bone cement > Polymer foams

(C)

Graphite-epoxy > Human compact bone > PMMA bone cement > Polymer foams

(D)

PMMA bone cement > Human compact bone > Polymer foams > Graphite-epoxy

Explanation

GATE→2023→Biomedical Engineering Core→Signals and Systems

Q21

MSQ[1 Mark]

A causal, discrete time system is described by the difference equation $$y[n] = 0.5\,y[n-1] + x[n] \quad \text{for all } n,$$\nwhere $y[n]$ denotes the output sequence and $x[n]$ denotes the input sequence. Which of the following statements is/are TRUE?

(A)

The system has an impulse response described by $0.5^n u[-n]$ where $u[n]$ is the unit step sequence.

(B)

The system is stable in the bounded input, bounded output sense.

(C)

The system has an infinite number of non-zero samples in its impulse response.

(D)

The system has a finite number of non-zero samples in its impulse response.

Explanation

GATE→2023→Biomedical Engineering Core→Human Anatomy and Physiology

Q22

MSQ[1 Mark]

Which of the following constituents is/are NOT normally found in serum obtained from human blood?

(A)

Platelets

(B)

Albumin

(C)

Glucose

(D)

Fibrinogen

Explanation

GATE→2023→Biomedical Engineering Core→Analog and Digital Electronics

Q23

MSQ[1 Mark]

$Q, R, S$ are Boolean variables and $\oplus$ is the XOR operator. Select the CORRECT option(s).

(A)

$(Q \oplus R) \oplus S = Q \oplus (R \oplus S)$

(B)

$(Q \oplus R) \oplus S = 0$ when any two of the Boolean variables ($Q, R, S$) are $0$ and the third variable is $1$

(C)

$(Q \oplus R) \oplus S = 1$ when $Q = R = S = 1$

(D)

$((Q \oplus R) \oplus (R \oplus S)) \oplus (Q \oplus S) = 1$

Explanation

GATE→2023→Biomedical Engineering Core→Human Anatomy and Physiology

Q24

MSQ[1 Mark]

In the human pancreas, which cell types secrete insulin and glucagon?

(A)

Alpha cells and delta cells, respectively

(B)

Beta cells and delta cells, respectively

(C)

Alpha cells and beta cells, respectively

(D)

Beta cells and alpha cells, respectively

Explanation

GATE→2023→Biomedical Engineering Core→Electrical Circuits

Q25

NAT[1 Mark]

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.)

Explanation

GATE→2023→Biomedical Engineering Core→Biomechanics

Q26

NAT[1 Mark]

For a tissue with Young's modulus of $3.6\text{ kPa}$ 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.)

Explanation

GATE→2023→Biomedical Engineering Core→Electrical Circuits

Q27

NAT[1 Mark]

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 $\text{rad/s}$)? (Round off the answer to one decimal place.)

Explanation

GATE→2023→Biomedical Engineering Core→Signals and Systems

Q28

NAT[1 Mark]

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

Explanation

GATE→2023→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q29

NAT[1 Mark]

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 $3\text{ mV}$. 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.)

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q30

NAT[1 Mark]

A $5\text{ MHz}$ 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 $200\text{ Hz}$ is observed in the echo. Assume that the velocity of sound is $1500\text{ m/s}$. What is the velocity (in $\text{cm/s}$) of the blood flow? (Round off the answer to one decimal place.)

Explanation

GATE→2023→Biomedical Engineering Core→Electrical Circuits

Q31

MCQ[2 Marks]

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 ________.

(A)

$(V_1 + V_2)^2$

(B)

$(3V_1 + V_2)^2$

(C)

$(2V_1 + V_2)^2$

(D)

$(V_1 + 2V_2)^2$

Explanation

GATE→2023→Biomedical Engineering Core→Signals and Systems

Q32

MCQ[2 Marks]

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)

The region of convergence of $X_1(s)$ is $\text{Re}(s) > 0$.

(B)

The region of convergence of $X_2(s)$ is confined to the left half-plane of $s$.

(C)

The region of convergence of $X_1(s)$ is confined to the right half-plane of $s$.

(D)

The imaginary axis in the $s$-plane is included in both the region of convergence of $X_1(s)$ and the region of convergence of $X_2(s)$.

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q33

MCQ[2 Marks]

A circular disc of radius $R$ (in cm) has a uniform absorption coefficient of $1\text{ cm}^{-1}$. 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 $\log\left(\frac{I_i}{I_o}\right)$ is given by ________.

(A)

$2\sqrt{R^2 - t^2}$

(B)

$2R$

(C)

$1$

(D)

$2\sqrt{R - t}$

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q34

MCQ[2 Marks]

The free induction decay (FID) in the MRI of an object can be approximated as $$s(t) = \iint m(x,y)e^{-j2\pi(K_x(t)x + K_y(t)y)}dx\,dy,$$\nwhere $K_x(t) = \int_0^t G_x(\tau)d\tau$ 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 ________.

(A)

over radial lines in $(K_x, K_y)$ space

(B)

over a parabolic contour in $(K_x, K_y)$ space

(C)

along $K_y$ only

(D)

along $K_x$ only

Explanation

GATE→2023→Biomedical Engineering Core→Electrical Circuits

Q35

MCQ[2 Marks]

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 $\text{rad/s}$)?

(A)

$10^4$

(B)

$10^3$

(C)

$10^3\pi$

(D)

$10^4\pi$

Explanation

GATE→2023→Biomedical Engineering Core→Biomaterials

Q36

MCQ[2 Marks]

In a biomaterial, formation of hydrogen bonds on alcoholic groups will lead to a ________.

(A)

shift in the infra-red peak around $1700\text{ cm}^{-1}$

(B)

shift in the infra-red peak around $2800\text{ cm}^{-1}$

(C)

broadening of the infra-red peak around $3500\text{ cm}^{-1}$

(D)

disappearance of the infra-red peak around $1700\text{ cm}^{-1}$

Explanation

GATE→2023→Biomedical Engineering Core→Analog and Digital Electronics

Q37

MCQ[2 Marks]

In the circuit shown below, the input voltage is sinusoidal and $2.5\text{ V}$ peak to peak. The capacitors are $20\text{ }\mu\text{F}$ each. Assume that the knee voltage of the diodes is $0\text{ V}$ 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?

(A)

1.25 V

(B)

2.50 V

(C)

5.00 V

(D)

10.0 V

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q38

MCQ[2 Marks]

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 ________.

(A)

$\frac{2 P_0 Z_2}{(Z_1 + Z_2)}$

(B)

$\frac{P_0 (Z_2 - Z_1)}{(Z_1 + Z_2)}$

(C)

$\frac{P_0 Z_2}{Z_1}$

(D)

$\frac{P_0 Z_1}{(Z_1 + Z_2)}$

Explanation

GATE→2023→Biomedical Engineering Core→Electrical Circuits

Q39

MCQ[2 Marks]

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

(A)

$1.2\text{ k}\Omega$

(B)

$2.2\text{ k}\Omega$

(C)

$3.2\text{ k}\Omega$

(D)

$4.2\text{ k}\Omega$

Explanation

GATE→2023→Biomedical Engineering Core→Signals and Systems

Q40

MSQ[2 Marks]

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

(A)

$x[2] = x[3]$

(B)

$x[1] = 2$

(C)

$x[4] = 3$

(D)

$x[2] = 5$

Explanation

GATE→2023→Biomedical Engineering Core→Signals and Systems

Q41

MSQ[2 Marks]

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

(A)

$y(t) = 0$ for all $t < 0$

(B)

$y(t) = 0$ for all $t > 1$

(C)

$y(t) = 0$ for all $t > 3$

(D)

$\int_{0.1}^{0.75} \frac{dy(t)}{dt} dt \neq 0$

Explanation

GATE→2023→Biomedical Engineering Core→Human Anatomy and Physiology

Q42

MSQ[2 Marks]

Which of the following relations is/are CORRECT in terms of various lung volume measurements?

(A)

Vital capacity minus expiratory reserve volume equals inspiratory capacity.

(B)

Vital capacity plus expiratory reserve volume equals inspiratory capacity.

(C)

Total lung capacity equals the sum of inspiratory capacity and functional residual capacity.

(D)

Functional residual capacity is the difference between expiratory reserve volume and residual volume.

Explanation

GATE→2023→Biomedical Engineering Core→Analog and Digital Electronics

Q43

MSQ[2 Marks]

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

(A)

It acts as a voltage follower.

(B)

It is bistable.

(C)

It is astable.

(D)

The output voltage is at saturation.

Explanation

GATE→2023→Biomedical Engineering Core→Biomaterials

Q44

MSQ[2 Marks]

A water insoluble polymeric biomaterial can become water soluble in vivo by which of the following mechanisms?

(A)

Cleavage of crosslinks between water soluble polymer chains

(B)

Cleavage of side chains leading to formation of non-polar groups

(C)

Cleavage of backbone linkages between polymer repeat units leading to the formation of polar groups

(D)

Enzymatic degradation of crosslinks between water soluble polymer chains

Explanation

GATE→2023→Biomedical Engineering Core→Measurements and Control Systems

Q45

NAT[2 Marks]

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

Explanation

GATE→2023→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q46

NAT[2 Marks]

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

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q47

NAT[2 Marks]

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

Explanation

GATE→2023→Biomedical Engineering Core→Medical Imaging Systems

Q48

NAT[2 Marks]

A two-dimensional square plate ($20\text{ mm}$ sides) contains a homogeneous circular inclusion of $5\text{ mm}$ diameter in it. A parallel beam of X-rays (beam width $30\text{ mm}$) 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?

Explanation

GATE→2023→Biomedical Engineering Core→Biomaterials

Q49

NAT[2 Marks]

In a cell viability experiment, $10,000$ cells were cultured in the absence and presence of a compound Q for $24\text{ h}$. The absorbance of a dye associated with cellular metabolic activity was measured at a wavelength of $570\text{ nm}$ at $24\text{ h}$. The measured absorbances were $0.8\text{ a.u.}$ in the absence of the compound Q, and $0.5\text{ a.u.}$ in its presence. If the dye gives an absorbance (at $570\text{ nm}$) of $0.1\text{ a.u.}$ 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.)

Explanation

GATE→2023→Biomedical Engineering Core→Human Anatomy and Physiology

Q50

NAT[2 Marks]

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 $12\text{ breaths per minute}$. Each breath is $500\text{ mL}$ in volume. The cardiac output is $5\text{ liters per minute}$. Assuming ideal, healthy lung and cardiac conditions, what is the change in percentage of oxygen in blood over $1\text{ minute}$? (Round off the answer to one decimal place.)

Explanation

GATE→2023→Biomedical Engineering Core→Human Anatomy and Physiology

Q51

NAT[2 Marks]

The intracellular and extracellular concentrations (in mM) of three important ions are given in the table below. The relative permeability of the cell membrane to each ion is provided. Universal gas constant is $8.31\text{ J/(mol}\cdot\text{K)}$ and Faraday's constant is $96500\text{ C/mol}$. What is the absolute value of the resting membrane potential (in mV) across the cell membrane at $27^\circ\text{C}$? (Round off the answer to one decimal place.) | Ion | Extracellular concentration (mM) | Intracellular concentration (mM) | Relative permeability | | :--- | :---: | :---: | :---: | | Sodium | 140 | 10 | 0.02 | | Potassium | 3 | 140 | 1.00 | | Chloride | 90 | 3 | 0.38 |

Explanation

GATE→2023→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q52

NAT[2 Marks]

A metallic strain gauge with negligible piezoresistive effect is subjected to a strain of $50 \times 10^{-6}$. For the metal, Young's Modulus $= 80\text{ GPa}$ and Poisson's Ratio $= 0.42$. What is the change in resistance (in $\text{m}\Omega$), if the unstrained resistance of the strain gauge is $200\text{ }\Omega$? (Round off the answer to one decimal place.)

Explanation

GATE→2023→Biomedical Engineering Core→Biomechanics

Q53

NAT[2 Marks]

Consider the total hip joint prosthesis as shown in the figure. The geometric parameters of the prosthesis are such that $L_1 = 40\text{ mm}$, $L_2 = 60\text{ mm}$, $\theta_1 = 45^\circ$, $\theta_2 = 90^\circ$. 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 $\text{N}\cdot\text{m}$) about point C. (Round off the answer to one decimal place.)

Explanation

GATE→2023→Biomedical Engineering Core→Measurements and Control Systems

Q54

NAT[2 Marks]

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 $10\text{ Volts}$. If all the resistors have a resistance of $200\text{ }\Omega$ in the absence of any force, and each resistance changes by $20\text{ }\Omega$ 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.)

Explanation

GATE→2023→Biomedical Engineering Core→Biomechanics

Q55

NAT[2 Marks]

A stone is thrown from an elevation of $2\text{ m}$ above ground level, at an angle of $30^\circ$ to the horizontal axis. If the stone hits the ground at a horizontal distance of $6\text{ m}$ from the point of release, at what speed (in $\text{m/s}$) 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.)

Explanation

General Aptitude

10 Questions

GATE→2023→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

"I cannot support this proposal. My ________ will not permit it."

(A)

conscious

(B)

consensus

(C)

conscience

(D)

consent

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q57

MCQ[1 Mark]

Courts : ________ :: Parliament : Legislature (By word meaning)

(A)

Judiciary

(B)

Executive

(C)

Governmental

(D)

Legal

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

What is the smallest number with distinct digits whose digits add up to $45$?

(A)

123555789

(B)

123457869

(C)

123456789

(D)

99999

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

In a class of $100$ students, (i) there are $30$ students who neither like romantic movies nor comedy movies, (ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and (iii) the number of students who like both romantic movies and comedy movies is $20$. How many students in the class like romantic movies?

(A)

40

(B)

20

(C)

60

(D)

30

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

How many rectangles are present in the given figure?

(A)

8

(B)

9

(C)

10

(D)

12

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

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?

(A)

All creatures with claws are animals.

(B)

Some creatures with claws are non-ferocious.

(C)

Some non-ferocious creatures have claws.

(D)

Some ferocious creatures are creatures with claws.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

Which one of the following options represents the given graph?

(A)

$f(x) = x^2 2^{-|x|}$

(B)

$f(x) = x\,2^{-|x|}$

(C)

$f(x) = |x| 2^{-x}$

(D)

$f(x) = x\,2^{-x}$

Explanation

GATE→2023→General Aptitude→Verbal Ability

Q63

MCQ[2 Marks]

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]*

(A)

It is a child's description of what he or she likes.

(B)

It is an adult's memory of what he or she liked as a child.

(C)

The child in the passage read stories about interplanetary travel only in parts.

(D)

It teaches us that stories are good for children.

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

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)

700

(B)

600

(C)

800

(D)

1000

Explanation

GATE→2023→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

A $100\text{ cm} \times 32\text{ cm}$ 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 $100\text{ cm} \times 1\text{ cm}$. The total number of creases visible when the sheet is unfolded is ________.

(A)

32

(B)

5

(C)

31

(D)

63

Explanation