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Engineering Mathematics(9)Biomedical Engineering Core(46)General Aptitude(10)

Engineering Mathematics

9 Questions

GATE→2024→Engineering Mathematics→Analysis of Complex Variables

Q1

MCQ[1 Mark]

What is the value of the following complex line integral counter-clockwise? $$\oint_{|z|=3} \frac{8}{z(z-2)(z-4)} dz$$

(A)

$+j2\pi$

(B)

$-j2\pi$

(C)

$-j10\pi$

(D)

$+j10\pi$

Explanation

GATE→2024→Engineering Mathematics→Numerical Methods

Q2

MCQ[1 Mark]

To solve the equation $x = 2\cos x$ using Newton-Raphson's method, which one of the following iterations should be used?

(A)

$x_{n+1} = x_n - \frac{x_n - 2\cos x_n}{1 + 2\sin x_n}$

(B)

$x_{n+1} = x_n + \frac{x_n - 2\cos x_n}{1 + 2\sin x_n}$

(C)

$x_{n+1} = x_n + \frac{1 + 2\sin x_n}{x_n - 2\cos x_n}$

(D)

$x_{n+1} = x_n - \frac{1 + 2\sin x_n}{x_n - 2\cos x_n}$

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q3

NAT[1 Mark]

A group of four people were residing together when a new virus was detected. If the probability of each person being infected is $0.1$, then the probability that at least two of them are infected is ________. Give your answer rounded off to 3 decimal places.

Explanation

GATE→2024→Engineering Mathematics→Probability and Statistics

Q4

NAT[1 Mark]

A random noise signal with Gaussian distribution has a mean of zero and a standard deviation of $1\text{ mV}$. The probability that an instantaneous measurement of this signal is greater than $2\text{ mV}$ or lesser than $-2\text{ mV}$ is ________. Give your answer as a percentage rounded off to the nearest integer.

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q5

NAT[1 Mark]

The trigonometric Fourier series expansion of the periodic function in the figure has coefficients $\{a_n\}$ and $\{b_n\}$ for cosine and sine terms, respectively. The value of $a_1 / a_3$ is ________. Give your answer rounded off to 1 decimal place.

Explanation

GATE→2024→Engineering Mathematics→Linear Algebra

Q6

MCQ[2 Marks]

If $A = \begin{pmatrix} 1 & -1 \\ 2 & -2 \end{pmatrix}$, the eigenvalues of $A$ are

(A)

-1 and 0.

(B)

-1 and +1.

(C)

-1 and -1.

(D)

+1 and 0.

Explanation

GATE→2024→Engineering Mathematics→Differential Equations

Q7

MCQ[2 Marks]

Consider a system of the following two partial differential equations: $$\frac{\partial \alpha}{\partial x} = -2\frac{\partial \beta}{\partial t}$$ $$\frac{\partial \beta}{\partial x} = -2\frac{\partial \alpha}{\partial t}$$ Which one of the following choices is a possible solution for the system?

(A)

$\alpha(t,x) = (x - t)^2 + (x + t)^2$ and $\beta(t,x) = (x - t)^2 - (x + t)^2$.

(B)

$\alpha(t,x) = (x - 2t)^2 + (x + 2t)^2$ and $\beta(t,x) = (x - 2t)^2 - (x + 2t)^2$.

(C)

$\alpha(t,x) = \left(x - \frac{t}{2}\right)^2 + \left(x + \frac{t}{2}\right)^2$ and $\beta(t,x) = \left(x - \frac{t}{2}\right)^2 - \left(x + \frac{t}{2}\right)^2$.

(D)

$\alpha(t,x) = \left(x - \frac{t}{2}\right)^2 + 2\left(x + \frac{t}{2}\right)^2$ and $\beta(t,x) = 2\left(x - \frac{t}{2}\right)^2 - \left(x + \frac{t}{2}\right)^2$.

Explanation

GATE→2024→Engineering Mathematics→Analysis of Complex Variables

Q8

MCQ[2 Marks]

What is the value of the following integral using the residue integration method? $$\int_{-\infty}^{\infty} \frac{dx}{1 + x^4}$$

(A)

$\frac{\pi}{\sqrt{2}}$

(B)

$\frac{\pi}{2\sqrt{2}}$

(C)

$\frac{\pi}{4}$

(D)

$\frac{\pi}{2}$

Explanation

GATE→2024→Engineering Mathematics→Calculus

Q9

NAT[2 Marks]

For $\vec{F} = (x + y)\hat{i} + (x + y)\hat{j}$, the value of $\oint \vec{F} \cdot d\vec{r}$ along the path shown in the figure is ________. Give your answer as an integer.

Explanation

Biomedical Engineering Core

46 Questions

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q10

MCQ[1 Mark]

During the repolarization phase of a neuron, the cell is brought back to the resting potential by the action of a Sodium-Potassium pump. Which one of the following statements is TRUE for the active transport of $\text{Na}^+$ and $\text{K}^+$ ions through the cell membrane?

(A)

For every $3\text{ Na}^+$ transported out of the cell $2\text{ K}^+$ is transported into the cell.

(B)

For every $3\text{ Na}^+$ transported into the cell $2\text{ K}^+$ is transported out of the cell.

(C)

For every $2\text{ Na}^+$ transported out of the cell $3\text{ K}^+$ is transported into the cell.

(D)

The ratio of $\text{Na}^+$ and $\text{K}^+$ transport is always equal to one.

Explanation

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q11

MCQ[1 Mark]

The cardiac rhythm in a healthy human heart originates from

(A)

Sinu-atrial node (SA)

(B)

Atrio-ventricular node (AV)

(C)

Bundle of His

(D)

Right atria

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q12

MCQ[1 Mark]

Which one of the following events is NOT typically encountered in diagnostic X-ray projection radiography?

(A)

Pair production

(B)

Photoelectric absorption

(C)

Compton scattering

(D)

Characteristic radiation

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q13

MCQ[1 Mark]

Which of the following statements is TRUE for a PET imaging system?

(A)

Two coincident photons of 511 keV energy are detected $180^\circ$ apart.

(B)

Photons of 51.1 keV energy are detected $360^\circ$ around the body.

(C)

Photons of energy 511 keV are detected $360^\circ$ around the body.

(D)

Coincident photons with 51.1 keV energy are detected $180^\circ$ apart.

Explanation

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q14

MCQ[1 Mark]

Consider the following layers: subcutaneous fat, viable epidermis, stratum corneum, and dermis. Which one of the following represents the correct sequence of the layers from skin surface to within?

(A)

Dermis, subcutaneous fat, viable epidermis, stratum corneum

(B)

Dermis, viable epidermis, subcutaneous fat, stratum corneum

(C)

Stratum corneum, viable epidermis, dermis, subcutaneous fat

(D)

Viable epidermis, stratum corneum, dermis, subcutaneous fat

Explanation

GATE→2024→Biomedical Engineering Core→Biomaterials

Q15

MCQ[1 Mark]

Bioglass 45S5 has a composition of

(A)

45 wt% $\text{SiO}_2$ and 5:1 molar ratio of Calcium to Phosphorus.

(B)

45 wt% Hydroxyapatite and 5 wt% $\text{SiO}_2$.

(C)

45 wt% Hydroxyapatite and 5:1 molar ratio of $\text{CaO}$ and $\text{Ca}_3(\text{PO}_4)_2$.

(D)

45 wt% $\text{SiO}_2$ and 5 wt% Hydroxyapatite.

Explanation

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q16

MCQ[1 Mark]

Macrophages that are resident in the liver are

(A)

Histiocyte cells

(B)

Langerhans cells

(C)

Kupffer cells

(D)

Fibroblast cells

Explanation

GATE→2024→Biomedical Engineering Core→Biomaterials

Q17

MCQ[1 Mark]

Which one of the following drug release kinetic curves will be ideal for developing an implantable slow-release drug delivery device?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→Biomedical Engineering Core→Analog and Digital Electronics

Q18

MCQ[1 Mark]

The circuit shown in the figure functions as which one of the following digital circuit blocks?

(A)

Negative level triggered D-latch

(B)

Positive level triggered D-latch

(C)

Negative edge triggered D-flip-flop

(D)

Positive edge triggered D-flip-flop

Explanation

GATE→2024→Biomedical Engineering Core→Signals and Systems

Q19

MCQ[1 Mark]

The Fourier transform of $e^{-2|t|}$ is

(A)

$\frac{4}{4 - \omega^2}$

(B)

$\frac{4}{4 + \omega^2}$

(C)

$\frac{2}{2 + \omega}$

(D)

$\frac{2}{2 - \omega}$

Explanation

GATE→2024→Biomedical Engineering Core→Electrical Circuits

Q20

MCQ[1 Mark]

The Bode plot of a $2^{\text{nd}}$ order low pass filter is shown in the figure below. What is the frequency at which the attenuation is $80\text{ dB}$?

(A)

10 kHz

(B)

10 MHz

(C)

100 kHz

(D)

100 MHz

Explanation

GATE→2024→Biomedical Engineering Core→Signals and Systems

Q21

MCQ[1 Mark]

The input $x(t)$ and output $y(t)$ of a linear time invariant system are related as follows: $$y(t) + \frac{dy(t)}{dt} + 0.5\frac{d^2y(t)}{dt^2} = x(t) + 0.1\frac{dx(t)}{dt}$$ What is the Laplace transform of the impulse response of the system?

(A)

$\frac{0.5s^2 + s + 1}{0.1s + 1}$

(B)

$\frac{0.1s + 1}{0.5s^2 + s + 1}$

(C)

$\frac{0.1s + s^2}{s^2 + s + 0.5}$

(D)

$\frac{s^2 + s + 0.5}{0.1s^2 + s}$

Explanation

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q22

MCQ[1 Mark]

Match the different chambers/locations of a healthy human heart in Column-1 to the ranges of diastolic pressures in Column-2. | Column-1 | Column-2 | | :--- | :--- | | (P) Arterial | (I) $2\text{--}6\text{ mm Hg}$ | | (Q) Pulmonary artery | (II) $8\text{--}12\text{ mm Hg}$ | | (R) Right ventricle | (III) $60\text{--}80\text{ mm Hg}$ |

(A)

(P) - (II), (Q) - (III), (R) - (I)

(B)

(P) - (II), (Q) - (I), (R) - (III)

(C)

(P) - (III), (Q) - (II), (R) - (I)

(D)

(P) - (III), (Q) - (I), (R) - (II)

Explanation

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q23

MSQ[1 Mark]

Which of the following is/are NOT TRUE about photoreceptor cells in a healthy human retina?

(A)

The distribution of rod and cone cells is uniform all over the retina.

(B)

The number of rods are higher than the number of cones in the retina.

(C)

Rods contain photopsin pigment.

(D)

Cones are responsible for colour vision in bright light.

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q24

MSQ[1 Mark]

A monochromatic beam of $\gamma$-ray photons is incident on a homogenous tissue. Which of the following relationships hold(s) TRUE for the half-value layer thickness?

(A)

The first half-value layer is thicker than the second half-value layer.

(B)

The second half-value layer is thicker than the first half-value layer.

(C)

All the half-value layers have equal thickness.

(D)

The ratio of thickness of the first and second half-value layers change based on the intensity of the incident beam.

Explanation

GATE→2024→Biomedical Engineering Core→Biomechanics

Q25

NAT[1 Mark]

A cylindrical engineered tissue was developed with a diameter of $2\text{ cm}$, height of $3\text{ cm}$ and Young's modulus of $20\text{ MPa}$. If an axial tensile force of $10\text{ N}$ is applied, the percentage change in the height of the tissue is ________ $\%$. Give your answer rounded off to 2 decimal places.

Explanation

GATE→2024→Biomedical Engineering Core→Measurements and Control Systems

Q26

NAT[1 Mark]

The measured current through a device is $5\text{ A}$, the voltage measured across the device is $20\text{ V}$. The ammeter and the voltmeter used for these measurements have a measurement uncertainty of $1\%$ each. The maximum error in estimation of resistance is ________ $\text{m}\Omega$. Give your answer rounded to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q27

NAT[1 Mark]

The Larmor frequency of a $\text{Na}$ nucleus when placed in a magnetic field strength of $3\text{ T}$ is ________. (The gyromagnetic ratio of $\text{Na}$ is given as $\gamma = 11.26\text{ MHz/T}$.) Give your answer in MHz rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q28

NAT[1 Mark]

A Doppler ultrasound transducer operating at $5\text{ MHz}$ gave maximum output frequency shift of $3\text{ kHz}$. The velocity of sound in blood is $1500\text{ m/s}$. If the probe was held at an angle of $45^\circ$ to the direction of blood flow, the maximum velocity of blood flow through the artery is ________ $\text{m/s}$. (Give your answer rounded off to two decimal places.)

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q29

NAT[1 Mark]

The wavelength of the peak emission from a human body at a temperature of $37^\circ\text{C}$ due to black-body radiation is ________ $\mu\text{m}$. The value of Wien's displacement constant is $2.898 \times 10^{-3}\text{ m K}$. (Give your answer rounded off to 2 decimal places.)

Explanation

GATE→2024→Biomedical Engineering Core→Human Anatomy and Physiology

Q30

MCQ[2 Marks]

The end-diastolic ventricular volume is found to be $125\text{ mL}$ and the end-systolic ventricular volume is found to be $50\text{ mL}$. If the heart rate is $65\text{ beats/minute}$, what is the cardiac output in liters per minute? (Rounded off to 2 decimal places.)

(A)

3.25

(B)

4.88

(C)

5.20

(D)

3.00

Explanation

GATE→2024→Biomedical Engineering Core→Analog and Digital Electronics

Q31

MCQ[2 Marks]

Which of the following waveforms represents the output $V_o$ of the circuit given below? The Zener diode used has a Zener breakdown voltage of $1\text{ V}$ and can be assumed ideal while in forward bias.

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q32

MCQ[2 Marks]

In magnetic resonance imaging (MRI), pulse repetition time ($TR$), time to echo ($TE$), $T_1$ relaxation time, $T_2$ relaxation time are some of the important pulse sequence design parameters. Which one of the following specifications is used for proton density weighted imaging?

(A)

$TR \gg T_1, TE \ll T_2$

(B)

$TR \gg T_1, TE \gg T_2$

(C)

$TR \ll T_1, TE \ll T_2$

(D)

$TR \ll T_1, TE \gg T_2$

Explanation

GATE→2024→Biomedical Engineering Core→Biomaterials

Q33

MCQ[2 Marks]

An orthopaedic implant when monitored over 6 months showed the following normalized curves for polymer molecular weight (MW), mass of implant and mechanical strength. Among the choices, what is the most probable reason for the observed changes?

(A)

Bulk erosion

(B)

Surface erosion

(C)

Bulk initially followed by surface erosion

(D)

No erosion but mechanical breakage due to injury

Explanation

GATE→2024→Biomedical Engineering Core→Biomaterials

Q34

MCQ[2 Marks]

In an attempt to integrate engineered tissue with native tissue, three samples of engineered tissue, X, Y, Z, with identical material properties, were co-cultured adjacent to three different native tissues (bone, cartilage and liver). The adhesive strengths of X, Y, Z were observed after 8 weeks as follows. Adhesive strength for $\text{X} = 150\text{ kPa}$, $\text{Y} = 250\text{ kPa}$, $\text{Z} = 350\text{ kPa}$. Match the native tissue that were used to co-culture X, Y and Z from the following. * **I:** Liver Tissue * **II:** Articular Cartilage * **III:** Devitalized Bone

(A)

X with I, Y with II and Z with III

(B)

X with II, Y with III and Z with I

(C)

X with I, Y with III and Z with II

(D)

X with III, Y with II and Z with I

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q35

MCQ[2 Marks]

In a catheter-sensor system to measure blood pressure ($P$) as shown in the below figure, the liquid resistance ($R_L$) of the catheter is due to friction between shearing molecules flowing through the catheter. Which of the following is TRUE for $R_L$ if only the radius of the catheter is doubled? Assume that the pressure difference across the catheter segment is fixed.

(A)

$R_L$ will decrease by 16 times

(B)

$R_L$ will decrease by 8 times

(C)

$R_L$ will decrease by 4 times

(D)

$R_L$ will decrease by 2 times

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q36

MCQ[2 Marks]

A neurologist needs to observe the alpha wave in EEG recordings of a patient. The system block diagram with ideal filter blocks is shown below. Which one of the following design choices is correct?

(A)

$f_h = 8\text{ Hz}, f_l = 12\text{ Hz}, f_s = 12\text{ Hz}$

(B)

$f_h = 4\text{ Hz}, f_l = 6\text{ Hz}, f_s = 24\text{ Hz}$

(C)

$f_h = 6\text{ Hz}, f_l = 4\text{ Hz}, f_s = 12\text{ Hz}$

(D)

$f_h = 8\text{ Hz}, f_l = 12\text{ Hz}, f_s = 48\text{ Hz}$

Explanation

GATE→2024→Biomedical Engineering Core→Electrical Circuits

Q37

MCQ[2 Marks]

In the circuit below, what is the value of $I_L$ to transfer the maximum power to load?

(A)

3 A

(B)

6 A

(C)

4 A

(D)

2 A

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q38

MCQ[2 Marks]

A mechanical ventilator operating in volume controlled mode is set to deliver $600\text{ mL}$ of tidal volume (TV) with a flow rate of $40\text{ L/min}$. The frequency of breathing is set at $15\text{ breaths per minute}$. If the flow rate is doubled which one of the following will happen?

(A)

The inspiratory time will increase.

(B)

The expiratory time will increase.

(C)

The tidal volume will increase.

(D)

The frequency of breathing will decrease.

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q39

MSQ[2 Marks]

The X-ray attenuation coefficients as a function of photon energy for three materials are shown in the figure below. A tissue phantom containing these three materials is imaged at two different X-ray photon energies of $50\text{ keV}$ and $150\text{ keV}$. When the developed X-ray film is viewed, which of the following statements is/are TRUE?

(A)

Bone will appear relatively brighter than DCA in 50 keV.

(B)

DCA will appear relatively brighter than bone in 50 keV.

(C)

Bone will appear relatively brighter than DCA in 150 keV.

(D)

DCA will appear relatively brighter than bone in 150 keV.

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q40

MSQ[2 Marks]

Which of the following is/are TRUE for a surface electromyography (sEMG) signal of a muscle experiencing fatigue?

(A)

The median frequency of power spectral density of sEMG will decrease.

(B)

The median frequency of power spectral density of sEMG will increase.

(C)

The root mean square (RMS) value of sEMG will increase.

(D)

The root mean square (RMS) value of sEMG will decrease.

Explanation

GATE→2024→Biomedical Engineering Core→Biomechanics

Q41

NAT[2 Marks]

The approximate total cross sectional areas of various types of blood vessels are given below. It was estimated that the velocity of blood in the aorta is $30\text{ cm s}^{-1}$. The time it will take for the blood to travel through a capillary of length $0.5\text{ mm}$ is ________ seconds. Give your answer rounded off to two decimal places. | Vessel Type | Approximate total cross sectional area ($\text{cm}^2$) | | :---: | :---: | | Aorta | 4.5 | | Artery | 20 | | Arteriole | 400 | | Capillary | 4500 | | Venule | 40 | | Vein | 15 |

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q42

NAT[2 Marks]

A DNA extract solution with a concentration of $15\text{ ng/}\mu\text{L}$ placed in a micro-cuvette of sample thickness $0.5\text{ mm}$ gave an absorbance of $0.24$ at a wavelength of $260\text{ nm}$ in a spectrophotometer. After further concentration, the sample was found to give an absorbance of $0.38$ at the same wavelength under identical conditions. The final concentration of the sample is ________ $\text{ng/}\mu\text{L}$. (Give your answer rounded off to 2 decimal places.)

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q43

NAT[2 Marks]

An X-ray beam of initial intensity $I_0$ of $70\text{ keV}$ imaging the chest is assumed to undergo attenuation through the muscle tissue for a thickness of $16\text{ cm}$ and further through the bone tissue for a thickness of $4\text{ cm}$. The half value layer (HVL) thicknesses for the muscle and bone are $3.5\text{ cm}$ and $1.8\text{ cm}$, respectively. The percentage of X-ray intensity transmitted through the body is ________. Give your answer rounded off to 2 decimal places.

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q44

NAT[2 Marks]

A person standing one meter away from a $4000\text{ curie}$ radioactive source receives a lethal dose of radiation in about $5\text{ minutes}$. At $3\text{ meters}$ away from the same source, the time in which he will receive the same lethal dose is ________ minutes. Give your answer rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Medical Imaging Systems

Q45

NAT[2 Marks]

If a circular ultrasound transducer of radius $a = 8\text{ mm}$ operating at a central frequency of $1\text{ MHz}$ has a pressure beam pattern in a medium as given below: $$P(r, 0) \propto \sin\left(\frac{ka^2}{4r}\right)$$ Here, $k$ is the wave number, $r$ is the axial distance from the transducer center. The speed of sound in the medium is $1600\text{ m s}^{-1}$. The reduction in intensity between $r = 8\text{ cm}$ and $r = 16\text{ cm}$ is ________ $\text{dB}$. Give your answer as a positive quantity rounded off to two decimal places.

Explanation

GATE→2024→Biomedical Engineering Core→Electrical Circuits

Q46

NAT[2 Marks]

The source in the figure is a current source and the circuit is in steady state. At $t = 1.57\text{ seconds}$, the value of $v$ in the circuit given below is ________ volts. Give your answer rounded off to two decimal places.

Explanation

GATE→2024→Biomedical Engineering Core→Electrical Circuits

Q47

NAT[2 Marks]

The equivalent impedance, $Z_{AB}$, in the circuit given below is ________ $\Omega$. Give your answer rounded off to one decimal place.

Explanation

GATE→2024→Biomedical Engineering Core→Signals and Systems

Q48

NAT[2 Marks]

The bandwidth of ECG signal ranges from $0.5\text{ Hz}$ to $100\text{ Hz}$. If a single ADC is used to digitize data from $8$ ECG channels then the minimum ADC sampling rate is ________ $\text{Hz}$. Give your answer rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Signals and Systems

Q49

NAT[2 Marks]

If $x[n] = u[n] - u[n-5]$, and $h[n] = \delta[n] - \delta[n-1]$ and $y[n] = x[n] * h[n]$, then the value of $\sum_{n=-\infty}^{\infty} y[n]$ is ________. Give your answer rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Electrical Circuits

Q50

NAT[2 Marks]

In the figure below, the diode is ideal. The current reading shown in the ammeter is ________ $\text{A}$. Give your answer rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Electrical Circuits

Q51

NAT[2 Marks]

In the figure below, the Fourier series of $v(t)$, in volts, is given as: $$v(t) = v_0 + 2\cos(\omega_0 t) + 5\cos(3\omega_0 t) + \cos(5\omega_0 t)$$ The capacitor is a short circuit for all AC signals. The power absorbed by the $1\text{ }\Omega$ resistor is ________ $\text{W}$. Give your answer rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Biomechanics

Q52

NAT[2 Marks]

An artificial fore-arm has a moment-of-inertia around the center of mass as $0.3\text{ kg}\cdot\text{m}^2$. The mass of the artificial fore-arm is $3\text{ kg}$. If the distance from the elbow joint to the center of mass of the fore-arm is $20\text{ cm}$, the moment-of-inertia of the fore-arm about the elbow joint is ________ $\text{kg}\cdot\text{m}^2$. Give your answer rounded off to two decimal places.

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q53

NAT[2 Marks]

A bio-potential signal of $4\text{ mV}$ on the skin surface was fed to an amplifier with a differential gain of $2000$. The noise in the signal is $1000\text{ mV}$. If the amplifier output produces a noise output of $200\text{ mV}$, the common mode rejection ratio of the amplifier is ________ $\text{dB}$. Give your answer rounded to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q54

NAT[2 Marks]

In a motor nerve conduction velocity experiment, the distance between the distal and the recording sites is $4\text{ cm}$ and the distance between the proximal and the recording sites is $24\text{ cm}$. The distal and proximal latencies were recorded as $6\text{ ms}$ and $10\text{ ms}$, respectively. The nerve conduction velocity is ________ meters per second. Give your answer rounded off to the nearest integer.

Explanation

GATE→2024→Biomedical Engineering Core→Biomechanics

Q55

NAT[2 Marks]

A person creates an apparatus as shown in the figure to exercise the extensor muscle of the hand. It is given that $OP = 0.15\text{ m}$, $OQ = 0.35\text{ m}$, $\theta = 30^\circ$, the weight of the lower arm $= 20\text{ N}$, the center of mass of the lower arm is at point $P$, the magnitude of the applied tensile force $F = 50\text{ N}$. If the extensor muscle is acting with a moment arm of $0.25\text{ m}$, the muscle force required to hold the hand at the position shown in the figure is ________ $\text{N}$. Give your answer rounded off to the nearest integer.

Explanation

General Aptitude

10 Questions

GATE→2024→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

If '$\rightarrow$' denotes increasing order of intensity, then the meaning of the words $[\text{simmer} \rightarrow \text{seethe} \rightarrow \text{smolder}]$ is analogous to $[\text{break} \rightarrow \text{raze} \rightarrow \underline{\hspace{1.5cm}}]$. Which one of the given options is appropriate to fill the blank?

(A)

obfuscate

(B)

obliterate

(C)

fracture

(D)

fissure

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q57

MCQ[1 Mark]

In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from $301$, while the house-numbers on the other side of the road are consecutive even numbers starting from $302$. The total number of houses is the same on both sides of the road. If the difference of the sum of the house-numbers between the two sides of the road is $27$, then the number of houses on each side of the road is

(A)

27

(B)

52

(C)

54

(D)

26

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1$, $\left(\frac{p}{q}\right)^{\frac{p}{q}} = p^{\left(\frac{p}{q} - 1\right)}$. Then,

(A)

$q^p = p^q$

(B)

$q^p = p^{2q}$

(C)

$\sqrt{q} = \sqrt{p}$

(D)

$\sqrt[p]{q} = \sqrt[q]{p}$

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

Which one of the given options is a possible value of $x$ in the following sequence? $$3, 7, 15, x, 63, 127, 255$$

(A)

35

(B)

40

(C)

45

(D)

31

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time $\text{12:05:00}$ hours to $\text{12:55:00}$ hours?

(A)

51

(B)

49

(C)

50

(D)

55

Explanation

GATE→2024→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

In the given text, the blanks are numbered (i)–(iv). Select the best match for all the blanks. From the ancient Athenian arena to the modern Olympic stadiums, athletics $\underline{\text{(i)}}$ the potential for a spectacle. The crowd $\underline{\text{(ii)}}$ with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to cross-step. Six cross-steps $\underline{\text{(iii)}}$ in an abrupt stop on his left foot. As his body $\underline{\text{(iv)}}$ like a door turning on a hinge, the javelin is launched skyward at a precise angle.

(A)

(i) hold (ii) waits (iii) culminates (iv) pivot

(B)

(i) holds (ii) wait (iii) culminates (iv) pivot

(C)

(i) hold (ii) wait (iii) culminate (iv) pivots

(D)

(i) holds (ii) waits (iii) culminate (iv) pivots

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

Three distinct sets of indistinguishable twins are to be seated at a circular table that has $8$ identical chairs. Unique seating arrangements are defined by the relative positions of the people. How many unique seating arrangements are possible such that each person is sitting next to their twin?

(A)

12

(B)

14

(C)

10

(D)

28

Explanation

GATE→2024→General Aptitude→Data Interpretation

Q63

MCQ[2 Marks]

The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation (MWh) in a time of $1000\text{ hours (h)}$. The Capacity Factor of a power generation technology is: $$\text{Capacity Factor} = \frac{\text{Electricity Generation (MWh)}}{\text{Installed Capacity (MW)} \times 1000\text{ (h)}}$$ Which one of the given technologies has the highest Capacity Factor?

(A)

T1

(B)

T2

(C)

T3

(D)

T4

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule. **Rule:** The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals). As per this rule, the maximum number of crosses possible in the empty column is

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2024→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^\circ$, the ratio of the Earth-Sun and Earth-Moon distances is closest to

(A)

328

(B)

382

(C)

238

(D)

283

Explanation