GATE 2023 Question Paper BM Biomedical Engineering

The Graduate Aptitude Test in Engineering

GATE 2023
Question Paper
GATE is an entrance examination conducted in India that
primarily tests the comprehensive understanding of
undergraduate subjects in engineering and sciences for
admission into technical postgraduate programs.

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General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each

Q.1 “I cannot support this proposal. My ________ will not permit it.”

(A) conscious

(B) consensus

(C) conscience

(D) consent

Q.2 Courts : _______ : : Parliament : Legislature

(By word meaning)

(A) Judiciary

(B) Executive

(C) Governmental

(D) Legal

Page 1 of 38

Q.3 What is the smallest number with distinct digits whose digits add up to 45?

(A) 123555789

(B) 123457869

(C) 123456789

(D) 99999

Q.4 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

Page 2 of 38

Q.5 How many rectangles are present in the given figure?

. .

(A) 8

(B) 9

(C) 10

(D) 12

Page 3 of 38

Q.6 – Q.10 Carry TWO marks Each

Q.6 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.

Page 4 of 38

Q.7 Which one of the following options represents the given graph?

(A) −x
f ( x ) = x2 2

(B) −x
f ( x ) = x. 2

(C)
f ( x ) = x 2− x

(D)
f ( x ) = x. 2− x

Page 5 of 38

Q.8 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.

Page 6 of 38

Q.9 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

Page 7 of 38

Q.10 A 100 cm × 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 × 1 cm.

The total number of creases visible when the sheet is unfolded is _______.

(A) 32

(B) 5

(C) 31

(D) 63

Page 8 of 38

Q.11 – Q.35 Carry ONE mark Each

Q.11 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

Q.12 For a Binomial random variable X, E(X) and Var(X) are the expectation and
variance, respectively. Which one of the following statements CANNOT be true?

(A) E(X) = 20 and Var(X) = 16

(B) E(X) = 6 and Var(X) = 5.4

(C) E(X) = 10 and Var(X) = 15

(D) E(X) = 64 and Var(X) = 12.8

Page 9 of 38

Q.13 1 −2
Q=[ ] is a 2 × 2 matrix. Which one of the following statements is TRUE?
2 1

(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.

Q.14 Which one of the following vectors is an eigenvector corresponding to the
eigenvalue = 1 for the matrix A?

1 1 0
A = [1 −1 0]
1 −1 1

(A) [1 0 1 ]𝑇

(B) [1 1 0 ]𝑇

(C) [0 1 0 ]𝑇

(D) [0 0 1 ]𝑇

Page 10 of 38

Q.15
𝑥 𝜕2 𝑓
For the function 𝑓(𝑥, 𝑦) = 𝑒 cos(𝑦), what is the value of at
𝜕𝑥𝜕𝑦
(𝑥 = 0, 𝑦 = 𝜋/2) ?

(A) 0

(B) 1

(C) –1

(D) 𝑒 𝜋/2

Q.16 For the circuit given below, choose the angular frequency ω0 (in rad/s) at which the
voltage across the capacitor has maximum amplitude?

(A) 1000

(B) 100

(C) 1

(D) 0

Page 11 of 38

Q.17 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 𝑗𝜔 ), as a function of the normalized angular
frequency ω. For the range |𝜔| ≤ 𝜋, |𝐻(𝑒 𝑗𝜔 )| is equal to _____________.

(A) 2 |cos(𝜔)|

(B) 2 |sin(𝜔)|

(C) 2 |cos(𝜔/2)|

(D) 2 |sin(𝜔/2)|

Q.18 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?

(A) 0.9 kHz

(B) 9.9 kHz

(C) 49.9 kHz

(D) 99.9 kHz

Page 12 of 38

Q.19 In the following circuit with an ideal operational amplifier, the capacitance of the
𝜖𝐴
parallel plate capacitor 𝐶 is given by the expression 𝐶 = ( ) , where 𝜖 is the
𝑥
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 = 𝑥0 + 𝑘𝑡, where 𝑡 is time; 𝑥0 and 𝑘 are positive non-zero
constants. If the input voltage 𝑣𝑖 is constant, then the output voltage 𝑣0 is given by
_____________.

(A) 𝑅𝑣𝑖 𝐶𝑘
𝑥

(B) 𝑅𝑣𝑖 𝐶
𝑘𝑥

(C) 𝑣𝑖 𝑘
𝑅𝐶𝑥

(D) 0

Page 13 of 38

Q.20 Which one of the following techniques makes use of Korotkoff sounds?

(A) Sphygmomanometry

(B) Audiometry

(C) Spirometry

(D) Tonometry

Q.21 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

Page 14 of 38

Q.22 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

Page 15 of 38

Q.23 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.

Figure P

50 200

(A)

50 200

(B)

50 200

(C)

50 200

(D)

50 200

Page 16 of 38

M, L and T correspond to dimensions representing mass, length and time,
Q.24
respectively. What is the dimension of viscosity?

(A) 𝑀1 𝐿−2 𝑇 −1

(B) 𝑀1 𝐿−1 𝑇 −1

(C) 𝑀1 𝐿−1 𝑇 1

(D) 𝑀1 𝐿−2 𝑇 −2

Q.25 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

Page 17 of 38

Q.26 A causal, discrete time system is described by the difference equation

𝑦[𝑛] = 0.5 𝑦[𝑛 − 1] + 𝑥[𝑛], 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?

(A) The system has an impulse response described by 0.5𝑛 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.

Q.27 Which of the following constituents is/are NOT normally found in serum obtained
from human blood?

(A) Platelets

(B) Albumin

(C) Glucose

(D) Fibrinogen

Page 18 of 38

Q.28 𝑄, 𝑅, 𝑆 are Boolean variables and ⊕ is the XOR operator. Select the CORRECT
option(s).

(A) (𝑄 ⊕ 𝑅) ⊕ 𝑆 = 𝑄 ⊕ (𝑅 ⊕ 𝑆)

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

(C) (𝑄 ⊕ 𝑅) ⊕ 𝑆 = 1 when 𝑄 = 𝑅 = 𝑆 = 1

(D) ( (𝑄 ⊕ 𝑅) ⊕ (𝑅 ⊕ 𝑆) ) ⊕ (𝑄 ⊕ 𝑆) = 1

Q.29 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

Page 19 of 38

Q.30 In the following circuit, the switch S is open for 𝑡 < 0 and closed for 𝑡 ≥ 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.)

Q.31 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.)

Q.32 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 ω0 (in rad/s)?
(Round off the answer to one decimal place.)

Page 20 of 38

Q.33 A continuous time, band limited signal 𝑥(𝑡) has its Fourier transform described by:

|𝑓|
1− , |𝑓| ≤ 200 Hz
𝑋(𝑓) = { 200
0, |𝑓| > 200 Hz

The signal is uniformly sampled at a sampling rate of 600 Hz. The Fourier transform
𝑋𝑠 (600)
of the sampled signal is 𝑋𝑠 (𝑓). What is the value of ? (Round off the
𝑋𝑠 (500)
the answer to one decimal place.)

Q.34 At time t, the cardiac dipole is oriented at – 45° (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.)

Q.35 A 5 MHz ultrasound transducer is being used to measure the velocity of blood.
When the transducer is placed at an angle of 45° 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.)

Page 21 of 38

Q.36 – Q.65 Carry TWO marks Each

Q.36 The time-dependent growth of a bacterial population is governed by the equation

𝑑𝑥 𝑥
= 𝑥 (1 − ),
𝑑𝑡 200
where 𝑥 is the population size at time 𝑡. The initial population size is 𝑥0 = 100
at 𝑡 = 0. As 𝑡 → ∞, the population size of bacteria asymptotically approaches
_________________.

(A) 150

(B) 200

(C) 300

(D) 500

Q.37 A 20 mV DC signal has been superimposed with a 10 mV RMS band-limited
Gaussian noise with a flat spectrum upto 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?

(A) 0.1

(B) 1.0

(C) 5.0

(D) 10.0

Page 22 of 38

Q.38 In the circuit below, the two DC voltage sources have voltages of value 𝑉1 and 𝑉2 .
The expression for the power dissipated in the 60 kΩ resistor is proportional to
____________.

(A) (𝑉1 + 𝑉2 )2

(B) (3𝑉1 + 𝑉2 )2

(C) (2𝑉1 + 𝑉2 )2

(D) (𝑉1 + 2𝑉2 )2

Q.39 The Laplace transform of 𝑥1 (𝑡) = 𝑒 −𝑡 𝑢(𝑡) is 𝑋1 (𝑠), where 𝑢(𝑡) is the unit
step function. The Laplace transform of 𝑥2 (𝑡) = 𝑒 𝑡 𝑢(−𝑡) is 𝑋2 (𝑠). Which one
of the following statements is TRUE?

(A) The region of convergence of 𝑋1 (𝑠) is 𝑅𝑒(𝑠) > 0.

(B) The region of convergence of 𝑋2 (𝑠) is confined to the left half-plane of 𝑠.

(C) The region of convergence of 𝑋1 (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
𝑋1 (𝑠) and the region of convergence of 𝑋2 (𝑠).

Page 23 of 38

Q.40 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 𝐼𝑖 is the intensity of
𝐼𝑖
the incident ray and 𝐼𝑜 is the intensity of the transmitted ray, then log ( ) is
𝐼𝑜
given by _______________.

(A)
2 √𝑅 2 − 𝑡 2

(B) 2𝑅

(C) 1

(D) 2√𝑅 − 𝑡

Page 24 of 38

Q.41 The free induction decay (FID) in the MRI of an object can be approximated as

𝑠(𝑡) = ∬ 𝑚(𝑥, 𝑦)𝑒 −𝑗2𝜋(𝐾𝑥(𝑡)𝑥+𝐾𝑦(𝑡)𝑦) 𝑑𝑥𝑑𝑦,
𝑡
where 𝐾𝑥 (𝑡) = ∫0 𝐺𝑥 (𝜏)𝑑𝜏 and

𝑡
𝐾𝑦 (𝑡) = ∫0 𝐺𝑦 (𝜏)𝑑𝜏 .

Here 𝐺𝑥 and 𝐺𝑦 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 (𝐾𝑥 , 𝐾𝑦 ) space

(B) over a parabolic contour in (𝐾𝑥 , 𝐾𝑦 ) space

(C) along 𝐾𝑦 only

(D) along 𝐾𝑥 only

Page 25 of 38

Q.42 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 ω0 (in rad/s)?

(A) 104

(B) 103

(C) 103 𝜋

(D) 104 𝜋

Q.43 In a biomaterial, formation of hydrogen bonds on alcoholic groups will lead to a
______________________________.

(A) shift in the infra-red peak around 1700 cm–1

(B) shift in the infra-red peak around 2800 cm–1

(C) broadening of the infra-red peak around 3500 cm–1

(D) disappearance of the infra-red peak around 1700 cm–1

Page 26 of 38

Q.44 In the circuit shown below, the input voltage is sinusoidal and 2.5 V peak to peak.
The capacitors are 20 μF each. Assume that the knee voltage of the diodes is 0 V
and 𝑅𝐿 is very large (almost infinite). Which one of the following options is closest
to the peak to peak voltage across 𝑅𝐿 , after a large number of cycles?

(A) 1.25 V

(B) 2.50 V

(C) 5.00 V

(D) 10.0 V

Page 27 of 38

Q.45 An ultrasound plane wave of amplitude 𝑃0 hits the semi-infinite boundary of two
media having acoustic impedances 𝑍1 and 𝑍2 . The sum of the amplitudes of the
reflected and the incident waves at the boundary is equal to _____________.

(A) 2𝑃0 𝑍2
(𝑍1 + 𝑍2 )

(B) 𝑃0 (𝑍2 − 𝑍1 )
(𝑍1 + 𝑍2 )

(C) 𝑃0 𝑍2
𝑍1

(D) 𝑃0 𝑍1
(𝑍1 + 𝑍2 )

Page 28 of 38

Q.46 In the circuit given below, what should be the value of the resistance R for
maximum dissipation of power in R?

(A) 1.2 kΩ

(B) 2.2 kΩ

(C) 3.2 kΩ

(D) 4.2 kΩ

Page 29 of 38

Q.47 Two sequences 𝑥1 [𝑛] and 𝑥2 [𝑛] are described as follows:

𝑥1 [0] = 𝑥2 [0] = 1

𝑥1 [1] = 𝑥2 [2] = 2

𝑥1 [2] = 𝑥2 [1] = 1

𝑥1 [𝑛] = 𝑥2 [𝑛] = 0 for all 𝑛 < 0 and 𝑛 > 2

If 𝑥[𝑛] is obtained by convolving 𝑥1 [𝑛] with 𝑥2 [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

Page 30 of 38

Q.48 1
The function 𝑓(𝑍) = of a complex variable 𝑍 is integrated on a closed
𝑍−1
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

Q.49 The continuous time signal 𝑥(𝑡) is described by

1, 0 ≤𝑡 ≤1
𝑥(𝑡) = {
0, elsewhere
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) 0.75 𝑑𝑦(𝑡)
∫0.1 𝑑𝑡 ≠ 0
𝑑𝑡

Page 31 of 38

Q.50 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.

Q.51 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.

Page 32 of 38

Q.52 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

Q.53 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.

Page 33 of 38

Q.54 A system is described by the following differential equation

𝑑 2 𝑦(𝑡) 𝑑𝑦(𝑡)
0.01 + 0.2 + 𝑦(𝑡) = 6𝑥(𝑡) ,
𝑑𝑡 2 𝑑𝑡
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.)

Q.55 The resistance of a thermistor is 1 kΩ at 25 °C and 500 Ω at 50 °C. Find the
temperature coefficient of resistance (in units of °C –1) at 35 °C. (Round off the
answer to three decimal places.)

Q.56 A normally incident X-ray of energy 140 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 cm–1 and a thickness of 1 cm, and
tissue Q with an absorption coefficient of 10 cm–1 and a thickness of 2 cm. Calculate
the intensity (in µeV) detected by the detector. (Round off the answer to one decimal
place.)

Q.57 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?

Page 34 of 38

Q.58 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.)

Q.59 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 the compound 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.)

Q.60 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.)

Page 35 of 38

Q.61 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 J/(mol.K) and Faraday’s constant is
96500 C/mol.

What is the absolute value of the resting membrane potential (in mV) across the cell
membrane at 27 °C? (Round off the answer to one decimal place.)

Extracellular Intracellular
Relative
Ion concentration concentration
permeability
(mM) (mM)
Sodium 140 10 0.02
Potassium 3 140 1.00
Chloride 90 3 0.38

Q.62 A metallic strain gauge with negligible piezoresistive effect is subjected to a strain
of 50 × 10−6. For the metal, Young’s Modulus = 80 GPa and Poisson’s Ratio =
0.42. What is the change in resistance (in mΩ), if the unstrained resistance of the
strain gauge is 200 Ω ? (Round off the answer to one decimal place.)

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Q.63 Consider the total hip joint prosthesis as shown in the figure. The geometric
parameters of the prosthesis are such that L1 = 40 mm, L2 = 60 mm, 𝜃1 = 45o ,
𝜃2 = 90o . 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.)

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Q.64 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 R1 and R4 will
be in compression, and the resistors R2 and R3 will be in tension.

The bridge excitation voltage (Ein) is 10 Volts. If all the resistors have a resistance
of 200 Ω in the absence of any force, and each resistance changes by 20 Ω upon
application of a force, what is the output voltage Vout (in Volts) from the
Wheatstone bridge? (Round off your answer to the nearest integer.)

Q.65 A stone is thrown from an elevation of 2 m above ground level, at an angle of 30o
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/s2 and assume that there is no air resistance. (Round off your answer to one
decimal place.)

END OF QUESTION PAPER

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