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GATE 2022 General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark each.
Q.1 The _________ is too high for it to be considered _________.
(A) fair / fare
(B) faer / fair
(C) fare / fare
(D) fare / fair
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Q.2 A function y(x) is defined in the interval [0, 1] on the 𝑥-axis as
1
⎧ 2 if 0 ≤ 𝑥 <
⎪ 3
1 3
𝑦(𝑥 ) = 3 if ≤𝑥<
⎨ 3 4
⎪ 3
⎩ 1 if ≤𝑥≤1
4
Which one of the following is the area under the curve for the interval [0, 1] on
the 𝑥-axis?
(A) 5
6
(B) 6
5
(C) 13
6
(D) 6
13
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Q.3 Let r be a root of the equation 𝑥 + 2𝑥 + 6 = 0.
Then the value of the expression (𝑟 + 2)(𝑟 + 3)(𝑟 + 4)(𝑟 + 5) is
(A) 51
(B) −51
(C) 126
(D) −126
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Q.4 Given below are four statements.
Statement 1: All students are inquisitive.
Statement 2: Some students are inquisitive.
Statement 3: No student is inquisitive.
Statement 4: Some students are not inquisitive.
From the given four statements, find the two statements that CANNOT BE
TRUE simultaneously, assuming that there is at least one student in the class.
(A) Statement 1 and Statement 3
(B) Statement 1 and Statement 2
(C) Statement 2 and Statement 4
(D) Statement 3 and Statement 4
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Q.5 A palindrome is a word that reads the same forwards and backwards. In a game
of words, a player has the following two plates painted with letters.
From the additional plates given in the options, which one of the combinations
of additional plates would allow the player to construct a five-letter palindrome.
The player should use all the five plates exactly once. The plates can be rotated
in their plane.
(A)
(B)
(C)
(D)
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Q. 6 – Q. 10 Carry TWO marks each.
Q.6 Some people believe that “what gets measured, improves”. Some others believe
that “what gets measured, gets gamed”. One possible reason for the difference in
the beliefs is the work culture in organizations. In organizations with good work
culture, metrics help improve outcomes. However, the same metrics are
counterproductive in organizations with poor work culture.
Which one of the following is the CORRECT logical inference based on the
information in the above passage?
(A) Metrics are useful in organizations with poor work culture
(B) Metrics are useful in organizations with good work culture
(C) Metrics are always counterproductive in organizations with good work culture
(D) Metrics are never useful in organizations with good work culture
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Q.7 In a recently conducted national entrance test, boys constituted 65% of those who
appeared for the test. Girls constituted the remaining candidates and they
accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the
information provided in the above passage?
(A) Equal number of boys and girls qualified
(B) Equal number of boys and girls appeared for the test
(C) The number of boys who appeared for the test is less than the number of girls
who appeared
(D) The number of boys who qualified the test is less than the number of girls who
qualified
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A box contains five balls of same size and shape. Three of them are green
Q.8
coloured balls and two of them are orange coloured balls. Balls are drawn from
the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball
is drawn, it is replaced with another orange ball.
First ball is drawn. What is the probability of getting an orange ball in the next
draw?
(A) 1
2
(B) 8
25
(C) 19
50
(D) 23
50
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Q.9 The corners and mid-points of the sides of a triangle are named using the distinct
letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the
following statements:
The line joining P and R is parallel to the line joining Q and S.
P is placed on the side opposite to the corner T.
S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above
information?
(A) P cannot be placed at a corner
(B) S cannot be placed at a corner
(C) U cannot be placed at a mid-point
(D) R cannot be placed at a corner
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Q.10 A plot of land must be divided between four families. They want their
individual plots to be similar in shape, not necessarily equal in area. The land
has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and
R2, are already present and cannot be moved.
What is the least number of additional straight ropes needed to create the
desired plots? A single rope can pass through three poles that are aligned in a
straight line.
(A) 2
(B) 4
(C) 5
(D) 3
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Q.11 – Q.35 Carry ONE mark Each
Q.11 3 2 1 0
If the given matrices A and I satisfy A kA 2 I , the
2
4 2 0 1
value of coefficient k is ________.
(A) 1
(B) 2
(C) 0
(D) 4
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Q.12 dx
Evaluation of the integral 2x x 2 results in
(A) sin 1 x 1 c
(B) cos 1 x 1 c
(C) x
sin 1 c
2
(D) x
cos 1 c
2
If V a iˆ b ˆj c kˆ , identify the INVALID operation on 𝑉⃗ .
Q.13
(A)
V
(B) V
(C)
V
(D)
V
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Q.14 𝑥(𝑡) is a real continuous-time signal whose magnitude frequency response
(|𝑋(𝑗𝜔)|) is shown below. After sampling 𝑥(𝑡) at 100 rad.s-1, the spectral point P
is down-converted to ________ rad.s-1 in the spectrum of the sampled signal.
(A) 12.5
(B) 25
(C) 6.25
(D) 37.5
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Q.15 Discrete signals 𝑥[𝑛] and 𝑦[𝑛] are shown below. The cross-correlation 𝑟 [0] is
_____________.
(A) 2√2
(B) 1
2√2
(C) 1
2
(D) 1
√2
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Q.16 In the circuit diagram shown below, the logic gates operate with a supply voltage
of 1 V. NAND and XNOR have 200 ps and 400 ps input-to-output delay,
respectively.
At time 𝑡 = 𝑇, 𝐴(𝑡) = 0, 𝐵(𝑡) = 1 and 𝑍(𝑡) = 0. When the inputs are changed to
𝐴(𝑡) = 1, 𝐵(𝑡) = 0 at 𝑡 = 2𝑇, a 1 V pulse is observed at 𝑍. The pulse width of
the 1 V pulse is _________ ps.
(A) 100
(B) 200
(C) 400
(D) 600
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Q.17 Input bits X and Y are added by using the combinational logic as shown below. 𝑆
represents the sum of the two bits. For a correct implementation of the sum, the
signals 𝐷 , 𝐷 , 𝐷 , 𝐷 are _____________, respectively.
(A) 1, 0, 0, 1
(B) 0, 1, 0, 1
(C) 1, 0, 1, 1
(D) 0, 1, 1, 0
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Q.18 The time delay between the peaks of the voltage signals 𝑣 (𝑡) = 2cos(6𝑡 + 60°)
and 𝑣 (𝑡) = −3 sin(6𝑡) is _______ s.
(A) 300π/360
(B) 10π/360
(C) 50π/360
(D) 200π/360
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Q.19 For the balanced Owen-bridge circuit shown in the figure, the values of 𝐿 and 𝑅
are:
(A) 𝑅 𝑅 𝑅 𝐶
𝐿 = , 𝑅 =
𝐶 𝐶
(B) 𝑅 𝐶
𝐿 = 𝑅 𝑅 𝐶, 𝑅 =
𝐶
(C) 𝑅 𝐶
𝐿 = 𝑅 𝑅 𝐶, 𝑅 =
𝐶
(D) 𝐿 = 𝑅 𝑅 𝐶, 𝑅 = 𝑅 𝐶𝐶
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Q.20 Myopia occurs when the focal point falls __________ the retina. This can be
corrected using a __________ lens.
(A) in front of, convex
(B) behind, convex
(C) in front of, concave
(D) behind, concave
Q.21 Choose the correct sequence for the direction of blood flow in a healthy human
being starting and ending with the left ventricle.
(A) Left ventricle → Aorta → Systemic arteries → Systemic veins → Vena cavae →
Pulmonary vein → Pulmonary artery → Right ventricle → Left ventricle
(B) Left ventricle → Aorta → Systemic arteries → Systemic veins → Vena cavae →
Right ventricle → Pulmonary artery → Pulmonary vein → Left ventricle
(C) Left ventricle → Systemic arteries → Aorta → Systemic veins → Right ventricle →
Pulmonary artery → Pulmonary vein → Left ventricle
(D) Left ventricle → Aorta → Systemic arteries → Vena cavae → Systemic veins →
Right ventricle → Pulmonary artery → Pulmonary vein → Left ventricle
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Q.22 In a healthy adult, which one of the following regions of the brain contains
primarily white matter?
(A) Cerebral cortex
(B) Basal ganglia
(C) Limbic system
(D) Corpus callosum
Q.23 Skeletal muscles are recruited to lift loads. If the force generated in the muscle due
to contraction is not sufficient to lift the load, it is known as _____ contraction.
(A) Isometric
(B) Isotonic
(C) Isokinetic
(D) Isoinertial
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Q.24 Backscattered electron detector of a scanning electron microscope is used to
(A) study surface topography of the sample
(B) quantify surface roughness
(C) measure atomic number
(D) contrast areas with different chemical compositions
Q.25 In the process of obtaining a Magnetic Resonance Image (MRI), the terms T1 and
T2 time constants of the material are very crucial to decide on getting suitable
weighted images. Choose the correct explanation relating to these two constants
from the following options.
(A) T1 is the spin-lattice or longitudinal relaxation time, and T2 is the spin-spin or
transverse relaxation time
(B) T1 and T2 indicate the durations that Free Induction Decay (FID) signal to be
recorded in x and y axes directions, respectively
(C) T1 and T2 refer to the durations of flipping pulses used to tilt the resultant
magnetic vector into x-y plane and inverse z-direction, respectively
(D) T1 is the spin-spin or transverse relaxation time, and T2 is the spin-lattice or
longitudinal relaxation time
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Q.26 Given 𝑥 is real, identify all the even-functions among the following:
(A) xx
(B) cos( x)
x
(C) sin x 2
(D) x
e
Q.27 An ideal coronary stent should
(A) be thromboresistant
(B) promote accumulation of smooth muscle cells
(C) be fatigue resistant
(D) support deposition of extracellular matrix
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Q.28 Which of the following statements related to the safety of biomedical instruments
are TRUE?
(A) When a person is exposed to an electrical hazard, let-go current is defined as the
maximum current at which the subject can withdraw voluntarily
(B) Microshock is a physiological response resulting from an electrical current
passing through heart
(C) The patient in an intensive care unit is being exposed to the danger of microshock
because of using internal conductive electrodes in the vicinity of the heart
(D) The 50 Hz safe current limit for a microshock is greater than 50 mA
Q.29 Which of the following statements related to the operating principle of pulse
oximetry are CORRECT?
(A) Pulse oximeter can non-invasively determine arterial oxygen saturation (SpO 2) by
analyzing the light transmitted through the skin during the systolic phase of the
blood flow through the tissue
(B) In a pulse oximeter, isosbestic wavelength is the wavelength at which Hb and
HbO2 have same optical absorbance
(C) Pulse oximeter can accurately determine the SpO2 of blood by computing the ratio
of absorbances at 660 nm and 905 nm wavelengths
(D) Pulse oximeter can accurately determine the SpO2 of blood by computing the ratio
of absorbances at 850 nm and 950 nm wavelengths
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Q.30 Which of the following statements related to biomedical measurements are
TRUE?
(A) Electrical activity of neurons in the peripheral nervous system can be measured by
ENG
(B) Electrical activity of the retina in response to light stimulus can be measured using
EOG
(C) In a human EEG, Gamma waves are high frequency waves compared to Beta,
Delta, and Theta waves
(D) P wave in ECG manifests ventricular repolarization
Q.31 Which of the following mechanical prosthetic valves were invented as a
replacement for diseased heart valves?
(A) Globe valve
(B) Ball and cage valve
(C) Bi-leaflet valve
(D) Swing check valve
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Q.32 Due to the current COVID pandemic conditions, assume that positive or negative
status of any individual are equally likely. There are 3 members in a family. If
one of the members has tested COVID positive, the conditional probability that at
least 2 members are COVID positive is _____ (rounded off to three decimal
places).
Q.33 A series RLC circuit with R = 10 Ω, L = 50 mH and C = 100 µF connected to
200 V, 50 Hz supply consumes power P. The value of L is changed such that this
circuit consumes same power P but operates with lagging power factor. The new
value of L is _____ mH (rounded off to two decimal places).
Q.34 The thickness of piezoelectric crystal (PZT5A) used in ultrasound applications
will determine the resonant frequency of the transducer. To work at a resonance
frequency of 5 MHz, the thickness of a PZT5A transducer must be
_______ mm (rounded off to three decimal places).
Given: The velocity of sound in PZT5A is 4350 m.s-1.
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Q.35 Power consumed by the 3 Ω resistor is 12 W in the given circuit. The value of the
resistor R in the circuit is ________ Ω.
3Ω
2Ω 2Ω
1Ω R
+ -
10 V
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Q.36 – Q.65 Carry TWO marks Each
Q.36 z3 9
In the complex 𝑧-domain, the value of the integral dz is
C
3 z i
(A) 2
6i
81
(B) 2
6 i
81
(C) 2
6i
81
(D) 2
6 i
81
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Q.37 dy
Solution of the differential equation y cos x is
dx
(A) sin x cos x
y ce x
2
(B) sin x cos x
y ce x
2
(C) sin x cos x
y ce x
2
(D) sin x cos x
y ce x
2
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Q.38 An input 𝑥(𝑡) is applied to a system with a frequency transfer function given by
H(jω) as shown below. The magnitude and phase response of the transfer function
are shown below. If 𝑦(𝑡 ) = 0 for 𝑥(𝑡) = 𝑢(𝑡), the time 𝑡 (> 0) is ______ µs.
X H(jω) Y
Phase(H(jω)) |H(jω)|
103 104 105 106
ω 1
0
-45o
-90o
-135o
-180o
ω
0 103 104 105 106
(A) 100 ln(2)
(B) 10 ln(2)
(C) 1000 ln(2)
(D) ln(2)
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Page 30
Q.39 The block diagram of a two-tap high-pass FIR filter is shown below. The filter
transfer function is given by 𝐻(𝑧) = 𝑌(𝑧)/𝑋(𝑧).
If ratio of the maximum to minimum value of 𝐻(𝑧) is 2 and |𝐻(𝑧)| = 1, the
coefficients 𝛽 and 𝛽 are _________ and ________, respectively.
(A) 0.75, −0.25
(B) 0.67, 0.33
(C) 0.60, −0.40
(D) −0.64, 0.36
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Q.40 The block diagrams of an ideal system and a real system with their impulse
responses are shown below. An auxiliary path is added to the delayed impulse
response in the real system.
For a unit impulse input (𝑥(𝑡) = 𝛿(𝑡)) to both systems, gain 𝛽 is chosen such that
𝑦(4𝑇) is same for both systems. The value of 𝛽 is __________.
(A) 𝑒 (1 − 𝑒 )
(B) −𝑒 (1 − 𝑒 )
(C) −𝑒 (1 − 𝑒 )
(D) 𝑒 (1 − 𝑒 )
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Q.41 A filter is designed using opamps, resistors, and capacitors as shown below.
Opamps are ideal with infinite gain and infinite bandwidth. If 𝑉 (𝑠)/𝑉 (𝑠) is an
all-pass transfer function, the value of resistor R2 is ______________ kΩ.
(A) 1
(B) 10
(C) 5
(D) 2
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Q.42 𝑑𝑓(𝑡) 1+𝑠
If 𝑔(𝑡) = , and 𝐹 (𝑠) =
𝑑𝑡 𝑠 + 12𝑠 + 32
where 𝐹 (𝑠) is the Laplace transform of the function 𝑓 (𝑡 ), then the value of 𝑔(𝑡) at
𝑡 = 0 is _______.
(A) -11
(B) -5
(C) -17
(D) ∞
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Q.43 Consider the Einthoven’s triangle of frontal ECG for the 3 electrodes RA, LA and
LL shown in the figure. The augmented lead vectors bisect the bipolar lead
vectors. At the peak of R wave, the cardiac vector M points vertically downwards
with |𝑀| = 5 𝑚𝑉.
The voltages on leads I and II are ______ mV and ______ mV, respectively.
(A) 0, 4.33
(B) 2.17, 0
(C) 0, 2.17
(D) 4.33, 0
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Page 35
Q.44 Which one of the following statements is TRUE?
(A) A myelinated axon has a greater ATP requirement than an unmyelinated axon of
the same diameter and length
(B) An unmyelinated axon has a greater ATP requirement than a myelinated axon of
the same diameter and length
(C) An unmyelinated axon has the same ATP requirement as a myelinated axon of the
same diameter and length
(D) An unmyelinated axon always has a greater ATP requirement than a myelinated
axon irrespective of their diameter and length
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Q.45 The deltoid muscle connects the humerus to the shoulder blade and facilitates out
stretching of the arm as shown in the figure. The humerus is connected to the
shoulder blade with a ball and socket joint.
Assume the equivalent weight (W) of the arm to be 30 N and acts vertically down
at a horizontal distance of 30 cm.
Assume that the deltoid muscle is connected to the humerus at a distance of 15 cm
and makes an average angle of 20º with the horizontal. The magnitude of tension
in the deltoid muscle is ________ N.
(A) 31.9
(B) 63.8
(C) 87.7
(D) 175.4
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Page 37
Q.46 For blood flow through arteries, which one of the following relations
approximates the pulse wave propagation speed (𝐶) as a function of the inner
diameter (𝐷) of the artery, wall thickness (𝑡), modulus of elasticity (𝐸), and fluid
density (𝜌)?
(A) Et
C
D
(B) D
C
Et
(C)
D 3 t 3
C
E
(D) E
C
Dt
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Page 38
Q.47 A person has a total blood volume of 5 L. Out of this total, assume that 4 L is
contained in the systemic circulation and 1 L in pulmonary circulation. The
cardiac output of the person is 5 L.min-1. Time taken for a drop of blood to go
from right ventricle to left ventricle is _________ s.
(A) 60
(B) 20
(C) 15
(D) 12
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Page 39
Q.48 Based on the stress-strain curves of three different materials (X, Y, and Z) shown
in the figure, which one of the following choices is CORRECT?
(A) X – Titanium, Y – Hydroxyapatite, Z – Polyethylene
(B) X – Hydroxyapatite, Y – Titanium, Z – Polyethylene
(C) X – Hydroxyapatite, Y – Polyethylene, Z – Titanium
(D) X – Polyethylene, Y – Titanium, Z – Hydroxyapatite
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Q.49 Consider two radionuclides P and Q. Suppose the half-life of P (𝑡 / ) is four times
that of Q (𝑡 / ). At time t = 0, there are N0 atoms of both radionuclides. When
will the radioactivity of the two radionuclides be equal?
(A) 𝑡=𝑡 /
(B) 𝑡 = 0.66𝑡 /
(C) 𝑡 = 0.75𝑡 /
(D) 𝑡 = 1.5𝑡 /
Q.50 In a biological study, the experimental values measured from 6 subjects are given
in the table below. Using this data, the linear regression coefficient for estimating
the weight of the heart based on the systolic pressure is _______ (rounded off to
two decimal places).
Systolic pressure 120 90 100 110 140 130
(in mm Hg)
Weight of the 500 300 420 390 490 450
heart (in g)
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Q.51
Using divergence theorem, evaluate the integral F n dA , where S is the
S
surface of the cone x y z , 0 z 3 . If F 4 x iˆ 3 zˆj 5 y kˆ is
2 2 2
vector function with outer unit normal vector n , the value of the integral is
_______ (rounded off to the nearest integer).
Q.52
The magnitude of the current gain in the circuit below is ______ (rounded
off to two decimal places).
Q.53 The linear temperature coefficient of the material of a wire is 𝑥 × 10 ℃ . The
resistance of this wire increased from 50 Ω at 25 ℃ to 60 Ω at 75 ℃. The value of
𝑥 is _________ (rounded off to two decimal places).
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Page 42
Q.54 A series RLC circuit is connected to 220 V, 50 Hz supply. For a fixed value of R
and C, the inductor L is varied to deliver the maximum current. This value is
0.4 A and the corresponding potential drop across the capacitor is 330 V. The
value of the inductor L is _________ H (rounded off to two decimal places).
Q.55 In the circuit diagram shown below, the MOSFET is biased in saturation region.
The MOSFET has a threshold voltage 𝑉 = 0.5 𝑉, width 𝑊 = 100 µ𝑚, length
𝐿 = 0.1 µ𝑚, and µ 𝐶 = 100 µ𝐴. 𝑉 .
Assuming 𝑣 = 1 𝑚𝑉 as a small-signal input to MOSFET, the magnitude of the
output voltage 𝑉 is ______ mV (accurate to two decimal places). Ignore channel-
length modulation for the MOSFET.
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Page 43
Q.56 In the circuit diagram shown below, BJTs are biased with 𝑉 = 0.7 𝑉. Neglect
the base current for operating point calculations. Assume infinite input and output
impedance for the BJTs.
The output voltage 𝑉 with small input voltage 𝑣 = 10 𝑚𝑉 is ________ 𝑚𝑉
(rounded off to one decimal place). The thermal voltage 𝑉 = 25 𝑚𝑉 at room
temperature.
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Page 44
Q.57 An ideal opamp with an infinite gain and infinite bandwidth is connected in
feedback as shown below. The output voltage 𝑉 for the given input voltages in
the circuit is _______ V (accurate to one decimal place).
Q.58 Independent voltage measurements (𝜇 ± 𝜎) of three sensors where 𝜇 and 𝜎 are
the mean and standard deviation of the measurements, respectively are as follows:
𝑣 = 4.52 ± 0.02 𝑉, 𝑣 = 4.21 ± 0.20 𝑉, 𝑣 = 3.96 ± 0.15 𝑉.
The measurement uncertainty in 𝑣 + 𝑣 + 𝑣 is ____ V (rounded off to two
decimal places).
Q.59 A moving coil voltmeter has an internal resistance of 50 Ω. The scale of the meter
is divided into 100 equal divisions. When a potential of 1 V is applied to terminals
of voltmeter, a deflection of 100 divisions is obtained. However, it is desired that
when a potential of 500 V is applied to the terminals, a deflection of 100 divisions
should be obtained.
The value of resistance that needs to be connected in series to achieve this is
________ Ω.
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Page 45
Q.60 A Hall effect flow meter is used to measure the volumetric flow through a blood
vessel. The flow meter induces a magnetic field across the vessel and uses a
voltmeter to measure the voltage across the vessel which is normal to both
magnetic field and blood flow. A caliper is used to measure the vessel diameter.
The system calculated the flow rate to be 100 cm3.s-1 using the known magnetic
field, and measured values of voltage and vessel diameter.
After the measurement, a calibration is performed, and it is discovered that the
voltmeter was measuring 40% larger than the actual value and the caliper was
measuring the diameter 10% smaller than the actual value.
Assuming a uniform flow profile along the vessel and ignoring viscosity, the
actual blood flow is ________ cm3.s-1 (rounded off to two decimal places).
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Page 46
Q.61 A catheter based arterial blood pressure measurement device uses a flexible
diaphragm mounted with four identical strain gauges in a Wheatstone bridge
configuration as shown in the figure. Assume that the strain gauges have a
nominal resistance value of RG = 10 kΩ, Gauge Factor G = 40 and Young’s
Modulus E = 10 MPa. Blood pressure variations results in small finite change in
strain 𝜖 (𝜖 > 0).
If Vo is the output voltage of the Wheatstone bridge and 𝜎 is the stress in MPa, the
𝑽𝒐
sensitivity is _______ V.MPa-1.
𝝈
Q.62 A patient has a breathing rate of 18 breaths per minute, with a tidal volume of 500
mL, having an anatomical dead space of 150 mL. If the person has a heart rate of
120 beats per minute and a stroke volume of 50 mL, the alveolar ventilation to
perfusion ratio is _____________ (accurate to two decimal places).
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Q.63 Assume that the ratio of total blood volume in liters to total body weight in kg is
0.07 and the blood consists of plasma and RBCs only. The plasma volume of a
70-kg man with 52% hematocrit is ______ L (rounded off to two decimal places).
Q.64 The 1st generation (1G) CT scanner uses a point X-ray source and a detector. The
source detector assembly can move linearly at a speed of 0.5 m.s-1 and that it takes
0.5 s for source-detector assembly to rotate one angular increment, regardless of
the angle.
This scanner is expected to collect 360 projections over 180° of span. The field of
view used for data collection has a diameter of 0.5 m. The scan time required is
______ s.
Q.65 The inverse square law has a very practical use in radiography. While taking an
acceptable chest radiograph of a subject at a distance of 0.75 m from the X-ray
generator, X-ray source settings were kept at 50 kVp, 50 mA.s.
If the subject is moved to a distance of 1 m, and the kVp is kept the same, the new
value of mA.s to obtain the same exposure will be _____ mA.s (rounded off to
two decimal places).
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