GATE 2025 Question Paper Biomedical Engineering (BM)

GATE
2025
Question Paper | Answer Key
Graduate Aptitude Test in Engineering
(GATE) is a prestigious national-level exam
that assesses candidates for
comprehensive understanding in various
undergraduate-level subjects in
Engineering, Technology, Science,
Architecture, and Humanities.

General Aptitude
Q.1 – Q.5 Carry ONE mark Each

Q.1 Here are two analogous groups, Group-I and Group-II, that list words in their
decreasing order of intensity. Identify the missing word in Group-II.

Group-I: Abuse → Insult → Ridicule

Group-II: ________ → Praise → Appreciate

(A) Extol

(B) Prize

(C) Appropriate

(D) Espouse

Q.2 Had I learnt acting as a child, I ________ a famous film star.

Select the most appropriate option to complete the above sentence.

(A) will be

(B) can be

(C) am going to be

(D) could have been

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Q.3 The 12 musical notes are given as 𝐶, 𝐶 # , 𝐷, 𝐷# , 𝐸, 𝐹, 𝐹 # , 𝐺, 𝐺 # , 𝐴, 𝐴# , and 𝐵.
12
Frequency of each note is √2 times the frequency of the previous note. If the
frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes 𝐹 # and 𝐶
is:

(A) 6
√2

(B)
√2

(C) 4
√2

(D) 2

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Q.4 The following figures show three curves generated using an iterative algorithm. The
total length of the curve generated after ‘Iteration 𝑛’ is:

Note: The figures shown are representative.

1
Iteration 0:

1 1
Iteration 1: Length of each segment:
3 3

1
1
Iteration 2: 9 Length of each segment:
9

𝑛
(A) 5 2
( )
3

(B) 5 𝑛
( )
3

(C) 5 2𝑛
( )
3

(D) 5 𝑛(2𝑛−1)
( )
3

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Q.5 |𝑥|
Which one of the following plots represents 𝑓 (𝑥 ) = − , where 𝑥 is a non-
𝑥
zero real number?

Note: The figures shown are representative.

f(x)
(A)
(0,1)

x
(0, −1)

f(x)
(B)
(0,1)

x
(0, −1)

f(x)
(C)

(1,0)
x
(−1,0)

f(x)
(D)
(0,1)

x
(0, −1)

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Q.6 – Q.10 Carry TWO marks Each

Q.6 Identify the option that has the most appropriate sequence such that a coherent
paragraph is formed:

P. Over time, such adaptations lead to significant evolutionary changes with
the potential to shape the development of new species.

Q. In natural world, organisms constantly adapt to their environments in
response to challenges and opportunities.

R. This process of adaptation is driven by the principle of natural selection,
where favorable traits increase an organism’s chances of survival and
reproduction.

S. As environments change, organisms that can adapt their behavior, structure
and physiology to such changes are more likely to survive.

(A) P→Q→R→S

(B) Q→S→R→P

(C) R→S→Q→P

(D) S→P→R→Q

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Q.7 A stick of length one meter is broken at two locations at distances of 𝑏1 and 𝑏2 from
the origin (0), as shown in the figure. Note that 0 < 𝑏1 < 𝑏2 < 1. Which one of the
following is NOT a necessary condition for forming a triangle using the three
pieces?

Note: All lengths are in meter. The figure shown is representative.

(A) 𝑏1 < 0.5

(B) 𝑏2 > 0.5

(C) 𝑏2 < 𝑏1 + 0.5

(D) 𝑏1 + 𝑏2 < 1

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Q.8 Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure
indicates their order of position at the start of the game. They play the game by
moving forward in a circle in the clockwise direction.

After the 1st round, 4th student behind P leaves the game. After 2nd round, 5th student
behind Q leaves the game. After 3rd round, 3rd student behind V leaves the game.
After 4th round, 4th student behind U leaves the game. Who all are left in the game
after the 4th round?

Note: The figure shown is representative.

P

W R

U T

Q
V

S

(A) P; T; Q; S

(B) V; P; T; Q

(C) W; R; Q; V

(D) Q; T; V; W

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Q.9 The table lists the top 5 nations according to the number of gold medals won in a
tournament; also included are the number of silver and the bronze medals won by
them. Based only on the data provided in the table, which one of the following
statements is INCORRECT?

Nation Gold Silver Bronze

USA 40 44 41

Canada 39 27 24

Japan 20 12 13

Australia 17 19 16

France 16 26 22

(A) France will occupy the third place if the list were made on the basis of the total
number of medals won.

(B) The order of the top two nations will not change even if the list is made on the basis
of the total number of medals won.

(C) USA and Canada together have less than 50% of the medals awarded to the nations
in the above table.

(D) Canada has won twice as many total medals as Japan.

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Q.10 An organization allows its employees to work independently on consultancy
projects but charges an overhead on the consulting fee. The overhead is 20% of the
consulting fee, if the fee is up to ₹ 5,00,000. For higher fees, the overhead is
₹ 1,00,000 plus 10% of the amount by which the fee exceeds ₹ 5,00,000. The
government charges a Goods and Services Tax of 18% on the total amount (the
consulting fee plus the overhead). An employee of the organization charges this
entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client
cannot pay more than ₹ 10,00,000, what is the maximum consulting fee that the
employee can charge?

(A) ₹ 7,01,438

(B) ₹ 7,24,961

(C) ₹ 7,51,232

(D) ₹ 7,75,784

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Q.11 – Q.35 Carry ONE mark Each

Q.11 Consider two cuboidal blocks of volume 1 cm3 each, one made of gold and the
other of undoped silicon. What will happen to the resistivity of these blocks if the
temperature is increased from 300 K to 350 K? Choose one of the following.

(A) Resistivity of gold increases and undoped silicon decreases

(B) Resistivity of gold decreases and undoped silicon increases

(C) Resistivity of gold remains same and undoped silicon increases

(D) Resistivity of gold decreases and undoped silicon remains same

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Q.12 Which one of the following represents the frequency response of a notch filter?

(A)

(B)

(C)

(D)

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Q. 13 Given the following statements, which one of the options is correct?

Statement (i): Histology is the study of histones

Statement (ii): Cytology is the study of tissues

(A) Both the statements are correct

(B) Both the statements are incorrect

(C) Statement (i) is correct; statement (ii) is incorrect

(D) Statement (i) is incorrect; statement (ii) is correct

Q. 14 Given the following statements, which one of the options is correct?

Statement (i): Structural Magnetic Resonance Imaging (sMRI) has better spatial
resolution than Electroencephalogram (EEG)

Statement (ii): EEG has better temporal resolution than sMRI

(A) Both the statements are correct

(B) Both the statements are incorrect

(C) Statement (i) is correct; statement (ii) is incorrect

(D) Statement (i) is incorrect; statement (ii) is correct

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Q. 15 In the circuit shown below, assuming an ideal op-amp, for an input voltage
Vin = 1V, the output voltage Vout = ______________ (in volts).

(A) 1.0

(B) 2.0

(C) 0.5

(D) 0.1

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Consider the following statements:
Q. 16
Assertion: Positron Emission Tomography (PET) uses radionuclides, such as 11C
and 15N, to study tissue metabolism.

Reason: Positron-emitting nuclides are incorporated in molecules that are essential
for metabolism.

(A) Both Assertion and Reason are true; Reason is not the correct explanation for the
Assertion

(B) Both Assertion and Reason are true; Reason is the correct explanation for the
Assertion

(C) Assertion is true, but Reason is false

(D) Both Assertion and Reason are false

Q. 17 The determinant of a 3 × 3 matrix 𝑀 is 8. If every element of 𝑀 is multiplied
by −2, the determinant of the modified matrix will be

(A) −64

(B) −16

(C) 8

(D) 64

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Q. 18 For any continuous and differentiable function 𝑓(𝑥) with first derivative
𝑓 ′ (𝑥) ≠ 0 for all values of 𝑥, which one of the following is ALWAYS TRUE for
𝑎 ≠ 𝑏?

Here, 𝑎 and 𝑏 are finite and real.

(A) 𝑓(𝑎) > 𝑓(𝑏)

(B) 𝑓(𝑎) = 𝑓(𝑏)

(C) 𝑓(𝑎) ≠ 𝑓(𝑏)

(D) 𝑓(𝑎) < 𝑓(𝑏)

Q. 19 The closed loop system shown below ______________.

(A) is overdamped

(B) is underdamped

(C) is critically damped

(D) has sustained oscillations

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Q. 20 Which one of the following statements is CORRECT for any second order linear
system with Proportional Integral Derivative (PID) controller?

(A) Integral component decreases residual steady state error

(B) Integral component integrates the output signal only

(C) Integral component increases residual steady state error

(D) Integral component integrates the input signal only

Q. 21 𝑐𝑜𝑠𝜃 −𝑠𝑖𝑛𝜃
The eigenvalues of the matrix ( ) are ______________.
𝑠𝑖𝑛𝜃 𝑐𝑜𝑠𝜃

(A) 𝑐𝑜𝑠𝜃 and 𝑠𝑖𝑛𝜃

(B) 𝑒 𝑖𝜃 and 𝑒 −𝑖𝜃 , where 𝑖 = √−1

(C) 𝑐𝑜𝑠𝜃 and – 𝑠𝑖𝑛𝜃

(D) 𝑐𝑜𝑠2𝜃 and 𝑠𝑖𝑛2𝜃

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Q. 22 Let 𝑅1 , 𝑅2 and 𝑅3 be the Reynolds numbers corresponding to the following three
cases, respectively

Case 1: A 1 𝜇m long bacterium swimming in water

Case 2: A 10 cm long fish swimming in water

Case 3: A 10 m long whale swimming in water

If each of them covers a distance equal to their respective body length in one
second, which one of the following is CORRECT?

(A) 𝑅1 > 𝑅2 > 𝑅3

(B) 𝑅1 < 𝑅2 < 𝑅3

(C) 𝑅3 < 𝑅1 < 𝑅2

(D) 𝑅2 < 𝑅1 < 𝑅3

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Q. 23 The shape of an elastic rod of length 𝑙 is represented by the position vector 𝑟⃗(𝑠)
corresponding to the arc length 𝑠. If the bending energy of the rod is

𝑙 2
𝜕 2 𝑟⃗
𝐸 = 𝐾 ∫ ( 2 ) 𝑑𝑠,
0 𝜕𝑠

what is the dimension of 𝐾 in terms of mass M, length L and time T ?

(A) 𝑀𝐿𝑇 −2

(B) 𝑀𝐿3 𝑇 −2

(C) 𝑀𝐿2 𝑇 −2

(D) 𝑀𝐿3 𝑇 −1

Q. 24 The duration of action potential in a ventricular muscle cell of a human heart ranges
from ______________ milliseconds.

(A) 2 to 3

(B) 200 to 300

(C) 2000 to 3000

(D) 20 to 30

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Q. 25 9 10 9 8
6C and 6C are ______________, whereas 6C and 5B are ______________.

(A) isotopes; isomers

(B) isomers; isotopes

(C) isotopes; isotones

(D) isotones; isotopes

Q. 26 Cerebrospinal fluid in humans is present in the ______________ space.

(A) subdural

(B) subarachnoid

(C) pericardial

(D) epidural

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Q.27 In the context of temperature sensitive polymers, LCST stands for
______________.

(A) Large Critical Solution Temperature

(B) Local Critical Solute Temperature

(C) Large Critical Solvent Temperature

(D) Lower/Lowest Critical Solution Temperature

Q.28 In the electrocardiogram (ECG) of humans, the electrical signature of atrial
repolarization is masked by the ______________.

(A) P wave

(B) QRS complex

(C) T wave

(D) ST segment

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Q.29 Which one of the following hormones is NOT secreted by the adrenal gland in
humans?

(A) Cortisol

(B) Epinephrine

(C) Oxytocin

(D) Aldosterone

Q.30 Which one of the following does NOT use piezoelectric transducers?

(A) Ultrasonography

(B) Phonocardiography

(C) Echocardiography

(D) Electroencephalography

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Q.31 A low pass filter with cutoff frequency of 250 Hz is NOT suitable for recording
______________.

(A) Electrocardiogram (ECG)

(B) Electroencephalogram (EEG)

(C) Electromyogram (EMG)

(D) Electrooculogram (EOG)

Q.32 1 𝑓(1+ ∆𝑥)− 𝑓(1)
If 𝑓(𝑥) = 𝑥 − , the value of lim is ______________.
𝑥 ∆𝑥→0 ∆𝑥

(A) 0

(B) 1
2

(C) 1

(D) 2

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Q.33 The elements of the dataset {−5,1, 𝑎, 5, 𝑏} are in ascending order. If both mean
and median of the dataset are equal to 3, what is the value of 𝑏?

(A) 7

(B) 11

(C) 9

(D) 12

Q.34 For a tissue with Young’s modulus 4 kPa and shear modulus 1.5 kPa, what is the
value of the Poisson’s ratio?

(A) 1
5

(B) 1
3

(C) 1
4

(D) 1
2

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Q.35 The Electroencephalogram (EEG) voltage measured by a test device is 2.4 µV,
while the reference device measured it to be 3.0 µV. What is the percentage error
of the test device?

(A) 25%

(B) 20%

(C) 10%

(D) 0.6%

Q.36 – Q.65 Carry TWO marks Each

Q.36
A time domain signal is given by

𝑥(𝑡) = 20 sin(100𝜋𝑡) + 36 sin(150𝜋𝑡) − 2sin (300𝜋𝑡),

where time t is in seconds. Among the following options, what is the frequency (in
Hz) at which 𝑥(𝑡) should be sampled for accurate signal reconstruction?

(A) 500

(B) 150

(C) 200

(D) 250

Organizing Institute: IIT Roorkee Page 24 of 39

Q.37 𝜋
A voltage source 𝑉𝑠 = 5sin (100𝑡 + ) volts is driving a current
2
𝜋
𝐼 = 10 sin (100𝑡 + ) mA through a circuit.
6

The average power dissipated in the circuit is ______________ mW.

(A) 0.0

(B) 12.5

(C) 25.0

(D) 50.0

Q.38 𝑁 independent trials of a binomial random variable yield an expectation value of 16
and variance of 12. What is the value of 𝑁?

(A) 80

(B) 60

(C) 45

(D) 64

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Q.39 Given a function 𝑦(𝑥) satisfying the differential equation

𝑦 ′′ − 0.25𝑦 = 0,

with initial conditions 𝑦(0) = 1; 𝑦 ′ (0) = 1, what is the value of 𝑦(log 𝑒 100)?

Here, 𝑦 ′ and 𝑦 ′′ are the first and second derivatives of 𝑦, respectively.

(A) 14.05

(B) 14.25

(C) 14.95

(D) 14.65

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Q.40 In the circuit shown below, Vin =10cos(1000𝑡) volts. The magnitude of the input
impedance of the circuit is ____________ kΩ. (rounded off to one decimal place)

(A) 5.0

(B) 3.5

(C) 6.0

(D) 4.5

Organizing Institute: IIT Roorkee Page 27 of 39

Q.41 Gelatin solutions P and Q of concentrations 3.5% and 0.5%, respectively, need to
be mixed to obtain a 3% solution R. How much volume (in ml) of P needs to be
mixed with 100 ml of Q to obtain R? (Choose the correct option)

All concentrations are in units of weight/volume.

(A) 100

(B) 250

(C) 500

(D) 1000

Q.42 Which of the following is/are CORRECT about the value of 𝑦 = log 𝑒 (−𝑒 𝑥 ),
where 𝑥 is a real number.

(A) 𝑦 is real valued

(B) 𝑦 is complex valued

(C) 𝑦 = 𝑥 ± 𝑖𝑛𝜋, where 𝑛 is an odd integer and 𝑖 = √−1

(D) 𝑦 = 𝑥 ± 𝑖𝑛𝜋, where 𝑛 is an even integer and 𝑖 = √−1

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Q.43 Which of the following statement(s) about ultrasound waves is/are true?

(A) Acoustic impedance of biological tissues is directly proportional to its density

(B) The reflection coefficient depends on the impedance mismatch at the interface of
two biological tissues

(C) The transmission coefficient is independent of the impedance of biological tissues

(D) Biological tissues do not reflect ultrasound waves

Q.44 Two systems 𝑈 and 𝑉 are defined as shown below. Which of the following
statement(s) is/are CORRECT?

(A) System 𝑈 is nonlinear; System 𝑉 is linear

(B) System 𝑈 is causal; System 𝑉 is noncausal

(C) System 𝑈 is noncausal; System 𝑉 is causal

(D) System 𝑈 is nonlinear; System 𝑉 is nonlinear

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Q.45 Which of the following statement(s) about pulse oximetry is/are TRUE?

(A) Oxygenated hemoglobin absorbs less infrared light (900 nm) compared to
deoxygenated hemoglobin

(B) Oxygenated hemoglobin absorbs less visible light (600 nm) compared to
deoxygenated hemoglobin

(C) Oxygenated hemoglobin absorbs more visible light (600 nm) compared to
deoxygenated hemoglobin

(D) Oxygenated hemoglobin absorbs more infrared light (900 nm) compared to
deoxygenated hemoglobin

Q.46 Which of the following statement(s) is/are CORRECT about neuronal membrane
and neuronal action potential?

(A) Application of an outward current depolarizes the neuronal membrane

(B) Application of an inward current depolarizes the neuronal membrane

(C) Increasing the stimulus strength increases the amplitude of neuronal action
potential

(D) Increasing the stimulus strength decreases the latency of neuronal action potential

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Q.47 A discrete linear time invariant system has an impulse response function given by
1 1
ℎ[𝑛] = 𝛿[𝑛] + 𝛿[𝑛 − 1] + 𝛿[𝑛 − 2].
2 3

For input signal 𝑥[𝑛] = 𝛿[𝑛] + 𝛿[𝑛 − 1], which of the following option(s)
is/are CORRECT for the output signal 𝑦[𝑛]?

(A) 𝑦[2] = 11/6

(B) 𝑦[2] = 5/6

(C) 𝑦[𝑘] = 0 for all 𝑘 ≥ 3

(D) 𝑦[𝑘] = 0 for all 𝑘 ≥ 4

Q.48 Which of the following statement(s) is/are CORRECT about isotonic and
isometric tests?

(A) In an isotonic test, muscle is subjected to a constant tension and its length is
recorded.

(B) In an isotonic test, muscle is held at constant length, and the contractile force
generated by the muscle is recorded.

(C) In an isometric test, muscle is held at constant length, and the contractile force
generated by the muscle is recorded.

(D) In an isometric test, muscle is subjected to a constant tension and its length is
recorded.

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Q.49 A Newtonian fluid of viscosity 𝜇 is undergoing laminar flow in a tube of radius 𝑅.
For a constant pressure drop per unit length along the tube, which of the following
statement(s) is/are CORRECT?

Note: 𝑟 represents the radial position; assume no slip condition at the boundaries.

(A) 𝑟2
The radial profile of the flow velocity is proportional to (1 − )
𝑅2

(B) 𝑟3
The radial profile of the flow velocity is proportional to (1 − )
𝑅3

(C) Shear stress is zero at 𝑟 = 𝑅

(D) Shear stress is zero at 𝑟 = 0

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Q.50 At a given frequency, the storage modulus (𝐺 ′ ) and loss modulus (𝐺 ′′ ) of four
biomaterials are shown in the table below. Which of the following option(s) is/are
CORRECT?

Biomaterial 𝐺 ′ (Pa) 𝐺 ′′ (Pa)

P 1000 50

Q 1000 80

R 1000 100

S 1000 0

(A) P, Q and R are viscoelastic solids

(B) P, Q and R are viscoelastic fluids

(C) R and S are viscoelastic solids

(D) S is an elastic solid

Q.51 For an 8-bit Digital to Analog Converter (DAC), the binary input 0000 0000 results
in 0 V, and 1111 1111 results in 5 V. The output of the DAC for an input of
1011 0111 is ______________ (in volts, rounded off to two decimal places).

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Q.52 What is the output voltage Vout for the circuit shown below?

______________ (in volts, rounded off to the nearest integer).

Q.53 Resistance 𝑅 of a thermistor varies as a function of temperature 𝑇 such that

1 1
𝑅(𝑇) = 𝑅0 exp [𝛽 ( − )],
𝑇 𝑇 0

where 𝛽 = 3100 K and, 𝑅0 and 𝑇0 are positive constants.

If the relative error in measuring 𝑅 is 10%, what is the relative error (in percentage)
in measuring 310 K temperature? ______________ (rounded off to the nearest
integer)

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Q.54 The frequency of the oscillator circuit shown in the figure below is
______________ kHz. (rounded off to two decimal places)

Given: R = 1 kΩ; R1 = 2 kΩ; R2 = 6 kΩ; C = 0.1 µF

Organizing Institute: IIT Roorkee Page 35 of 39

Q.55 For the RLC circuit shown below, the root mean square current (𝐼𝑟𝑚𝑠 ) at the
resonance frequency is ______________ amperes. (rounded off to the nearest
integer)

Q.56 The plot of log10 (𝐵𝑀𝑅) as a function of log10 (𝑀) is a straight line with slope 0.75,
where 𝑀 is the mass of the person and 𝐵𝑀𝑅 is the Basal Metabolic Rate. If a child
with 𝑀 = 10 kg has a 𝐵𝑀𝑅 = 600 kcal/day, the 𝐵𝑀𝑅 for an adult with
𝑀 = 100 kg is ______________ kcal/day. (rounded off to the nearest integer)

Q.57 Newton Raphson method is used to solve the equation 𝑥 3 − 2𝑥 − 5 = 0 with an
initial guess 𝑥0 = 3. What is 𝑥1 , the value after ONE iteration? ______________
(rounded off to two decimal places)

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Q.58 For pulsatile blood flow through an artery of internal diameter 20 mm, wall
thickness 1 mm and Young’s Modulus 1 MPa, what is the wave speed in metres per
second? ______________ (rounded off to one decimal place).

Assume the density of blood to be 1050 kg/m3.

Q.59 An ideal, massless spring with spring constant 1 N/m (upper panel of the given
figure) is cut into 5 equal parts. If two of these parts are connected in parallel (lower
panel of the given figure), what is the resultant spring constant in N/m?
______________ (rounded off to the nearest integer)

Assume linear behavior of the springs.

Q.60 Polylactic-co-glycolic acid (PLGA) is combined with an equal amount (by weight)
of hydroxyapatite (HA) to make a bone scaffold. If the porosity of the scaffold is
80%, what is the scaffold density in g/cm3? ______________ (rounded off to two
decimal places)

Assume densities of PLGA and HA to be 1 g/cm3 and 3 g/cm3, respectively.

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Q.61 Strength (𝜎) of an implanted suture is given by the equation

𝜎 = 𝜎0 − 2 log 𝑒 (𝑡) for 𝑡 ≥ 1,

where 𝜎0 represents the original strength and time 𝑡 is measured in weeks. If the
strength of the suture is 2 MPa at 4 weeks, what will be its strength (in MPa)
at 8 weeks? ______________ (rounded off to two decimal places)

Q.62 If the gyromagnetic ratio of proton is 42.58 MHz per Tesla, the resonance frequency
for protons in a magnetic field of 1.5 Tesla is ______________ MHz. (rounded off
to two decimal places)

Organizing Institute: IIT Roorkee Page 38 of 39

Q.63 A Wheatstone bridge is used to measure strain as shown in the figure below.
Initially the bridge was balanced. When a strain is applied to the resistor Rstrain,
along its length, the output voltage VOUT is 10 mV.

If Rstrain is a cylindrical resistor of length 𝑙 and cross-sectional area 𝐴, the
magnitude of the applied strain is ______________. (rounded off to two decimal
places)

The storage modulus (𝐺 ′ ) of a collagen gel scales as 𝐺 ′ ~[𝐶]3 , where [𝐶] represents
Q.64 the collagen concentration in mg/ml. If the storage modulus of a 1 mg/ml collagen
gel is 100 Pa, then the storage modulus of a 3 mg/ml collagen gel is
______________ Pa. (rounded off to the nearest integer)

The cardiac output of a person at rest is 5 litres per minute and the mean aortic
Q.65 pressure is 100 mmHg. During exercise, if the cardiac output doubles and mean
aortic pressure rises to 110 mmHg, then the peripheral resistance in the systemic
circulation will decrease by ______________%. (rounded off to the nearest integer)

Assume venous pressure in systemic circulation to be negligible.

Organizing Institute: IIT Roorkee Page 39 of 39

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