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

Engineering Mathematics

9 Questions

GATE→2025→Engineering Mathematics→Linear Algebra

Q1

MCQ[1 Mark]

The determinant of a $3 \times 3$ 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

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q2

MCQ[1 Mark]

For any continuous and differentiable function $f(x)$ with first derivative $f'(x) \neq 0$ for all values of $x$, which one of the following is ALWAYS TRUE for $a \neq b$? Here, $a$ and $b$ are finite and real.

(A)

$f(a) > f(b)$

(B)

$f(a) = f(b)$

(C)

$f(a) \neq f(b)$

(D)

$f(a) < f(b)$

Explanation

GATE→2025→Engineering Mathematics→Linear Algebra

Q3

MCQ[1 Mark]

The eigenvalues of the matrix $\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$ are

(A)

$\cos\theta$ and $\sin\theta$

(B)

$e^{i\theta}$ and $e^{-i\theta}$ where $i = \sqrt{-1}$

(C)

$\cos\theta$ and $-\sin\theta$

(D)

$\cos 2\theta$ and $\sin 2\theta$

Explanation

GATE→2025→Engineering Mathematics→Calculus

Q4

MCQ[1 Mark]

If $f(x) = x - \frac{1}{x}$, the value of $\lim_{\Delta x \to 0} \frac{f(1 + \Delta x) - f(1)}{\Delta x}$ is

(A)

0

(B)

$\frac{1}{2}$

(C)

1

(D)

2

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q5

MCQ[1 Mark]

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

Explanation

GATE→2025→Engineering Mathematics→Probability and Statistics

Q6

MCQ[2 Marks]

$N$ 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)

32

(C)

48

(D)

64

Explanation

GATE→2025→Engineering Mathematics→Differential Equations

Q7

MCQ[2 Marks]

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

Explanation

GATE→2025→Engineering Mathematics→Analysis of Complex Variables

Q8

MSQ[2 Marks]

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)

$y = x \pm i n\pi$, where $n$ is an odd integer and $i = \sqrt{-1}$

(D)

$y = x \pm i n\pi$, where $n$ is an even integer and $i = \sqrt{-1}$

Explanation

GATE→2025→Engineering Mathematics→Numerical Methods

Q9

NAT[2 Marks]

Newton Raphson method is used to solve the equation $x^3 - 2x - 5 = 0$ with an initial guess $x_0 = 3$. What is $x_1$, the value after ONE iteration? (rounded off to two decimal places)

Explanation

Biomedical Engineering Core

46 Questions

GATE→2025→Biomedical Engineering Core→Analog and Digital Electronics

Q10

MCQ[1 Mark]

Consider two cuboidal blocks of volume $1\text{ cm}^3$ 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 $300\text{ K}$ to $350\text{ K}$? 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

Explanation

GATE→2025→Biomedical Engineering Core→Electrical Circuits

Q11

MCQ[1 Mark]

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

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q12

MCQ[1 Mark]

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

Explanation

GATE→2025→Biomedical Engineering Core→Medical Imaging Systems

Q13

MCQ[1 Mark]

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

Explanation

GATE→2025→Biomedical Engineering Core→Analog and Digital Electronics

Q14

MCQ[1 Mark]

In the circuit shown below, assuming an ideal op-amp, for an input voltage $V_{\text{in}} = 1\text{ V}$, the output voltage $V_{\text{out}} =$ ________ (in volts).

(A)

1.0

(B)

2.0

(C)

0.5

(D)

0.1

Explanation

GATE→2025→Biomedical Engineering Core→Medical Imaging Systems

Q15

MCQ[1 Mark]

Consider the following statements: **Assertion:** Positron Emission Tomography (PET) uses radionuclides, such as $^{11}\text{C}$ and $^{15}\text{N}$, 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

Explanation

GATE→2025→Biomedical Engineering Core→Measurements and Control Systems

Q16

MCQ[1 Mark]

The closed loop system shown below with open-loop transfer function $G(s) = \frac{25}{s(s+5)}$ and unity negative feedback

(A)

is overdamped

(B)

is underdamped

(C)

is critically damped

(D)

has sustained oscillations

Explanation

GATE→2025→Biomedical Engineering Core→Measurements and Control Systems

Q17

MCQ[1 Mark]

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

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q18

MCQ[1 Mark]

Let $R_1$, $R_2$ and $R_3$ be the Reynolds numbers corresponding to the following three cases, respectively: * **Case 1:** A $1\text{ }\mu\text{m}$ long bacterium swimming in water * **Case 2:** A $10\text{ cm}$ long fish swimming in water * **Case 3:** A $10\text{ m}$ 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)

$R_1 > R_2 > R_3$

(B)

$R_1 < R_2 < R_3$

(C)

$R_3 < R_1 < R_2$

(D)

$R_2 < R_1 < R_3$

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q19

MCQ[1 Mark]

The shape of an elastic rod of length $l$ is represented by the position vector $\vec{r}(s)$ corresponding to the arc length $s$. If the bending energy of the rod is $$E = K \int_0^l \left(\frac{\partial^2 \vec{r}}{\partial s^2}\right)^2 ds,$$ what is the dimension of $K$ in terms of mass $M$, length $L$ and time $T$?

(A)

$MLT^{-2}$

(B)

$ML^3T^{-2}$

(C)

$ML^2T^{-2}$

(D)

$ML^3T^{-1}$

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q20

MCQ[1 Mark]

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

Explanation

GATE→2025→Biomedical Engineering Core→Medical Imaging Systems

Q21

MCQ[1 Mark]

$_{6}^{9}\text{C}$ and $_{6}^{10}\text{C}$ are ________, whereas $_{6}^{9}\text{C}$ and $_{5}^{8}\text{B}$ are ________.

(A)

isotopes; isomers

(B)

isomers; isotopes

(C)

isotopes; isotones

(D)

isotones; isotopes

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q22

MCQ[1 Mark]

Cerebrospinal fluid in humans is present in the ________ space.

(A)

subdural

(B)

subarachnoid

(C)

pericardial

(D)

epidural

Explanation

GATE→2025→Biomedical Engineering Core→Biomaterials

Q23

MCQ[1 Mark]

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

Explanation

GATE→2025→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q24

MCQ[1 Mark]

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

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q25

MCQ[1 Mark]

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

(A)

Cortisol

(B)

Epinephrine

(C)

Oxytocin

(D)

Aldosterone

Explanation

GATE→2025→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q26

MCQ[1 Mark]

Which one of the following does NOT use piezoelectric transducers?

(A)

Ultrasonography

(B)

Phonocardiography

(C)

Echocardiography

(D)

Electroencephalography

Explanation

GATE→2025→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q27

MCQ[1 Mark]

A low pass filter with cutoff frequency of $250\text{ Hz}$ is NOT suitable for recording

(A)

Electrocardiogram (ECG)

(B)

Electroencephalogram (EEG)

(C)

Electromyogram (EMG)

(D)

Electrooculogram (EOG)

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q28

MCQ[1 Mark]

For a tissue with Young's modulus $4\text{ kPa}$ and shear modulus $1.5\text{ kPa}$, what is the value of the Poisson's ratio?

(A)

$\frac{1}{5}$

(B)

$\frac{1}{3}$

(C)

$\frac{1}{4}$

(D)

$\frac{1}{2}$

Explanation

GATE→2025→Biomedical Engineering Core→Measurements and Control Systems

Q29

MCQ[1 Mark]

The Electroencephalogram (EEG) voltage measured by a test device is $2.4\text{ }\mu\text{V}$, while the reference device measured it to be $3.0\text{ }\mu\text{V}$. What is the percentage error of the test device?

(A)

25%

(B)

20%

(C)

10%

(D)

0.6%

Explanation

GATE→2025→Biomedical Engineering Core→Signals and Systems

Q30

MCQ[2 Marks]

A time domain signal is given by $$x(t) = 20\sin(100\pi t) + 36\sin(150\pi t) - 2\sin(300\pi t),$$ 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)

125

(D)

250

Explanation

GATE→2025→Biomedical Engineering Core→Electrical Circuits

Q31

MCQ[2 Marks]

A voltage source $V_s = 5\sin\left(100t + \frac{\pi}{2}\right)\text{ volts}$ is driving a current $I = 10\sin\left(100t + \frac{\pi}{6}\right)\text{ mA}$ through a circuit. The average power dissipated in the circuit is ________ $\text{mW}$.

(A)

0.0

(B)

12.5

(C)

25.0

(D)

50.0

Explanation

GATE→2025→Biomedical Engineering Core→Electrical Circuits

Q32

MCQ[2 Marks]

In the circuit shown below, $V_{\text{in}} = 10\cos(1000t)\text{ volts}$. The magnitude of the input impedance of the circuit is ________ $\text{k}\Omega$. (rounded off to one decimal place)

(A)

5.0

(B)

3.5

(C)

6.0

(D)

4.5

Explanation

GATE→2025→Biomedical Engineering Core→Biomaterials

Q33

MCQ[2 Marks]

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 $100\text{ mL}$ 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

Explanation

GATE→2025→Biomedical Engineering Core→Medical Imaging Systems

Q34

MSQ[2 Marks]

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

Explanation

GATE→2025→Biomedical Engineering Core→Signals and Systems

Q35

MSQ[2 Marks]

Two systems U and V are defined as shown below. Which of the following statement(s) is/are CORRECT? * **System U:** $x(t) \longrightarrow y(t) = x(t)^2 + 1$ * **System V:** $x(t) \longrightarrow y(t) = x(t+1)$

(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

Explanation

GATE→2025→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q36

MSQ[2 Marks]

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

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q37

MSQ[2 Marks]

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

Explanation

GATE→2025→Biomedical Engineering Core→Signals and Systems

Q38

MSQ[2 Marks]

A discrete linear time invariant system has an impulse response function given by $$h[n] = \delta[n] + \frac{1}{2}\delta[n-1] + \frac{1}{3}\delta[n-2].$$ For input signal $x[n] = \delta[n] + \delta[n-1]$, 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 $k \ge 3$

(D)

$y[k] = 0$ for all $k \ge 4$

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q39

MSQ[2 Marks]

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.

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q40

MSQ[2 Marks]

A Newtonian fluid of viscosity $\mu$ 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)

The radial profile of the flow velocity is proportional to $\left(1 - \frac{r^2}{R^2}\right)$

(B)

The radial profile of the flow velocity is proportional to $\left(1 - \frac{r^3}{R^3}\right)$

(C)

Shear stress is zero at $r = R$

(D)

Shear stress is zero at $r = 0$

Explanation

GATE→2025→Biomedical Engineering Core→Biomaterials

Q41

MSQ[2 Marks]

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 | $G'\text{ (Pa)}$ | $G''\text{ (Pa)}$ | | :---: | :---: | :---: | | 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

Explanation

GATE→2025→Biomedical Engineering Core→Analog and Digital Electronics

Q42

NAT[2 Marks]

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

Explanation

GATE→2025→Biomedical Engineering Core→Analog and Digital Electronics

Q43

NAT[2 Marks]

What is the output voltage $V_{\text{out}}$ for the circuit shown below? (in volts, rounded off to the nearest integer).

Explanation

GATE→2025→Biomedical Engineering Core→Measurements and Control Systems

Q44

NAT[2 Marks]

Resistance $R$ of a thermistor varies as a function of temperature $T$ such that $$R(T) = R_0 \exp\left[\beta\left(\frac{1}{T} - \frac{1}{T_0}\right)\right],$$ where $\beta = 3100\text{ K}$, and $R_0$ and $T_0$ are positive constants. If the relative error in measuring $R$ is $10\%$, what is the relative error (in percentage) in measuring $310\text{ K}$ temperature? (rounded off to the nearest integer)

Explanation

GATE→2025→Biomedical Engineering Core→Analog and Digital Electronics

Q45

NAT[2 Marks]

The frequency of the oscillator circuit shown in the figure below is ________ $\text{kHz}$. (rounded off to two decimal places) Given: $R = 1\text{ k}\Omega$; $R_1 = 2\text{ k}\Omega$; $R_2 = 6\text{ k}\Omega$; $C = 0.1\text{ }\mu\text{F}$

Explanation

GATE→2025→Biomedical Engineering Core→Electrical Circuits

Q46

NAT[2 Marks]

For the RLC circuit shown below, the root mean square current ($I_{\text{rms}}$) at the resonance frequency is ________ amperes. (rounded off to the nearest integer)

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q47

NAT[2 Marks]

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

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q48

NAT[2 Marks]

For pulsatile blood flow through an artery of internal diameter $20\text{ mm}$, wall thickness $1\text{ mm}$ and Young's Modulus $1\text{ MPa}$, what is the wave speed in metres per second? ________ (rounded off to one decimal place). Assume the density of blood to be $1050\text{ kg/m}^3$.

Explanation

GATE→2025→Biomedical Engineering Core→Biomechanics

Q49

NAT[2 Marks]

An ideal, massless spring with spring constant $1\text{ N/m}$ (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 $\text{N/m}$? (rounded off to the nearest integer) Assume linear behavior of the springs.

Explanation

GATE→2025→Biomedical Engineering Core→Biomaterials

Q50

NAT[2 Marks]

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 $\text{g/cm}^3$? (rounded off to two decimal places) Assume densities of PLGA and HA to be $1\text{ g/cm}^3$ and $3\text{ g/cm}^3$, respectively.

Explanation

GATE→2025→Biomedical Engineering Core→Biomaterials

Q51

NAT[2 Marks]

Strength ($\sigma$) of an implanted suture is given by the equation $$\sigma = \sigma_0 - 2\log_e(t) \quad \text{for } t \ge 1,$$ where $\sigma_0$ represents the original strength and time $t$ is measured in weeks. If the strength of the suture is $2\text{ MPa}$ at $4\text{ weeks}$, what will be its strength (in MPa) at $8\text{ weeks}$? (rounded off to two decimal places)

Explanation

GATE→2025→Biomedical Engineering Core→Medical Imaging Systems

Q52

NAT[2 Marks]

If the gyromagnetic ratio of proton is $42.58\text{ MHz per Tesla}$, the resonance frequency for protons in a magnetic field of $1.5\text{ Tesla}$ is ________ $\text{MHz}$. (rounded off to two decimal places)

Explanation

GATE→2025→Biomedical Engineering Core→Measurements and Control Systems

Q53

NAT[2 Marks]

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 $R_{\text{strain}}$ along its length, the output voltage $V_{\text{OUT}}$ is $10\text{ mV}$. If $R_{\text{strain}}$ 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)

Explanation

GATE→2025→Biomedical Engineering Core→Biomaterials

Q54

NAT[2 Marks]

The storage modulus ($G'$) of a collagen gel scales as $G' \sim [C]^3$, where $[C]$ represents the collagen concentration in $\text{mg/mL}$. If the storage modulus of $1\text{ mg/mL}$ collagen gel is $100\text{ Pa}$, then the storage modulus of a $3\text{ mg/mL}$ collagen gel is ________ $\text{Pa}$. (rounded off to the nearest integer)

Explanation

GATE→2025→Biomedical Engineering Core→Human Anatomy and Physiology

Q55

NAT[2 Marks]

The cardiac output of a person at rest is $5\text{ litres per minute}$ and the mean aortic pressure is $100\text{ mmHg}$. During exercise, if the cardiac output doubles and mean aortic pressure rises to $110\text{ mmHg}$, 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.

Explanation

General Aptitude

10 Questions

GATE→2025→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

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: $\text{Abuse} \rightarrow \text{Insult} \rightarrow \text{Ridicule}$ Group-II: $\underline{\hspace{2cm}} \rightarrow \text{Praise} \rightarrow \text{Appreciate}$

(A)

Extol

(B)

Prize

(C)

Appropriate

(D)

Espouse

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q57

MCQ[1 Mark]

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

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

The 12 musical notes are given as $\text{C}, \text{C}^\#, \text{D}, \text{D}^\#, \text{E}, \text{F}, \text{F}^\#, \text{G}, \text{G}^\#, \text{A}, \text{A}^\#,$ and $\text{B}$. Frequency of each note is $\sqrt[12]{2}$ times the frequency of the previous note. If the frequency of the note $\text{C}$ is $130.8\text{ Hz}$, then the ratio of frequencies of notes $\text{F}^\#$ and $\text{C}$ is:

(A)

$\sqrt[6]{2}$

(B)

$\sqrt{2}$

(C)

$\sqrt[4]{2}$

(D)

$2$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q59

MCQ[1 Mark]

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.

(A)

$\left(\frac{5}{3}\right)^{\frac{n}{2}}$

(B)

$\left(\frac{5}{3}\right)^n$

(C)

$\left(\frac{5}{3}\right)^{2n}$

(D)

$\left(\frac{5}{3}\right)^{n(2n-1)}$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

Which one of the following plots represents $f(x) = -\frac{|x|}{x}$, where $x$ is a non-zero real number? Note: The figures shown are representative.

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

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)

$P \rightarrow Q \rightarrow R \rightarrow S$

(B)

$Q \rightarrow S \rightarrow R \rightarrow P$

(C)

$R \rightarrow S \rightarrow Q \rightarrow P$

(D)

$S \rightarrow P \rightarrow R \rightarrow Q$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q62

MCQ[2 Marks]

A stick of length one meter is broken at two locations at distances of $b_1$ and $b_2$ from the origin ($0$), as shown in the figure. Note that $0 < b_1 < b_2 < 1$. 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)

$b_1 < 0.5$

(B)

$b_2 > 0.5$

(C)

$b_2 < b_1 + 0.5$

(D)

$b_1 + b_2 < 1$

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q63

MCQ[2 Marks]

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 $1^{\text{st}}$ round, $4^{\text{th}}$ student behind P leaves the game. After $2^{\text{nd}}$ round, $5^{\text{th}}$ student behind Q leaves the game. After $3^{\text{rd}}$ round, $3^{\text{rd}}$ student behind V leaves the game. After $4^{\text{th}}$ round, $4^{\text{th}}$ student behind U leaves the game. Who all are left in the game after the $4^{\text{th}}$ round? Note: The figure shown is representative.

(A)

P; T; Q; S

(B)

V; P; T; Q

(C)

W; R; Q; V

(D)

Q; T; V; W

Explanation

GATE→2025→General Aptitude→Data Interpretation

Q64

MCQ[2 Marks]

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 | 19 | 17 | 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.

Explanation

GATE→2025→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

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

Explanation