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Engineering Mathematics(10)Biomedical Engineering Core(45)General Aptitude(10)

Engineering Mathematics

10 Questions

GATE→2026→Engineering Mathematics→Linear Algebra

Q1

MCQ[1 Mark]

The eigenvalues of the matrix $P = \begin{pmatrix} 1 & -2 \\ 3 & -4 \end{pmatrix}$ are

(A)

-1 and -2

(B)

1 and 2

(C)

0 and -1

(D)

0 and 1

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q2

MCQ[1 Mark]

$X$ is a random variable whose mean is $3$ and standard deviation is $2$. A new random variable $Y$ is defined as: $$Y = \frac{X - 3}{4}$$ The standard deviation of $Y$ is

(A)

0.5

(B)

1

(C)

2

(D)

8

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q3

MCQ[1 Mark]

Let $f$ be a function of real variables $x$ and $y$, defined as: $$f(x,y) = x^2 y + 3y^2 x$$ The value of $\frac{\partial^2 f}{\partial x^2}$ at $x = 1$, $y = 1$ is

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q4

MCQ[1 Mark]

An invertible $n \times n$ matrix $P$ satisfies $P^3 = I$, where $I$ is the identity matrix of size $n$. Which one of the following options is true?

(A)

$P^5 = P$

(B)

$P^5 = P^{-1}$

(C)

$P^4 = P^{-1}$

(D)

$P^4 = P^2$

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q5

MCQ[1 Mark]

A biased coin has a probability of heads equal to $1/3$ and a probability of tails equal to $2/3$. A binary random variable $X$ assumes a value $1$ for heads and $-1$ for tails. The variance of $X$ is

(A)

$1/3$

(B)

$5/9$

(C)

$8/9$

(D)

$1$

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q6

MCQ[2 Marks]

The Newton-Raphson method is used to find the roots of the equation $x = e^{-2x}$. If the initial guess $x_0 = 0$, the estimate of the root after the first iteration, $x_1 =$ _______

(A)

$1$

(B)

$1/2$

(C)

$1/3$

(D)

$1/4$

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q7

MCQ[2 Marks]

Let $f$ be a function of two real variables $x$ and $y$, defined as: $$f(x,y) = x^2 + y^2$$ The value of the line integral $\int \vec{\nabla} f \cdot d\vec{l}$ from point $P(1,0)$ to point $Q(0,1)$ along the path $L$ shown in the figure below is _______. Here $\vec{\nabla} = \hat{x}\frac{\partial}{\partial x} + \hat{y}\frac{\partial}{\partial y}$, with $\hat{x}$ and $\hat{y}$ as the unit vectors along X and Y axes, respectively.

(A)

0

(B)

1

(C)

-1

(D)

$\pi$

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q8

MSQ[2 Marks]

Which of the following conditions result(s) in a higher statistical power for comparing means of two samples using $t$-test?

(A)

An increase in the sizes of both the samples from 100 to 1000

(B)

An increase in the significance level from $\alpha = 0.01$ to $\alpha = 0.2$

(C)

A decrease in the significance level from $\alpha = 0.2$ to $\alpha = 0.01$

(D)

A decrease in the sizes of both the samples from 1000 to 100

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q9

NAT[2 Marks]

If $\begin{pmatrix} 2 \\ a \end{pmatrix}$ is an eigenvector corresponding to the smallest eigenvalue of the matrix $\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}$, the value of $a$ is _______ (Answer in integer)

Explanation

GATE→2026→Engineering Mathematics→Differential Equations

Q10

NAT[2 Marks]

The concentration $p$ (in $\mu\text{g/dL}$ i.e., micrograms/deciliter) of a hormone, as a function of time $t$ (in hours) is governed by the following differential equation for $t \ge 0$: $$\frac{dp}{dt} = e^{-0.1t} - 0.1p$$ If $p(0) = 20\text{ }\mu\text{g/dL}$, then $p(10) =$ _______ $\mu\text{g/dL}$. (Round off to one decimal place)

Explanation

Biomedical Engineering Core

45 Questions

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q11

MCQ[1 Mark]

Which one of the following will not coagulate when placed on a glass slide that does not have any surface coatings?

(A)

Blood serum

(B)

Fresh blood obtained from an artery

(C)

Fresh blood obtained from a vein

(D)

Blood depleted of neutrophils alone

Explanation

GATE→2026→Biomedical Engineering Core→Biomechanics

Q12

MCQ[1 Mark]

Which one of the following options represents the tissues/organs of a healthy adult human, arranged in the correct decreasing order of their Young's modulus?

(A)

Bone > Cartilage > Liver > Lung

(B)

Bone > Cartilage > Lung > Liver

(C)

Bone > Lung > Cartilage > Liver

(D)

Bone > Lung > Liver > Cartilage

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q13

MCQ[1 Mark]

Which one of the following is not a polymer?

(A)

DNA

(B)

Albumin

(C)

Cholesterol

(D)

Dextran

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q14

MCQ[1 Mark]

Electrostatic interaction between a positively charged polymer and a negatively charged polymer in an aqueous medium most likely results in the formation of a

(A)

chemical-crosslinked hydrogel

(B)

complex coacervate

(C)

photo-crosslinked hydrogel

(D)

liposome

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q15

MCQ[1 Mark]

Which one of the following cell types is the most abundant in healthy adult human blood?

(A)

Erythrocytes

(B)

Lymphocytes

(C)

Basophils

(D)

Neutrophils

Explanation

GATE→2026→Biomedical Engineering Core→Biomechanics

Q16

MCQ[1 Mark]

Consider an incompressible cylindrical tissue with a diameter of $2\text{ cm}$ and a height of $3\text{ cm}$. If this tissue is stretched by $10\%$ in the axial direction, its diameter in the stretched configuration is _______ $\text{cm}$. Assume homogeneous deformation of the tissue.

(A)

2.4

(B)

2.2

(C)

1.6

(D)

1.9

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q17

MCQ[1 Mark]

Which one of the following options represents the correct order of the speed of ultrasound wave propagation in bone, air, and soft tissue?

(A)

bone > air > soft tissue

(B)

bone > soft tissue > air

(C)

air > bone > soft tissue

(D)

soft tissue > bone > air

Explanation

GATE→2026→Biomedical Engineering Core→Biomechanics

Q18

MCQ[1 Mark]

The three curves shown in the figure represent the trends in Stress-Strain relationship in Bone, Glass and Steel. Which one of the following options correctly matches the curve labels ($P$, $Q$, and $R$) with these three materials?

(A)

P-Bone; Q-Glass; R-Steel

(B)

P-Steel; Q-Bone; R-Glass

(C)

P-Steel; Q-Glass; R-Bone

(D)

P-Glass; Q-Bone; R-Steel

Explanation

GATE→2026→Biomedical Engineering Core→Measurements and Control Systems

Q19

MCQ[1 Mark]

A control system shown in the figure below has a forward gain $G = 100$. An input $V_{\text{in}} = 5\text{ volts}$ is supplied to the system. What is the absolute error between the output $V_{\text{out}}$ and input $V_{\text{in}}$ in volts?

(A)

0.00

(B)

0.05

(C)

0.50

(D)

1.00

Explanation

GATE→2026→Biomedical Engineering Core→Electrical Circuits

Q20

MCQ[1 Mark]

The circuit given below is initially in steady-state with the switch S open. Immediately after the switch S is closed, the voltage $V_A$ is _______ volts.

(A)

0

(B)

10

(C)

5

(D)

-10

Explanation

GATE→2026→Biomedical Engineering Core→Analog and Digital Electronics

Q21

MCQ[1 Mark]

A standard n-type MOSFET, biased in the saturation region, has the following parasitic capacitances: 1. $C_{GS}$: gate to source capacitance 2. $C_{GD}$: gate to drain capacitance 3. $C_{DS}$: drain to source capacitance Which one of the following options is correct?

(A)

$C_{GS} > C_{GD} > C_{DS}$

(B)

$C_{GD} > C_{DS} > C_{GS}$

(C)

$C_{DS} > C_{GD} > C_{GS}$

(D)

$C_{GD} > C_{GS} > C_{DS}$

Explanation

GATE→2026→Biomedical Engineering Core→Signals and Systems

Q22

MCQ[1 Mark]

$x[n]$ is a real and odd signal. Which one of the following statements is true about its Discrete Time Fourier Transform (DTFT) $X(e^{j\omega})$?

(A)

$X(e^{j\omega})$ is real and even

(B)

$X(e^{j\omega})$ is imaginary and even

(C)

$X(e^{j\omega})$ is real and odd

(D)

$X(e^{j\omega})$ is imaginary and odd

Explanation

GATE→2026→Biomedical Engineering Core→Analog and Digital Electronics

Q23

MCQ[1 Mark]

The IV characteristics of a diode with a knee voltage $V_{\text{knee}} = 0.8\text{ volts}$ is shown in Figure 1. This diode is used in the circuit shown in Figure 2, in which an input signal of $V_{\text{in}} = 100\sin(1000t)\text{ volts}$ is applied. What is the voltage $V_{\text{out}}$ (in volts) across the capacitor at steady state? Assume that the capacitor is initially discharged and the reverse breakdown voltage of the diode is much greater than $100\text{ volts}$.

(A)

99.2

(B)

$99.2\cos(1000t)$

(C)

$99.2\sin(1000t)$

(D)

-99.2

Explanation

GATE→2026→Biomedical Engineering Core→Electrical Circuits

Q24

MCQ[1 Mark]

Which one of the following options is the Thevenin voltage (in volts) across the resistor $R_{\text{Load}}$ in the circuit given below?

(A)

7.5

(B)

5.0

(C)

15.0

(D)

10.0

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q25

MCQ[1 Mark]

In humans, the pyloric sphincter is located between

(A)

esophagus and stomach

(B)

stomach and duodenum

(C)

mouth and esophagus

(D)

ileum and large intestine

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q26

MCQ[1 Mark]

Which one of the following epithelial cell types is primarily located in the tracheal mucosa of a healthy adult human?

(A)

Transitional

(B)

Keratinized stratified squamous

(C)

Simple squamous

(D)

Ciliated pseudostratified columnar

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q27

NAT[1 Mark]

The shell of a hollow spherical nanoparticle has a uniform thickness of $3\text{ nanometers (nm)}$. The outer radius of the nanoparticle is $5\text{ nm}$. The ratio of the volume of the shell to the volume of the hollow core is _______ (Round off to one decimal place)

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q28

NAT[1 Mark]

An MRI signal acquired from a tissue has a transverse relaxation time ($T_2$) of $100\text{ milliseconds (ms)}$. If the signal intensity at time $t = 0\text{ ms}$ is $500\text{ a.u.}$, the signal intensity at $t = 50\text{ ms}$ is _______ $\text{a.u.}$ (Round off to one decimal place)

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q29

NAT[1 Mark]

The gyromagnetic ratio of $^{31}\text{P}$ nucleus is $17.23\text{ MHz/Tesla}$. The Larmor frequency of $^{31}\text{P}$ nucleus in an MRI scanner with a field strength of $3\text{ Tesla}$ is _______ $\text{MHz}$. (Round off to one decimal place)

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q30

NAT[1 Mark]

The vital capacity, tidal volume, and inspiratory reserve volume of the lungs of a healthy individual are $4600\text{ milliliters (mL)}$, $500\text{ mL}$, and $2500\text{ mL}$, respectively. The expiratory reserve volume of the lungs of this individual is _______ $\text{mL}$. (Round off to the nearest integer)

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q31

MCQ[2 Marks]

A drug is loaded in a polymeric device through a process. Which one of the following ratios defines the drug encapsulation efficiency of this process?

(A)

$\frac{\text{Amount of drug successfully loaded}}{\text{Amount of polymer in the device}}$

(B)

$\frac{\text{Amount of drug successfully loaded}}{\text{Amount of drug used in the process}}$

(C)

$\frac{\text{Amount of drug used in the process}}{\text{Amount of drug successfully loaded}}$

(D)

$\frac{\text{Amount of polymer in the device}}{\text{Amount of drug used in the process}}$

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q32

MCQ[2 Marks]

Which one of the following complement system pathways is most likely to be activated on biomaterials implanted in a healthy human?

(A)

classical pathway

(B)

lectin pathway

(C)

alternative pathway

(D)

extrinsic pathway

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q33

MCQ[2 Marks]

Choose one of the following options that correctly fills the blanks labelled as $\text{I}$ and $\text{II}$ in the paragraph below. Lower critical solution temperature (LCST) polymers exhibit a decrease in their water solubility with an increase in temperature. This happens because, at low temperatures, the hydrogen bonding between the $\underline{\text{ I }}$ segments of polymer chain and the water molecules dominates. At high temperatures, the interactions between the $\underline{\text{ II }}$ segments dominate.

(A)

I-hydrophilic; II-hydrophobic

(B)

I-hydrophobic; II-hydrophilic

(C)

I-hydrophilic; II-polar

(D)

I-hydrophobic; II-polar

Explanation

GATE→2026→Biomedical Engineering Core→Signals and Systems

Q34

MCQ[2 Marks]

The output $y[n]$ of a digital moving average filter for an input $x[n]$ is given by $$y[n] = \frac{1}{4}(x[n] + 2x[n-1] + x[n-2])$$ Which one of the following options is a correct statement about the transfer function of this filter?

(A)

It has two poles and two zeros

(B)

It has two poles and no zeros

(C)

It has no poles and two zeros

(D)

It has one pole and one zero

Explanation

GATE→2026→Biomedical Engineering Core→Biomechanics

Q35

MCQ[2 Marks]

A uniform shear force of magnitude $0.01\text{ Newton (N)}$ is applied to the top surface of a cubical tissue sample with side of length $1\text{ cm}$ (marked with dashed lines in the figure below). In the deformed configuration (marked with solid lines), the angle $\theta = 5\text{ degrees}$. The shear modulus of the tissue is _______ $\text{kilopascals (kPa)}$. Assume the tissue to be a linear, isotropic and homogenous elastic solid.

(A)

1.14

(B)

10.40

(C)

5.14

(D)

3.14

Explanation

GATE→2026→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q36

MCQ[2 Marks]

The table below shows the average values of the power spectral density (PSD) of an EEG signal in different frequency bands. | Frequency bands (Hertz) | Average PSD ($\mu\text{V}^2/\text{Hertz}$) | | :---: | :---: | | 0.4–4.0 | 3 | | 4.0–8.0 | 4 | | 8.0–13.0 | 8 | | 13.0–30.0 | 5 | | 30.0–100.0 | 3 | The PSD of the EEG signal has a noise floor of $2\text{ }\mu\text{V}^2/\text{Hertz}$. The signal to noise ratio for the alpha-band, expressed in decibels, is

(A)

1.76

(B)

3.01

(C)

6.02

(D)

3.98

Explanation

GATE→2026→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q37

MCQ[2 Marks]

Which one of the following options correctly matches the ECG signals in Panel-1 with the cardiac conditions in Panel-2? **Panel-2: Cardiac Conditions** * (i) Normal condition * (ii) Atrial flutter * (iii) Atrioventricular block

(A)

X-(i); Y-(iii); Z-(ii)

(B)

X-(i); Y-(ii); Z-(iii)

(C)

X-(ii); Y-(i); Z-(iii)

(D)

X-(ii); Y-(iii); Z-(i)

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q38

MCQ[2 Marks]

An ultrasound wave is incident normal to the interface of muscle and bone. The acoustic impedances of muscle and bone are $1.7 \times 10^{-4}\text{ kg m}^{-2}\text{ sec}^{-1}$ and $6.1 \times 10^{-4}\text{ kg m}^{-2}\text{ sec}^{-1}$, respectively. The fraction of the incident energy that is reflected is

(A)

0.98

(B)

0.32

(C)

0.50

(D)

0.65

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q39

MCQ[2 Marks]

An ultrasound beam traversing through $5\text{ cm}$ of a material is attenuated at a rate of $2\text{ dB/cm}$. The intensity of the beam at the exit of the material is $I_{\text{exit}}$ and the intensity at the entry into the material is $I_{\text{entry}}$. The ratio $\frac{I_{\text{exit}}}{I_{\text{entry}}} =$ _______

(A)

0.5

(B)

0.9

(C)

0.1

(D)

0.7

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q40

MCQ[2 Marks]

A Magnetic Resonance Imaging (MRI) sequence is shown in the figure below, wherein $T_R$ is the repetition time and $T_E$ is the echo time. Which one of the following options is the correct name of this MRI sequence?

(A)

Spin echo sequence

(B)

Echo planar imaging sequence

(C)

Inversion recovery sequence

(D)

Saturation recovery sequence

Explanation

GATE→2026→Biomedical Engineering Core→Analog and Digital Electronics

Q41

MCQ[2 Marks]

If the operational amplifier in the circuit below is ideal, the input impedance looking into terminal $V_{\text{in}}$ is _______

(A)

$\infty$

(B)

$-\frac{R \times R_1}{R_F}$

(C)

$\frac{R \times R_F}{R_1}$

(D)

$R$

Explanation

GATE→2026→Biomedical Engineering Core→Analog and Digital Electronics

Q42

MCQ[2 Marks]

The figure below shows the Karnaugh map (K-map) for a truth table with 4 variables $A, B, C$ and $D$. Which one of the following expressions represents the minimum sum of products? Note: The empty cells in the K-map are $0$'s.

(A)

$BC + \overline{A}BD + AC\overline{D} + AB\overline{D}$

(B)

$AB\overline{C}\overline{D} + \overline{A}B\overline{C}D + A\overline{B}C\overline{D} + BC$

(C)

$BC + AC\overline{D} + \overline{A}BD + AB\overline{C}\overline{D}$

(D)

$AB\overline{D} + \overline{A}BD + AC\overline{D} + BCD + BC\overline{D}$

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q43

MCQ[2 Marks]

Which one of the following options correctly matches the cell types (Panel-1) with the organs in which they are primarily located (Panel-2)? | Panel-1 | Panel-2 | | :--- | :--- | | (p) Microglia | (i) Brain | | (q) Mesangial cells | (ii) Kidney | | (r) Microfold cells | (iii) Small intestine |

(A)

(p)-(i); (q)-(ii); (r)-(iii)

(B)

(p)-(i); (q)-(iii); (r)-(ii)

(C)

(p)-(ii); (q)-(i); (r)-(iii)

(D)

(p)-(iii); (q)-(ii); (r)-(i)

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q44

MCQ[2 Marks]

Which one of the following options correctly matches the lobes of the cerebral cortex of a healthy human being (Panel-1) with their canonical sensory function (Panel-2)? | Panel-1 | Panel-2 | | :--- | :--- | | (p) Parietal lobe | (i) Sight | | (q) Occipital lobe | (ii) Touch | | (r) Temporal lobe | (iii) Hearing |

(A)

(p)-(i); (q)-(ii); (r)-(iii)

(B)

(p)-(ii); (q)-(i); (r)-(iii)

(C)

(p)-(iii); (q)-(i); (r)-(ii)

(D)

(p)-(i); (q)-(iii); (r)-(ii)

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q45

MSQ[2 Marks]

Which of the following cells is/are primarily located in the epidermis of healthy human skin?

(A)

Keratinocytes

(B)

Melanocytes

(C)

Oxyntic cells

(D)

Goblet cells

Explanation

GATE→2026→Biomedical Engineering Core→Human Anatomy and Physiology

Q46

MSQ[2 Marks]

Select the peptide hormone(s) from the following options.

(A)

Cortisol

(B)

Testosterone

(C)

Oxytocin

(D)

Insulin

Explanation

GATE→2026→Biomedical Engineering Core→Analog and Digital Electronics

Q47

MSQ[2 Marks]

The circuit shown below is used as an instrumentation amplifier. Among the resistors used in the input stage, the value of resistance of one of the resistors ($R^*$) is slightly mismatched from that of the rest of the resistors ($R$). Assume all operational amplifiers are ideal. Which of the following statements is/are true?

(A)

The resistance mismatch introduces a gain error

(B)

The resistance mismatch degrades the common mode rejection ratio (CMRR)

(C)

The resistance mismatch introduces an offset error

(D)

$V_{\text{out}}$ is not sensitive to any resistance mismatch

Explanation

GATE→2026→Biomedical Engineering Core→Measurements and Control Systems

Q48

NAT[2 Marks]

A resistor with $60 \pm 2\text{ }\Omega$ resistance is part of a circuit. The voltage measured across this resistor is $120 \pm 10\text{ mV}$ (millivolts). The uncertainty in the estimation of the power dissipated by the resistor is _______ $\text{mW}$ (milliwatts). (Round off to one decimal place).

Explanation

GATE→2026→Biomedical Engineering Core→Sensors and Bioinstrumentation

Q49

NAT[2 Marks]

A photodiode is in series with a $10\text{ k}\Omega$ resistor. A laser beam with wavelength $532\text{ nanometer}$ shines on this photodiode such that the entire beam is incident on its active area. The photodiode responsivity is $0.5\text{ ampere per watt (A/W)}$ at this wavelength. If a voltage of $10\text{ millivolts (mV)}$ is developed across the $10\text{ k}\Omega$ resistor, the laser power incident on the photodiode is _______ $\text{microwatts (}\mu\text{W)}$. (Round off to one decimal place). Assume that the dark current of the photodiode is zero.

Explanation

GATE→2026→Biomedical Engineering Core→Biomechanics

Q50

NAT[2 Marks]

There is a steady laminar blood flow in a tapered cylindrical vessel of circular cross-section, as shown in the figure below. Two cross-sections, labeled A and B in the figure, have radii $0.5\text{ centimeter (cm)}$ and $0.45\text{ cm}$, respectively. If the average flow speed of the blood at cross-section A is $1\text{ cm/second}$, the average flow speed at cross-section B is _______ $\text{cm/second}$. (Round off to one decimal place). Assume blood to be an incompressible fluid.

Explanation

GATE→2026→Biomedical Engineering Core→Biomechanics

Q51

NAT[2 Marks]

Figure 1 depicts an arm holding a ball in static equilibrium. Figure 2 shows the free-body diagram of the lower arm where $F$ is the force applied by the biceps muscle at an angle of $\theta = 60\text{ degrees}$ with respect to the lower arm, and $R_1$ and $R_2$ are the reaction forces acting at point $O$. The weights of the ball and the lower arm are $W_1 = 50\text{ Newtons (N)}$ and $W_2 = 20\text{ N}$ respectively. The force exerted by the biceps muscle is $F =$ _______ $\text{N}$. (Round off to the nearest integer) Assume the lower arm to be a rigid body.

Explanation

GATE→2026→Biomedical Engineering Core→Medical Imaging Systems

Q52

NAT[2 Marks]

The half-life of $^{113\text{m}}\text{In}$ nuclei is $1.7\text{ hours}$, and the $^{99\text{m}}\text{Tc}$ nuclei is $6.0\text{ hours}$. If the initial activity levels of $^{113\text{m}}\text{In}$ and $^{99\text{m}}\text{Tc}$ in their respective samples are $100\text{ Gigabecquerels (GBq)}$ and $20\text{ GBq}$, the time at which their activity levels become equal is _______ $\text{hours}$. (Round off to one decimal place)

Explanation

GATE→2026→Biomedical Engineering Core→Signals and Systems

Q53

NAT[2 Marks]

The figure below shows the impulse response of a linear time-invariant (LTI) system, $h[n] = [0, 0.6, 0.8, 0.5, 0.3, 0]$. For an input $x[n] = [1, 0.6, 0, 0, 0, 0]$, the maximum value of its output $y[n]$ is _______ (Round off to one decimal place)

Explanation

GATE→2026→Biomedical Engineering Core→Analog and Digital Electronics

Q54

NAT[2 Marks]

In the following digital circuit, the delay of both the NAND gates is $4\text{ nanoseconds (ns)}$ and the delay of the NOT gate is $1\text{ ns}$. If a $10\text{ MHz}$ clock signal with $50\%$ duty cycle is provided as the input, the duty cycle of the output is _______ $\%$ (Answer in integer)

Explanation

GATE→2026→Biomedical Engineering Core→Biomaterials

Q55

NAT[2 Marks]

Solid polymeric particles of diameter $20\text{ micrometers (}\mu\text{m)}$ are suspended in water such that the concentration of polymeric particles in the solution is $1\%$ weight/volume (w/v). If the mass density of the polymeric particle is $1\text{ g/cm}^3$, the number of polymeric particles present in $1\text{ mL}$ of this solution is _______ $\times 10^6$. (Round off to one decimal place)

Explanation

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q56

MCQ[1 Mark]

'The team _______ more than 300 runs in 20 overs _______ rains. However, some players needed to improve their batting skills.' Choose the option with the correct sequence of words to fill the blanks.

(A)

score; despite

(B)

scoring; instead of

(C)

scored; despite

(D)

scoring; in spite of

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q57

MCQ[1 Mark]

If a positive real $x$ satisfies the following equation $$\log_2 x + \log_{\sqrt{2}} x = 48,$$ then the value of $x$ is

(A)

$2^{16}$

(B)

$4^{16}$

(C)

$2^{14}$

(D)

$4^{14}$

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q58

MCQ[1 Mark]

The next figure (indicated by '?') in the sequence is

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q59

MCQ[1 Mark]

'All the mangoes in the basket are good.' If the above statement is false, then which one of the following statements is necessarily true?

(A)

All the mangoes in the basket are not good.

(B)

No mango in the basket is good.

(C)

In the basket, some of the mangoes are good and some are not good.

(D)

There exists at least one mango in the basket that is not good.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q60

MCQ[1 Mark]

Consider the following statements about four numbers: (S1) The average of the four numbers is 25 (S2) Each number is at most 40 (S3) Each number is at least 20 Choose the option that is necessarily correct.

(A)

(S1) and (S2) together imply (S3)

(B)

(S2) and (S3) together imply (S1)

(C)

(S1) and (S3) together imply (S2)

(D)

(S1) implies (S3)

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q61

MCQ[2 Marks]

'People are crowding around _______ pit into which _______ elephant has fallen. I have never seen an elephant looking more bewildered _______ miserable. Here it is in a most undignified position, thrust into a pit and made to look up _______ a vast, curiosity-stricken crowd.' Choose the option with the correct sequence of words to fill the blanks.

(A)

an; a; at; and

(B)

a; an; and; at

(C)

and; a; an; at

(D)

at; a; an; and

Explanation

GATE→2026→General Aptitude→Data Interpretation

Q62

MCQ[2 Marks]

The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, $250$ items were sold with the average selling price of Rs. $60$. The following observations were made: (i) The quantity of S sold was twice that of T. (ii) The quantity of R sold was thrice that of T. (iii) The quantity of Q sold was four times that of T. | Product | Unit selling price (Rs.) | | :---: | :---: | | P | 100 | | Q | 60 | | R | 60 | | S | 40 | | T | 50 | What is the quantity of product P sold on that day?

(A)

40

(B)

50

(C)

60

(D)

70

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q63

MCQ[2 Marks]

Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as represented in Figure (i). When both the strings are shortened by a length $x$ they can be re-arranged such that the shortened string K forms a full circle with the shortened string P as its diameter, as represented in Figure (ii). The value of $x/l$ is _______

(A)

$\pi$

(B)

$\frac{\pi - 1}{2\pi}$

(C)

$\frac{\pi}{2(\pi - 1)}$

(D)

$\frac{\pi}{\pi - 1}$

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q64

MCQ[2 Marks]

The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels. They are seated in rows and columns as shown in the figure with exactly one person sitting in each box. It is known that (i) Meritorius' daughter and his brother are seated in the same column. (ii) His son is seated diagonally across the sibling of the worst orator. (iii) The best and worst orators are seated in the same row. Who is the best orator?

(A)

Meritorius

(B)

Meritorius' brother

(C)

Meritorius' son

(D)

Meritorius' daughter

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q65

MCQ[2 Marks]

Which one of the patterns labelled P, Q, R, and S is used to generate the following figure?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation