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General Aptitude(10)Engineering Mathematics(9)Structural Engineering(11)Geotechnical Engineering(8)Water Resources Engineering(10)Environmental Engineering(5)Transportation Engineering(6)Geomatics Engineering(5)

General Aptitude

10 Questions

GATE→2026→General Aptitude→Verbal Ability

Q1

MCQ[1 Mark]

In the sentence 'The shopkeeper sells lemons.', the word 'lemons' is the

(A)

object

(B)

subject

(C)

predicate

(D)

verb

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q2

MCQ[1 Mark]

The figure below is supposed to show three non-overlapping shapes - one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by '?' and completes the oval and the two triangles?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q3

MCQ[1 Mark]

At how many points will the curves $y = x^2$ and $y = -x^2 - 2x - 1$ intersect in the real $(x, y)$ plane?

(A)

0

(B)

1

(C)

2

(D)

3

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q4

MCQ[1 Mark]

Based on the given paragraph regarding Anish's match performance and captaincy, which statement is true?

(A)

Anish made hundred runs but was denied captaincy.

(B)

Anish was the captain of his team before the game today.

(C)

The current captain is older than Anish.

(D)

Anish is the youngest player in his team.

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q5

MCQ[1 Mark]

Which one of the following figures P, Q, R, or S, correctly shows the 45° clockwise-rotated version of figure (I)?

(A)

P

(B)

Q

(C)

R

(D)

S

Explanation

GATE→2026→General Aptitude→Verbal Ability

Q6

MCQ[2 Marks]

Match the words in Column I with their synonyms in Column II.

(A)

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

(B)

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

(C)

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

(D)

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

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q7

MCQ[2 Marks]

In the given figure, $\overline{PQ}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle ROS = 80^{\circ}$. When $\overline{PR}$ and $\overline{QS}$ are extended, they meet at $T$. The value of $\angle RTS$ is

(A)

40°

(B)

50°

(C)

60°

(D)

80°

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q8

MCQ[2 Marks]

Based on the relationship between each polygon and the number inside it, the value of 'X' is

(A)

720

(B)

596

(C)

24

(D)

240

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q9

MCQ[2 Marks]

Consider a linear arrangement of seven bulbs under specified state change rules. The number of bulbs which are ON at the end of Step 8 is

(A)

5

(B)

4

(C)

3

(D)

0

Explanation

GATE→2026→General Aptitude→Quantitative Aptitude

Q10

MCQ[2 Marks]

P and Q are two positive integers such that $P^2 = Q^2 + 13$. The product of the numbers P and Q is

(A)

13

(B)

26

(C)

39

(D)

42

Explanation

Engineering Mathematics

9 Questions

GATE→2026→Engineering Mathematics→Linear Algebra

Q11

MCQ[1 Mark]

Matrix $P$ is given as $P = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix}$. The TRUE option is

(A)

Trace of P is equal to the sum of the Eigen values of P.

(B)

$P^T P$ is an identity matrix.

(C)

P is a skew-symmetric matrix.

(D)

Absolute magnitude of each Eigen value is 1.

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q12

MCQ[1 Mark]

Given $\begin{bmatrix} 1 & 1 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{Bmatrix} x_1 \\ x_2 \\ x_3 \end{Bmatrix} = \begin{Bmatrix} 0 \\ 0 \end{Bmatrix}$. The above system of equations represents a

(A)

plane

(B)

line

(C)

volume

(D)

point

Explanation

GATE→2026→Engineering Mathematics→Probability and Statistics

Q13

NAT[1 Mark]

Bag I contains 4 white and 6 black balls. Bag II contains 4 white and 3 black balls. One ball is drawn at random from any one of the two bags and it is found to be a black ball. The probability that the black ball was drawn from Bag I is

Explanation

GATE→2026→Engineering Mathematics→Linear Algebra

Q14

NAT[1 Mark]

A matrix is given as $\begin{bmatrix} 9 & 15 \\ 15 & 50 \end{bmatrix}$. By performing Cholesky decomposition, $|l_{22}|$ of the lower triangular matrix is

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q15

NAT[1 Mark]

It is given that $x$ and $y$ are integers in the equation $(x + y - 7)^2 + (y + 3x - 13)^2 = 0$. The value of $(x^3 + y^3)$ is

Explanation

GATE→2026→Engineering Mathematics→Calculus

Q16

MCQ[2 Marks]

Let $f(x)$ be a continuous function defined in $[0,2] \to \mathbb{R}$ satisfying $\int_{0}^{2} f(x)[x - f(x)] dx = \frac{2}{3}$. The value of $f(1)$ is

(A)

1

(B)

2

(C)

1/2

(D)

0

Explanation

GATE→2026→Engineering Mathematics→Ordinary Differential Equations (ODE)

Q17

MCQ[2 Marks]

An Euler-Cauchy ODE is given by $x^2 \frac{d^2y}{dx^2} = 6y$. The general solution is

(A)

$y(x) = ax^3 + \frac{b}{x^2}$

(B)

$y(x) = ax^2 + \frac{b}{x^3}$

(C)

$y(x) = ax^2 + b \ln x$

(D)

$y(x) = ax^3 + b \ln x$

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q18

NAT[2 Marks]

Starting with $x = 0.5$, the second approximation for the root of $f(x) = e^{-x} - x$ by Newton-Raphson method is

Explanation

GATE→2026→Engineering Mathematics→Numerical Methods

Q19

NAT[2 Marks]

Tabulated data values used for second-degree Lagrange/Newton interpolation polynomial $P_2(x)$. The value of $P_2(0)$ is

Explanation

Structural Engineering

11 Questions

GATE→2026→Structural Engineering→Solid Mechanics

Q20

MCQ[1 Mark]

A thin-walled spherical gas balloon of radius $R$ and wall thickness $t$ ($t \ll R$) is subjected to an internal (gauge) pressure $p$. The maximum tensile and shear stresses in the balloon wall are, respectively:

(A)

Zero and $pR/2t$

(B)

$pR/2t$ and Zero

(C)

$pR/2t$ and $pR/4t$

(D)

$pR/4t$ and Zero

Explanation

GATE→2026→Structural Engineering→Solid Mechanics

Q21

MCQ[1 Mark]

Black dot shown in the figure qualitatively represents the shear centre of the angle section. The option which represents the position of the shear centre is:

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→Structural Engineering→Concrete Structures

Q22

MCQ[1 Mark]

Which one of the following is utilized to determine the long-term deformation of concrete under sustained loading?

(A)

Creep

(B)

Shrinkage

(C)

Modulus of rupture

(D)

Split tensile strength

Explanation

GATE→2026→Structural Engineering→Concrete Structures

Q23

NAT[1 Mark]

The required centre-to-centre spacing of 10 mm diameter bars is 150 mm to resist the design moment in a concrete slab. Instead of 10 mm diameter bars, if 12 mm diameter bars of the same grade are used, the required centre-to-centre spacing (in mm) becomes

Explanation

GATE→2026→Structural Engineering→Steel Structures

Q24

NAT[1 Mark]

Two steel plates are connected together by a 5 mm fillet weld of length 150 mm to transfer a design load. If the size of the fillet weld is changed to 6 mm, the weld length (in mm) needed is

Explanation

GATE→2026→Structural Engineering→Structural Analysis

Q25

MCQ[2 Marks]

A plane truss consists of two members PQ and QR inclined at $45^{\circ}$ with hinge supports at P and R. After boundary conditions, the stiffness matrix is

(A)

$\frac{AE}{L}\begin{bmatrix}1&1\\1&1\end{bmatrix}$

(B)

$\frac{AE}{L}\begin{bmatrix}1&0.5\\0.5&1\end{bmatrix}$

(C)

$\frac{AE}{L}\begin{bmatrix}1&0\\0&1\end{bmatrix}$

(D)

$\frac{AE}{L}\begin{bmatrix}1&-1\\-1&1\end{bmatrix}$

Explanation

GATE→2026→Structural Engineering→Structural Analysis

Q26

MCQ[2 Marks]

The plane frame has a hinge and a roller support with applied loads. The absolute value of the maximum bending moment (in kN-m) in the frame is

(A)

165

(B)

150

(C)

240

(D)

195

Explanation

GATE→2026→Structural Engineering→Concrete Structures

Q27

MSQ[2 Marks]

Select ALL CORRECT option(s) which can be considered to check whether flexural stresses in a prestressed concrete beam are within allowable limits at transfer and service stages:

(A)

Limiting zone for prestressing

(B)

Magnel's graph

(C)

Hoyer effect

(D)

Load balancing method

Explanation

GATE→2026→Structural Engineering→Engineering Mechanics

Q28

NAT[2 Marks]

Two identical blocks A and B connected by a rigid rod rest against vertical and horizontal planes. If sliding impends when $\theta = 45^{\circ}$, the coefficient of static friction is

Explanation

GATE→2026→Structural Engineering→Solid Mechanics

Q29

NAT[2 Marks]

Homogeneous elastic rod AB connected to a spring BC between fixed supports. Rod area = $500 \text{ mm}^2$, $E = 60 \times 10^3 \text{ MPa}$, $\alpha = 12 \times 10^{-6}/^{\circ}\text{C}$. Spring stiffness $k = 2500 \text{ N/mm}$. Temperature increase = $100^{\circ}\text{C}$. Internal force in spring BC (in kN) is

Explanation

GATE→2026→Structural Engineering→Steel Structures

Q30

NAT[2 Marks]

The cross-section of a steel T-beam with given dimensions has a plastic section modulus of $\times 10^4 \text{ mm}^3$ equal to

Explanation

Geotechnical Engineering

8 Questions

GATE→2026→Geotechnical Engineering→Sub-surface Investigations, Earth Pressure & Slope Stability

Q31

MCQ[1 Mark]

Match Column 1 (Menard, Marchetti, Casagrande, Proctor) with Column 2 (Dilatometer test, Pressuremeter test, Compaction test, Liquid limit test).

(A)

(I)-(Q); (II)-(P); (III)-(S); (IV)-(R)

(B)

(I)-(R); (II)-(S); (III)-(Q); (IV)-(P)

(C)

(I)-(P); (II)-(Q); (III)-(S); (IV)-(R)

(D)

(I)-(R); (II)-(S); (III)-(P); (IV)-(Q)

Explanation

GATE→2026→Geotechnical Engineering→Soil Properties, Classification & Seepage

Q32

NAT[1 Mark]

For a liquid, the permeability of a sandy soil having a void ratio of 0.60 was determined as $0.14 \text{ cm/s}$. Using Taylor's equation, the permeability corresponding to void ratio 0.80 is

Explanation

GATE→2026→Geotechnical Engineering→Sub-surface Investigations, Earth Pressure & Slope Stability

Q33

NAT[1 Mark]

To obtain undisturbed clay soil sample, an Area Ratio of 10% needs to be achieved for a thin walled sampling tube. If outer diameter is 50.8 mm, the inner diameter (in mm) is

Explanation

GATE→2026→Geotechnical Engineering→Sub-surface Investigations, Earth Pressure & Slope Stability

Q34

MSQ[2 Marks]

As per Rankine's earth pressure theory, which of the following statements is/are FALSE?

(A)

For active earth pressure, failure plane inclination is $(45^{\circ} + \phi/2)$ with major principal plane.

(B)

For active earth pressure, failure plane inclination is $(45^{\circ} - \phi/2)$ with major principal plane.

(C)

For passive earth pressure, failure plane inclination is $(45^{\circ} + \phi/2)$ with major principal plane.

(D)

For passive earth pressure, failure plane inclination is $(45^{\circ} - \phi/2)$ with major principal plane.

Explanation

GATE→2026→Geotechnical Engineering→Sub-surface Investigations, Earth Pressure & Slope Stability

Q35

NAT[2 Marks]

An infinite slope with slope angle $\beta = 22^{\circ}$ consists of soil with unit weight $\gamma = 15.72 \text{ kN/m}^3$, $c' = 12 \text{ kPa}$, $\phi' = 15^{\circ}$. The critical height of the slope (in m) is

Explanation

GATE→2026→Geotechnical Engineering→Shallow & Deep Foundations

Q36

NAT[2 Marks]

A circular pile of 600 mm diameter and 6 m length in saturated clay. If diameter is doubled to 1200 mm (keeping length constant), the ratio of pile capacity of 1200 mm pile to 600 mm pile is

Explanation

GATE→2026→Geotechnical Engineering→Shallow & Deep Foundations

Q37

NAT[2 Marks]

A group of 25 circular piles ($5 \times 5$) in soft clay. Friction piles with unity group efficiency. Optimum ratio of pile spacing to pile diameter is

Explanation

GATE→2026→Geotechnical Engineering→Shallow & Deep Foundations

Q38

NAT[2 Marks]

A shallow strip footing of width 2 m embedded at depth 1.5 m in pure clay ($c_u = 20 \text{ kN/m}^2$, $\phi=0$). Due to water table rise to ground surface, percentage change in net ultimate bearing capacity is

Explanation

Water Resources Engineering

10 Questions

GATE→2026→Water Resources Engineering→Fluid Mechanics

Q39

MCQ[1 Mark]

Two reservoirs having different water levels are connected by two long parallel pipelines of same length and same material but having diameters of 600 mm and 400 mm. Using Darcy-Weisbach equation, the ratio of flowrate of water in the bigger diameter pipe to that in the smaller diameter pipe is

(A)

0.54

(B)

1.22

(C)

1.84

(D)

2.76

Explanation

GATE→2026→Water Resources Engineering→Irrigation

Q40

MCQ[1 Mark]

An irrigation canal is to be designed to deliver 10 cumec to meet the peak demand of 7500 hectare of cropped area. The estimated canal losses are 50% of the head discharge. The duty (in hectare/cumec) on capacity of this canal is

(A)

375

(B)

1125

(C)

1500

(D)

1875

Explanation

GATE→2026→Water Resources Engineering→Hydraulics

Q41

MSQ[1 Mark]

Which of the following options is/are NOT correct when matching GVF profiles (M1, M2, M3) with channel bed slopes?

(A)

(P)-(I); (Q)-(II); (R)-(I)

(B)

(P)-(I); (Q)-(II); (R)-(III)

(C)

(P)-(II); (Q)-(I); (R)-(I)

(D)

(P)-(I); (Q)-(III); (R)-(II)

Explanation

GATE→2026→Water Resources Engineering→Hydraulics

Q42

MCQ[2 Marks]

For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is 2. The Froude number of supercritical stream is

(A)

$\sqrt{3}$

(B)

$\sqrt{5}$

(C)

$\sqrt{6}$

(D)

$\sqrt{8}$

Explanation

GATE→2026→Water Resources Engineering→Fluid Mechanics

Q43

MCQ[2 Marks]

In a laminar flow of a Newtonian fluid through a circular pipe of radius 5 cm, the maximum velocity is found to be 2 m/s. The velocity (in m/s) at a radial distance of 2.50 cm from the axis is

(A)

1.00

(B)

1.25

(C)

1.50

(D)

1.75

Explanation

GATE→2026→Water Resources Engineering→Hydrology

Q44

NAT[2 Marks]

A fully-penetrating well in an unconfined aquifer with pumping rate $63 \text{ m}^3/s$ and drawdowns at observation wells. Transmissibility (in $\text{m}^2/s$) is

Explanation

GATE→2026→Water Resources Engineering→Hydraulics

Q45

NAT[2 Marks]

A wide unlined channel carries water at depth 1 m. Max permissible bed tractive stress = $10 \text{ N/m}^2$. Maximum bed slope 1 in $n$. The value of $n$ is

Explanation

GATE→2026→Water Resources Engineering→Hydrology

Q46

NAT[2 Marks]

A bridge with expected life of 50 years is designed for a flood corresponding to a return period of 100 years. The risk associated with this design is

Explanation

GATE→2026→Water Resources Engineering→Hydrology

Q47

NAT[2 Marks]

Rainfall intensity-duration relationship $I = 25/(t+10)$ on a 7 ha plot with runoff coefficient 0.60 and entry times. Design storm-sewer flowrate (in $\text{m}^3/\text{h}$) is

Explanation

GATE→2026→Water Resources Engineering→Fluid Mechanics

Q48

NAT[2 Marks]

Maximum demand 12 MLD. For rectangular sedimentation tank with depth 4 m, detention period 6 hours, and flow velocity 0.003 m/s, the width (in m) of the tank is

Explanation

Environmental Engineering

5 Questions

GATE→2026→Environmental Engineering→Water and Wastewater Quality and Treatment

Q49

MCQ[1 Mark]

A rapid sand filter bed of depth 0.8 m has 40% porosity during service cycle. Recommended backwash expanded porosity is 70%. The uniform expanded depth (in m) during backwash is

(A)

1.0

(B)

1.2

(C)

1.4

(D)

1.6

Explanation

GATE→2026→Environmental Engineering→Water and Wastewater Quality and Treatment

Q50

MCQ[1 Mark]

The settling velocity of inorganic particles in the sedimentation tank of a water treatment plant is governed by

(A)

Darcy's law

(B)

Stokes' law

(C)

Dupuit's law

(D)

Bernoulli's law

Explanation

GATE→2026→Environmental Engineering→Water and Wastewater Quality and Treatment

Q51

MSQ[1 Mark]

Which of the following components is/are NOT removed in the secondary treatment of sewage?

(A)

Suspended settleable organic solids

(B)

Colloids including dissolved organic matter

(C)

Pathogens

(D)

Fat and grease

Explanation

GATE→2026→Environmental Engineering→Water and Wastewater Quality and Treatment

Q52

MCQ[2 Marks]

Average sewage from a city is 90 MLD and BOD5 is 300 mg/L. Standard domestic BOD5 per person is 0.08 kg/day. The population equivalent is

(A)

337500

(B)

216000

(C)

270000

(D)

168750

Explanation

GATE→2026→Environmental Engineering→Water and Wastewater Quality and Treatment

Q53

NAT[2 Marks]

Activated Sludge Process parameters provided. To maintain equilibrium, the flowrate (in $\text{m}^3/\text{day}$) of sludge to be wasted from the system is

Explanation

Transportation Engineering

6 Questions

GATE→2026→Transportation Engineering→Transportation Infrastructure

Q54

MSQ[1 Mark]

Cant on a Broad Gauge railway track is calculated for an equilibrium speed $V$ (in km/h), dynamic gauge $G$ (in mm) and radius of curve $R$ (in m) using formula/formulae:

(A)

$C = \frac{GV^2}{127 R}$

(B)

$C = \frac{13.76 V^2}{R}$

(C)

$C = \frac{13.20 V^2}{R}$

(D)

$C = \frac{8.33 V^2}{R}$

Explanation

GATE→2026→Transportation Engineering→Traffic Engineering

Q55

NAT[1 Mark]

The travel times of three vehicles on a 2 km stretch of road are 4, 5, and 8 minutes. Assuming constant speed, the Space Mean Speed (in km/h) is

Explanation

GATE→2026→Transportation Engineering→Traffic Engineering

Q56

MCQ[2 Marks]

Traffic flow and density relationships across four road sections with bottleneck constraints.

(A)

S2-D4; S3-D3; S4-D2

(B)

S2-D3; S3-D2; S4-D1

(C)

S2-D3; S3-D4; S4-D2

(D)

S2-D4; S3-D3; S4-D1

Explanation

GATE→2026→Transportation Engineering→Transportation Infrastructure

Q57

MSQ[2 Marks]

Which of the following statements is/are TRUE in the context of the geometric design of highways?

(A)

Friction coefficient for horizontal curve design is lower than for sight distance.

(B)

Centrifugal force at horizontal curve is counteracted by raising middle pavement.

(C)

Grade compensation is achieved by increasing gradient of horizontal curve.

(D)

Summit curve design length for unidirectional flow is greater than bidirectional.

Explanation

GATE→2026→Transportation Engineering→Traffic Engineering

Q58

NAT[2 Marks]

Traffic volume on dual 3-lane carriageway is 6000 veh/h/dir. A truck blocks one lane from 08:00 to 08:30. Normal capacity 2000 veh/h/ln, queue capacity 1600 veh/h/ln. Number of vehicles in queue at 10:00 am is

Explanation

GATE→2026→Transportation Engineering→Highway Pavements

Q59

NAT[2 Marks]

Bituminous mix composition percentages and specific gravities provided. The Voids Filled with Bitumen (VFB, in percentage) is

Explanation

Geomatics Engineering

5 Questions

GATE→2026→Geomatics Engineering→Principles of Surveying & Cartography

Q60

MCQ[1 Mark]

The Whole Circle Bearing (WCB) of line AB is $150^{\circ}$. The length of AB is 100 m. The latitude and departure values, respectively, for this line are:

(A)

+86.60; +50.00

(B)

+86.60; -50.00

(C)

-86.60; +50.00

(D)

-86.60; -50.00

Explanation

GATE→2026→Geomatics Engineering→Principles of Surveying & Cartography

Q61

NAT[1 Mark]

A 30 m long tape is standardized at $25^{\circ}\text{C}$ and used to measure a 200 m line at $35^{\circ}\text{C}$. Coefficient of expansion = $11 \times 10^{-6}/^{\circ}\text{C}$. Temperature correction in mm is

Explanation

GATE→2026→Geomatics Engineering→Principles of Surveying & Cartography

Q62

NAT[1 Mark]

The height of the plane of collimation of a levelling instrument is 100.000 m. Back Sight = 1.500 m on staff at ground point P. Reduced level of P is

Explanation

GATE→2026→Geomatics Engineering→Principles of Surveying & Cartography

Q63

MCQ[2 Marks]

Locations P and Q are separated by a wide valley. Level difference measured near P is 3.0 m, and near Q is -1.0 m. True difference in levels (in m) is

(A)

1.0

(B)

1.5

(C)

2.0

(D)

4.0

Explanation

GATE→2026→Geomatics Engineering→Principles of Surveying & Cartography

Q64

NAT[2 Marks]

Consecutive staff readings taken at 20 m intervals. Instrument shifted after 6th reading. The gradient (in %) of the ground between the first and last location is

Explanation