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GATE XE 2026 | GA | Question: 1
To continue the sequence of tiles shown, the tile indicated by the question mark should be 
#2
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GATE XE 2026 | GA | Question: 2
Consider an art gallery whose walkways are shown as lines in the diagram. A black dot represents a junction of two walkways. A guard may be placed at a junction to watch ...
#3
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GATE XE 2026 | GA | Question: 3
The $2^{\text {nd }}$ of June is a Thursday in a certain year. Which day of the week is the $3^{\text {rd }}$ of July in that year?ThursdayFridaySaturdaySunday
#4
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GATE XE 2026 | GA | Question: 4
A coin with heads facing up is shown as and a coin with tails facing up is shown as .Six coins are placed in the Starting Arrangement, as shown in the figure below. A “s...
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GATE XE 2026 | GA | Question: 5
Exacerbate : Mitigate :: $\_\_\_\_$Choose the option with the correct pair of words to fill the blank.Aggravate: AlleviateAlleviate : PrecipitateAggravate: PrecipitateEma...
#6
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GATE XE 2026 | GA | Question: 6
A paper shown in Panel $\text{I}$ is folded along the dashed lines $(- - -)$ to construct a cube. The shaded regions shown in Panel $\text{I}$ appear on the outer surfac...
#7
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GATE XE 2026 | GA | Question: 7
In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both...
#8
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GATE XE 2026 | GA | Question: 8
Four people $\mathrm{P}, \mathrm{Q}, \mathrm{R}$, and $\mathrm{S}$, of different ages, make the following observations.$\mathrm{P}$ - I am younger than $\mathrm{S}$.$\mat...
#9
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GATE XE 2026 | GA | Question: 9
Circles $C_{1}, C_{2}$, and $C_{3}$, with centers $O_{1}, O_{2}$, and $O_{3}$, and radii $r_{1}, r_{2}$, and $r_{3}$, respectively, touch each other as shown in the follo...
#10
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GATE XE 2026 | GA | Question: 10
Suresh said, "I did it yesterday."Which one of the following options is the correct form of this sentence in indirect speech?Suresh said that I did it yesterday.Suresh sa...
#11
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GATE XE 2026 | Question: 1
For the complex function$$f(z)=f(x+i y)=x^{3}-4 x y^{2}+i\left(4 x^{2} y-2 y^{3}\right)$$consider the following two statements$P: f$ is not analytic at $(0,0)$.$Q: f$ doe...
#12
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GATE XE 2026 | Question: 2
Let $C$ be the circle $(x-1)^{2}+y^{2}=25$ oriented counterclockwise. Then, the value of the line integral$$\oint_{C}\left[\left(x^{5}-3 y\right) d x+\left(-2 x+e^{y^{2}}...
#13
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GATE XE 2026 | Question: 3
Let $W(x)$ denote the Wronskian of two linearly independent solutions $y_{1}(x)$ and $y_{2}(x)$ of the differential equation$$(x-1) \frac{d^{2} y}{d x^{2}}+2 \frac{d y}{d...
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GATE XE 2026 | Question: 4
Which of the following statements is/are true?$Y=1+1.8 X$ and $X=1-0.5 Y$ are estimated as lines of regression of $Y$ on $X$ and $X$ on $Y$, respectively.$Y=1+1.3 X$ and ...
#15
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GATE XE 2026 | Question: 5
Consider the matrix $A=\left[\begin{array}{ccc}1 & \sqrt{2} & 0 \\ \sqrt{2} & 0 & 0 \\ 0 & 0 & 1\end{array}\right]$. Then, which of the following statements is/are true?A...
#16
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GATE XE 2026 | Question: 6
Let $L$ be the lamina of the form $x^{2}+4 y^{2} \leq 64,0 \leq y \leq 4$, with density $\rho(x, y)=\mid x \mid y$. Then, the mass of $L$ (in integer) is $\_\_\_\_$
#17
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GATE XE 2026 | Question: 7
Let $X$ be a random variable having probability density function (pdf)$$f_X(x) =\left\{\begin{array}{ll}\dfrac{e}{2(e-1)} e^{-x}, & 0 < x < 1, \\\dfrac{1}{2}, & 1 < x < 2...
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GATE XE 2026 | Question: 8
Match each entry of $\text{List-1}$ with a suitable entry in $\text{List-2}$ and choose the correct option.$\textbf{List-1}$$\textbf{List-2}$$\mathrm{P}$$\text{The sum of...
#19
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GATE XE 2026 | Question: 9
Consider the following partial differential equation (PDE)$$(y-1) \frac{\partial^{2} u}{\partial x^{2}}-(x-3)^{2} \frac{\partial^{2} u}{\partial y^{2}}+y^{2} \frac{\parti...
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GATE XE 2026 | Question: 10
Let $\left[\begin{array}{ccc}l_{11} & 0 & 0 \\ l_{21} & l_{22} & 0 \\ l_{31} & l_{32} & -10\end{array}\right]\left[\begin{array}{ccc}1 & u_{12} & u_{13} \\ 0 & 1 & u_{23}...
#21
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GATE XE 2026 | Question: 11
The initial value problem$$\begin{array}{l}\dfrac{d u}{d t}=u^{2}+t^{2}, \quad t \geq 0 \\\text { with } u(0)=1\end{array}$$is solved by using the explicit Euler method w...
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GATE XE 2026 | Question: 12
For a laminar, incompressible, and fully-developed flow through a circular pipe, the ratio of the maximum velocity to the average velocity of the flow is$1.5$$2$$3$$4$
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GATE XE 2026 | Question: 13
Air flows with a freestream velocity $U$ over four different bodies having same frontal area facing to the flow direction, as shown in the figure. Which one of the follow...
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GATE XE 2026 | Question: 14
Consider a steady, and incompressible flow over a body with characteristic length $\text{L}$. The boundary layer thickenss at a distance $x$ from the leading edge is $\de...
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GATE XE 2026 | Question: 15
Three different siphons steadily discharge water at velocities $V_{\mathrm{I}}, V_{\mathrm{II}}$, and $V_{\mathrm{IIII}}$, as shown in the figure. The tubes of the siphon...
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GATE XE 2026 | Question: 16
Consider the following statements:Assertion (a)Surface tension acts along the interface of two fluids.Reason (r)The pressure of the fluid inside a bubble is higher than t...
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GATE XE 2026 | Question: 17
The basic dimensions, i.e., mass, length, and time are represented by $M, L$, and $T$, respectively. The correct dimension of dynamic viscosity is$M L T^{-2}$$M^{0} L^{2}...
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GATE XE 2026 | Question: 18
The velocity components in $x$ - and $y$-directions of a two-dimensional, incompressible flow field are $u(x, y)=2 x^{2}+y^{3}$ and $v(x, y)=x^{3}-2 x y+f(x, y)$, respect...
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GATE XE 2026 | Question: 19
Which of the following statements about streamlines, pathlines, and streaklines is/are correct?A streamline is a curve that is everywhere tangent to the instantaneous loc...
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GATE XE 2026 | Question: 20
A piezometer and a Pitot tube are tapped into a horizontal water pipe, as shown in the figure, where $h_{1}=4 \mathrm{~cm}, h_{2}=6 \mathrm{~cm}$ and $h_{3}=5 \mathrm{~cm...
#31
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GATE XE 2026 | Question: 21
A steady, laminar, and incompressible flow between a pair of infinite parallel plates is driven by a constant pressure gradient $(-d p / d x)$. The plates are separated b...
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GATE XE 2026 | Question: 22
An incompressible fluid flows between a pair of infinite plates separated by a distance $L$. The top plate is moving with a constant velocity $U$, whereas the bottom plat...
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GATE XE 2026 | Question: 23
Consider two different cases of water flowing through a smooth pipe of $50$ $\mathrm{cm}$ diameter. The mass flow rates for the two cases are $\text{(i)}$ $0.25 \mathrm{~...
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GATE XE 2026 | Question: 24
A two-dimensional source flow (with stream function, $\psi_{1}=m \tan ^{-1} \dfrac{y}{x}$ ) is placed at the origin in a uniform flow (with stream function, $\psi_{2}=U y...
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GATE XE 2026 | Question: 25
Consider a steady, laminar, and incompressible flow over a flat plate, as shown in the figure. With freestream velocity $U_{\infty}$ and kinematic viscosity $v_{1}$, the ...
#36
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GATE XE 2026 | Question: 26
A vertical jet of diameter $d_{1}$ strikes a horizontal plate with a velocity $U$, as shown in the figure. The plate has a hole of diameter $d_{2}(<d_{1})$ concentric to ...
#37
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GATE XE 2026 | Question: 27
The velocity of a fluid particle in a flow is given as:$$\vec{V}=(a-x) \hat{\imath}+(b+y) \hat{\jmath}+(c+z) \hat{k}$$where $a, b, c$ are constants, and $\hat{\imath}, \h...
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GATE XE 2026 | Question: 28
A gas is pressurized in a vertical frictionless piston-cylinder device, as shown in the figure. The piston has a mass of $4$ kg and a cross-sectional area of $40 \mathrm{...
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GATE XE 2026 | Question: 29
A ship is designed to sail at a speed of $8 \mathrm{~m} \cdot \mathrm{~s}^{-1}$. A designer makes a $1/10$ scaled model to test the ship in a water tunnel. The model and ...
#40
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GATE XE 2026 | Question: 30
A rectangular block (density $=600 \mathrm{~kg} \cdot \mathrm{~m}^{-3}$ ) with base area of $0.06 \mathrm{~m}^{2}$ and height $15$ cm is partially submerged in water (den...
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