GATE Overflow for GATE ESE - Recent questions in Spatial Aptitude

GATE ES 2026 | GA | Question: 1

Mon, 23 Feb 2026 13:18:44 +0000

To continue the sequence of tiles shown, the tile indicated by the question mark should be

GATE ES 2026 | GA | Question: 6

Mon, 23 Feb 2026 13:18:34 +0000

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 surface of the cube. Referring to cubes shown in Panel $\text{II}$, which one of the options is correct?

Only $\text{(i)}$ can correspond to the unfolded cube in Panel $\text{I}$.
Only $\text{(ii)}$ can correspond to the unfolded cube in Panel $\text{I}$.
Both $\text{(i)}$ and $\text{(ii)}$ can correspond to the unfolded cube in Panel $\text{I}$.
Neither $\text{(i)}$ nor $\text{(ii)}$ can correspond to the unfolded cube in Panel $\text{I}$.

GATE ES 2025 | GA Question: 4

Thu, 06 Mar 2025 16:56:30 +0000

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are $1,2$, and $3$, respectively. Which one among the given options is the most appropriate combination of $\mathrm{P}, \mathrm{Q}$, and $\mathrm{R}$?

$P=6 ; Q=5 ; R=3$
$P=5 ; Q=6 ; R=3$
$P=3 ; Q=6 ; R=6$
$P=5 ; Q=3 ; R=6$

GATE ES 2025 | GA Question: 8

Thu, 06 Mar 2025 16:56:18 +0000

A regular dodecagon ($12$-sided regular polygon) is inscribed in a circle of radius $r$ cm as shown in the figure. The side of the dodecagon is $d \mathrm{~cm}$. All the triangles (numbered $1$ to $12$) in the figure are used to form squares of side $r \mathrm{~cm}$ and each numbered triangle is used only once to form a square.

The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Note: The figure shown is representative.

$3 ; 4$
$4 ; 3$
$3 ; 3$
$3 ; 2$

GATE ES 2024 | GA Question: 10

Mon, 19 Feb 2024 10:29:49 +0000

Visualize two identical right circular cones such that one is inverted over the other and they share a common circular base. If a cutting plane passes through the vertices of the assembled cones, what shape does the outer boundary of the resulting cross-section make?

A rhombus
A triangle
An ellipse
A hexagon

GATE ES 2024 | GA Question: 9

Mon, 19 Feb 2024 10:29:49 +0000

Three different views of a dice are shown in the figure below.

The piece of paper that can be folded to make this dice is

GATE ES 2021 | GA Question: 3

Tue, 14 Mar 2023 03:48:46 +0000

The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is

GATE ES 2021 | GA Question: 8

Tue, 14 Mar 2023 03:48:29 +0000

Consider a square sheet of side $1$ unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is________

$\frac{\pi}{3}$
$\frac{2 \pi}{3}$
$\frac{3 \pi}{2}$
$3 \pi$

GATE ES 2021 | GA Question: 10

Tue, 14 Mar 2023 03:48:27 +0000

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.

The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is

$2: 3$
$3: 4$
$4: 5$
$5: 6$

GATE ES 2022 | GA Question: 5

Fri, 17 Feb 2023 06:57:00 +0000

An art gallery engages a security guard to ensure that the items displayed are \end{tabular} protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) of the gallery is within the line of sight of the security guard.

If the security guard does not move around the posted location and has a $360^{\circ}$ view, which one of the following correctly represents the set of ALL possible locations among the locations $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$, where the security guard can be posted to watch over the entire inner space of the gallery.

$\text{P and Q}$
$\mathrm{Q}$
$\text{Q and S}$
$\mathrm{R}$ and $\mathrm{S}$

GATE ES 2022 | GA Question: 10

Fri, 17 Feb 2023 06:56:55 +0000

Consider the following square with the four corners and the center marked as $\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{S}$ and $\mathrm{T}$ respectively.

Let $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$ represent the following operations:
$\mathrm{X}$ : rotation of the square by $180$ degree with respect to the $\mathrm{S}-\mathrm{Q}$ axis.
Y: rotation of the square by $180$ degree with respect to the $\text{P-R}$ axis.
$\mathrm{Z}$ : rotation of the square by $90$ degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point $T$.
Consider the following three distinct sequences of operation (which are applied in the left to right order).

$\text{XYZZ}$
$\text{XY}$
$\mathrm{ZZZZ}$

Which one of the following statements is correct as per the information provided above?

The sequence of operations $(1)$ and $(2)$ are equivalent
The sequence of operations $(1)$ and $(3)$ are equivalent
The sequence of operations $(2)$ and $(3)$ are equivalent
The sequence of operations $(1)$, $(2)$ and $(3)$ are equivalent