Question 1

Look at the main figure. Which one of the four options (A, B, C, D) is exactly embedded in it?

[Main figure: A large rectangle subdivided by internal lines creating multiple sections, with one section containing a clear diamond shape]

Identify the embedded figure:

Accepted Answer

This question assesses the ability to locate and recognize a specific simple shape (diamond/rhombus) within a partitioned complex figure.

Question 2

In the given complex figure, identify which simple shape is embedded within it.

[Main figure: An intricate design with overlapping circles, lines, and curves forming a mandala-like pattern]

Which shape is hidden in the figure?

Accepted Answer

This question tests the ability to identify a simple circular shape embedded within a complex, ornate figure with multiple overlapping elements.

Question 3

Examine the main figure carefully. Which of the following options shows a shape that is embedded (contained) within it?

[Main figure: A large irregular polygon with multiple internal line segments creating compartments, one of which clearly shows a rectangle]

Find the embedded figure:

Accepted Answer

This question assesses the ability to identify a rectangular shape as an embedded figure within a complex partitioned polygon.

Question 4

A rectangle is divided into 6 equal sections (2 rows × 3 columns). Section 1 (top-left) contains a star. Section 2 (top-middle) contains a star. Section 3 (top-right) is empty. Section 4 (bottom-left) contains a star. Section 5 (bottom-middle) is empty. Section 6 (bottom-right) contains a star. How many stars are embedded in this composite figure?

Accepted Answer

This question tests the ability to count embedded identical shapes across multiple compartments of a structured figure. It requires systematic scanning and accurate tallying.

Question 5

A square is divided into 4 equal smaller squares arranged in a 2×2 grid. The top-left square contains a diagonal line from bottom-left to top-right. The top-right square is completely shaded black. The bottom-left square contains a small circle in the center. The bottom-right square is empty. Which of the following figures is embedded in this composite figure?

(A) A diagonal line and a circle
(B) A diagonal line, a shaded square, and a circle
(C) Only a shaded square
(D) A circle and an empty square

Accepted Answer

This question tests the ability to identify and extract specific embedded elements from a structured composite figure made of distinct compartments. Students must recognize which individual shapes/patterns exist within the larger whole.

Question 6

Study the figure: A large triangle contains within it a smaller triangle (inverted), a rectangle, and a hexagon, all overlapping. Which shape is NOT embedded in this figure?

(A) Triangle (inverted)
(B) Rectangle
(C) Pentagon
(D) Hexagon

Accepted Answer

This question tests the ability to identify which shapes are present and, critically, which shapes are absent from a composite figure. It requires careful visual analysis and the ability to distinguish between shapes that look similar.

Question 7

In the figure shown below, a large composite shape contains several overlapping geometric forms. Identify which simple shape is embedded within it.

[Main figure: A complex arrangement of overlapping rectangles, triangles, and lines forming an abstract composition]

Which shape is embedded in the figure?

Accepted Answer

This question tests the ability to isolate and identify a simple triangle as an embedded figure within a complex composite arrangement of multiple overlapping shapes.

Question 8

In the given composite figure, identify which of the following shapes is embedded exactly as shown:

[Figure shows: A large hexagon containing a smaller pentagon, and the pentagon contains a triangle]

Options show: (a) Pentagon inside hexagon with triangle inside pentagon, (b) Triangle inside hexagon with pentagon outside, (c) Hexagon inside pentagon inside triangle, (d) Pentagon inside triangle inside hexagon

Accepted Answer

The figure shows a clear hierarchical structure: the hexagon is the outermost shape, the pentagon is embedded inside it, and the triangle is embedded inside the pentagon. Option (a) correctly represents this exact nesting order.

Question 9

A complex figure contains multiple overlapping shapes. Identify which simple shape is NOT embedded within this composite figure:

[Figure shows: A circle overlapping with a square, both overlapping with a pentagon]

Options show: (a) Circle, (b) Square, (c) Triangle, (d) Pentagon

Accepted Answer

The composite figure clearly shows a circle, square, and pentagon overlapping. A triangle is not present in the figure. The correct answer is (c) Triangle.

Question 10

Study the main figure provided. It contains several overlapping shapes and internal divisions. Which of the following figures is embedded within it?

Main Figure: A large hexagon with internal lines creating multiple sections, including a square, two triangles, and a small circle positioned at the center.

(A) A square with a circle at its center
(B) A circle surrounded by four triangles
(C) A hexagon with a square inside
(D) A square with triangles at two adjacent corners

Accepted Answer

This embedded figures question tests the ability to identify shape combinations and their spatial arrangements. The correct answer is (A) because the main figure contains a square with a circle positioned at its center point, forming this specific embedded configuration.

Question 11

In a complex pattern, an embedded figure is marked. It shows: a rectangle with a diagonal line running from top-left to bottom-right, a circle positioned in the upper-right quadrant (created by the diagonal), and a small square positioned in the lower-left quadrant. Which option correctly represents this embedded figure?

a) Rectangle with diagonal, circle in upper-right quadrant, square in lower-left quadrant
b) Rectangle with diagonal, circle in lower-left quadrant, square in upper-right quadrant
c) Rectangle with diagonal, circle in upper-left quadrant, square in lower-right quadrant
d) Rectangle with diagonal, circle in upper-right quadrant, square in lower-right quadrant

Accepted Answer

The embedded figure contains a rectangle divided by a diagonal from top-left to bottom-right. The circle is positioned in the upper-right quadrant (above and to the right of the diagonal), and the square is in the lower-left quadrant (below and to the left of the diagonal). Option A is correct.

Question 12

Study the complex figure shown below containing multiple intersecting lines and shapes. A specific small figure is highlighted with a square border. Which of the following options is the correct embedded figure?

[Complex figure: Grid-like pattern with intersecting horizontal and vertical lines, with some diagonal lines, and a small region marked with a square containing: 2 small circles, 1 triangle, and 1 horizontal line]

Options show: (A) 2 circles, 1 triangle, 1 horizontal line, (B) 2 circles, 1 triangle, 1 vertical line, (C) 3 circles, 1 triangle, 1 horizontal line, (D) 2 circles, 2 triangles, 1 horizontal line

Accepted Answer

This embedded figure question requires careful counting and identification of multiple elements within a bounded region. Students must accurately count shapes and identify line orientation.

Question 13

A composite figure is displayed containing several overlapping shapes and internal divisions. One section is marked with a diamond outline. Identify which option correctly represents this embedded figure.

[Composite figure: Contains overlapping rectangles, triangles, and a hexagon. A diamond-outlined section shows: a rectangle divided by 1 diagonal line creating 2 triangles, with a small dot in the upper triangle]

Options show: (A) Rectangle with 1 diagonal, dot in upper triangle, (B) Rectangle with 1 diagonal, dot in lower triangle, (C) Rectangle with 2 diagonals, dot in upper triangle, (D) Rectangle with 1 diagonal, no dot

Accepted Answer

This question tests the ability to identify both structural elements (diagonal division) and positional details (dot location) within an embedded figure. It requires attention to multiple attributes simultaneously.

Question 14

A large intricate figure contains multiple geometric shapes arranged in layers. A target region is marked with a hexagonal border. Which option correctly shows this embedded figure?

[Intricate figure: Multiple overlapping shapes including circles, squares, and triangles. A hexagonal-bordered region contains: a circle with a horizontal line through its center, and a small square positioned to the right of the circle]

Options show: (A) Circle with horizontal line, square to the right, (B) Circle with vertical line, square to the right, (C) Circle with horizontal line, square to the left, (D) Circle with horizontal line, square above it

Accepted Answer

This embedded figure question requires identifying both the internal structure of a shape (circle with line) and the relative positioning of multiple elements (square's location relative to circle).

Question 15

A figure shows a large equilateral triangle divided by lines. Which of the following shapes is necessarily embedded (hidden) within a regular hexagon that has all its diagonals drawn from each vertex to the opposite vertex?
(A) A small equilateral triangle
(B) A rectangle with unequal sides
(C) A pentagon
(D) A trapezium with three equal sides

Accepted Answer

When a regular hexagon has all three main diagonals drawn (connecting opposite vertices), it is divided into 6 equilateral triangles of equal size. Each of these 6 smaller triangles is an equilateral triangle embedded within the hexagon. A rectangle with unequal sides does not appear because all inner angles and segments are multiples of 60°. A pentagon is not formed by any subset of lines. A trapezium with three equal sides (isosceles trapezium) does appear but is not 'necessarily' the simplest embedded figure. The most directly and clearly embedded shape is the small equilateral triangle formed between the intersection points and the vertices. Answer: (A).

Question 16

In a complex figure, an embedded pattern is highlighted. It consists of: a large circle, inside which is a rectangle, and inside the rectangle is a small triangle positioned at the center-right of the rectangle. Which option correctly shows this embedded figure?

a) Large circle containing rectangle, with triangle at center-right inside the rectangle
b) Large circle containing rectangle, with triangle at center-left inside the rectangle
c) Large rectangle containing circle, with triangle at center-right inside the circle
d) Large circle containing rectangle, with triangle at the bottom-center inside the rectangle

Accepted Answer

The embedded figure shows a large circle as the outermost element, containing a rectangle inside it, and within that rectangle is a small triangle positioned at the center-right location. Option A correctly represents all three elements and their spatial relationships.

Question 17

A complex figure contains a star shape (5-pointed star) embedded within overlapping rectangles and circles. The star has one point facing directly upward. Additionally, there is a small circle positioned exactly at the center of the star. Which option correctly identifies this embedded configuration?

(A) 5-pointed star with one point facing upward + small circle at center
(B) 5-pointed star with one point facing upward + small circle offset to the right of center
(C) 5-pointed star with one point facing downward + small circle at center
(D) 5-pointed star with one point facing upward + no circle (circle is part of background only)

Accepted Answer

This question requires identifying two embedded elements simultaneously and verifying their relative spatial relationship. Students must correctly identify both the star's orientation and the circle's position relative to the star's center.

Question 18

A complex figure consists of a large square divided into 4 equal smaller squares arranged in a 2×2 grid. The top-left square contains a triangle pointing upward. The top-right square contains a circle with a horizontal line through its center. The bottom-left square contains a diamond shape. The bottom-right square contains a triangle pointing downward. Now, identify which of the following figures is embedded within the complex figure:

(A) A triangle pointing upward adjacent to a circle with a horizontal line
(B) A diamond shape directly below a circle with a horizontal line
(C) A triangle pointing upward with a diamond shape directly below it
(D) A circle with a horizontal line adjacent to a triangle pointing downward

Accepted Answer

This question tests the ability to identify embedded figures by recognizing spatial relationships and adjacency patterns within a composite figure. The solver must mentally isolate sub-regions and verify that the required elements exist in the specified spatial arrangement.

Question 19

A figure contains a regular pentagon with all five diagonals drawn. These diagonals create a smaller regular pentagon in the center. A circle is inscribed in the central pentagon. How many triangles (of any size) are embedded in this figure, excluding any that contain the inscribed circle as a proper subset?

(A) 25
(B) 30
(C) 35
(D) 40

Accepted Answer

The correct answer is (B) 30. A regular pentagon with all five diagonals drawn creates a complex figure with multiple embedded triangles. The five diagonals intersect to form a smaller regular pentagon in the center, and these intersections create triangles of various sizes. Systematic counting: (1) 5 small triangles at the tips of the outer pentagon, (2) 5 triangles formed between the outer pentagon and the inner pentagon, (3) 5 medium triangles formed by diagonals, (4) 5 larger triangles formed by combinations of sides and diagonals, (5) 5 additional triangles from the inner pentagon structure, (6) 5 more from diagonal intersections = 30 total. The inscribed circle constraint eliminates any triangles that would have the circle as a proper subset. Option (A) undercounts by missing medium and larger triangles. Option (C) overcounts by including triangles that contain the circle. Option (D) significantly overcounts.

Question 20

A complex figure consists of a regular hexagon with all three long diagonals drawn (connecting opposite vertices). Inside, a smaller regular hexagon is inscribed with vertices at the midpoints of the larger hexagon's sides. Additionally, a circle is drawn passing through all six vertices of the smaller hexagon. How many equilateral triangles of different sizes can be embedded in this figure?

(A) 7
(B) 9
(C) 13
(D) 15

Accepted Answer

The correct answer is (C) 13. A regular hexagon with all three long diagonals creates 6 small equilateral triangles at the center and 6 larger equilateral triangles formed by alternate vertices. The inscribed hexagon (vertices at midpoints) creates additional equilateral triangles: 6 small ones between the two hexagons, and 1 large one formed by the overall structure. Counting systematically: 6 (smallest, center) + 6 (medium, from long diagonals) + 1 (formed by inscribed hexagon structure) = 13 equilateral triangles. Option (A) undercounts by missing the medium-sized triangles. Option (B) misses the largest triangle. Option (D) overcounts by including non-equilateral triangles or counting overlaps.

UGC NET Embedded Figures

Embedded Figures— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Embedded Figures — Practice Questions

60-Second Revision — Embedded Figures