This page covers Agniveer Army GD Counting Figures with complete concept notes, 13 graded practice MCQs, key points and exam-specific tips. Free to study.
13graded MCQs · easy to hard · full solution & trap analysis
A rectangle is divided into 12 equal smaller rectangles arranged in 3 rows and 4 columns. Count the total number of rectangles of all possible sizes that can be formed by combining these smaller rectangles. [A 3×4 grid of rectangles is shown.]
In the given figure, a rectangle is divided into smaller sections by horizontal and vertical lines. There are 3 horizontal lines and 4 vertical lines drawn inside the rectangle (including the borders). How many rectangles of all sizes can be formed in this grid?
A square grid of 5×5 contains some cells shaded black and others white. A 'region' is defined as a connected group of cells of the same colour (horizontally or vertically adjacent, not diagonally). If the grid has exactly 8 black regions and 6 white regions, what is the minimum number of black cells required?
A figure shows a hexagon divided by internal lines into smaller polygons. The hexagon has 2 diagonals drawn from one vertex, creating internal divisions. Additionally, 3 horizontal lines cross the entire hexagon. How many distinct polygons (triangles, quadrilaterals, pentagons, or hexagons) are formed in total?
In a complex figure, there is a large triangle subdivided by internal lines into smaller triangles. The internal lines create 3 horizontal divisions and 2 vertical divisions within the triangle. Count the total number of triangles of all sizes visible in the figure.
A rectangular grid contains horizontal and vertical lines. There are 5 horizontal lines and 6 vertical lines. How many rectangles of all possible sizes can be formed by these lines?
A figure consists of a square subdivided by 2 horizontal lines and 2 vertical lines, creating a 3×3 grid of 9 cells. Additionally, both diagonals of the main square are drawn. How many quadrilaterals (including squares and rectangles) of all sizes are present in the figure?
A square is divided into 16 equal smaller squares (4×4 grid). Additionally, there are diagonal lines drawn from two opposite corners of the large square, creating further subdivisions. Count the total number of triangles of all sizes that can be identified in this figure.
A hexagon is divided into 6 equilateral triangles by drawing lines from the center to each vertex. Additionally, lines are drawn connecting alternate vertices, creating a smaller hexagon in the center. Count the total number of triangles of all sizes visible in the final figure.
A rectangle is divided into a 3×4 grid of smaller rectangles. Additionally, one diagonal is drawn from the top-left corner to the bottom-right corner of the entire large rectangle. Count the total number of triangles formed by this diagonal and the grid lines.
A figure shows a cube with all six faces visible. Some faces contain patterns. If the cube is unfolded into a net, and we know that opposite faces never touch in the net, how many distinct nets can be formed from a standard cube?
A figure shows a large triangle subdivided by internal lines into smaller triangles. The large triangle has 2 internal parallel lines to its base, creating 3 rows of smaller triangles. The top row has 1 triangle, the middle row has 3 triangles, and the bottom row has 5 triangles. Count the total number of triangles of all sizes (including those formed by combining smaller triangles).
A hexagon is divided into smaller regions by drawing 3 lines from the center to alternate vertices, and 2 additional lines parallel to two of its sides. How many triangles of all sizes are formed? (Assume the hexagon is regular and all internal divisions are clearly defined.)