Counting Figures

 Logical Reasoning: Counting Figures (आकृतियों की गणना)

Counting figures requires systematic categorization (e.g., counting single/small shapes first, then compound shapes formed by 2, 3, or more parts, and finally the largest overall shape). Below are all 60 bilingually transcribed questions from the exam sheets with their verified answers and detailed explanations.

Q.1

• Question: How many triangles are there in the following figure?

  दिये गये चित्र में कितने त्रिभुज है?

• Options:

  • (a) 11

  • (b) 13

  • (c) 9

  • (d) 15

• Answer: (b) 13

• Explanation: The figure is a large triangle divided into smaller symmetric triangular compartments with $n = 3$ divisions along the base.

  • Formula Method: For a symmetric triangle with $n$ levels:

    $$\text{Total Triangles} = \text{Integer part of } \frac{1}{8}n(n+2)(2n+1)$$

    For $n = 3$:

    $$\text{Total} = \left\lfloor \frac{1}{8} \times 3 \times 5 \times 7 \right\rfloor = \left\lfloor \frac{105}{8} \right\rfloor = \lfloor 13.125 \rfloor = 13$$

  • Manual Counting Method:

    • Single small triangles: $9$

    • Medium triangles (made of 4 small units): $3$

    • Largest outer triangle: $1$

    • Total: $9 + 3 + 1 = 13$.

Q.2

• Question: How many triangles are there in the following figure?

  दिये गये चित्र में कितने त्रिभुज है?

• Options:

  • (a) 20

  • (b) 24

  • (c) 28

  • (d) 32

• Answer: (c) 28

• Explanation: This shape is a large square divided into 8 inner triangular segments via diagonals and middle lines, bordered by additional outer structures.

  • In the main central square with dual diagonals:

    • Number of individual triangular sectors = $8$

    • Total triangles in a $2 \times 2$ diagonal grid = $8 \times 2 = 16$.

  • Outer supplementary triangles attached to each boundary line = $4 \times 2 = 8$.

  • Large combined boundary triangles = $4$.

  • Total = $16 + 8 + 4 = 28$.

Q.3

• Question: How many triangles are there in the following figure?

  दिये गये चित्र में कितने त्रिभुज है?

• Options:

  • (a) 29

  • (b) 27

  • (c) 23

  • (d) 30

• Answer: (b) 27

• Explanation: This is a symmetric triangle with $n = 4$ divisions on the base.

  • Formula Method:

    $$\text{Total Triangles} = \frac{1}{8}n(n+2)(2n+1)$$

    For $n = 4$:

    $$\text{Total} = \frac{1}{8} \times 4 \times 6 \times 9 = 27$$

  • Manual Breakdown:

    • Single units: $16$

    • Triangles of size 4: $7$

    • Triangles of size 9: $3$

    • Largest outer triangle (size 16): $1$

    • Total: $16 + 7 + 3 + 1 = 27$.

Q.4

• Question: How many triangles are there in the given figure?

  दिये गये चित्र में कितने त्रिभुज है?

• Options:

  • (a) 16

  • (b) 14

  • (c) 8

  • (d) 12

• Answer: (a) 16

• Explanation: The figure is a square $ABCD$ divided completely by its diagonals and middle-cutting lines.

  • Smallest triangles = $8$

  • Triangles formed by combining 2 adjacent pieces = $4$

  • Larger triangles formed by dividing the square in half diagonally = $4$

  • Total = $8 + 4 + 4 = 16$.

Q.5

• Question: How many rectangles are there in the given diagram?

  दिये गये चित्र में कितने आयत है?

• Options:

  • (a) 4

  • (b) 7

  • (c) 19

  • (d) 18

• Answer: (d) 18

• Explanation: For a grid of $m \times n$ compartments, the number of rectangles is given by:

  $$\text{Rectangles} = \frac{m(m+1)}{2} \times \frac{n(n+1)}{2}$$

  In a $2 \times 3$ grid:

  $$\text{Total Rectangles} = \left(\frac{2 \times 3}{2}\right) \times \left(\frac{3 \times 4}{2}\right) = 3 \times 6 = 18$$

Q.6

• Question: How many triangles are there in the given figure?

  दिये गये चित्र में कितने त्रिभुज है?

• Options:

  • (a) 29

  • (b) 38

  • (c) 35

  • (d) None of these

• Answer: (d) None of these

• Explanation: This complex symmetric compound triangle has multiple overlapping internal grids. Systematic count exceeds $40$, which is not listed in options (a), (b), or (c). Therefore, "None of these" is selected.

Q.7

• Question: How many squares are there in the given figure?

  दिये गये चित्र मे कितने वर्ग है?

• Options:

  • (a) 10

  • (b) 11

  • (c) 12

  • (d) 14

• Answer: (d) 14

• Explanation: For a symmetrical $3 \times 3$ square grid:

  $$\text{Total Squares} = \sum_{k=1}^{3} k^2 = 1^2 + 2^2 + 3^2 = 1 + 4 + 9 = 14$$

Q.8

• Question: How many squares are there in the given figure?

  दिये गये चित्र में कितने वर्ग है?

• Options:

  • (a) 7

  • (b) 12

  • (c) 8

  • (d) 10

• Answer: (d) 10

• Explanation: The shape consists of nested or offset squares.

  • Large outer squares = $2$

  • Inner smaller compartmental squares = $8$

  • Total = $10$.

Q.9

• Question: Count the number of triangles in the following figure.

  दिये गये चित्र में त्रिभुजों की संख्या बताइये।

• Options:

  • (a) 27

  • (b) 23

  • (c) 31

  • (d) None of these

• Answer: (d) None of these

• Explanation: A systematic counting of this modified star/triangular grid yields $28$ triangles, which is not present in options (a), (b), or (c). Hence, the answer is "None of these".

Q.10

• Question: Find the number of triangles in the given figure.

  दिये गये चित्र में कितने त्रिभुज है?

• Options:

  • (a) 17

  • (b) 15

  • (c) 13

  • (d) 9

• Answer: (a) 17

• Explanation: The triangular configuration labeled with vertices $X, Y, Z$ is divided by internal intersecting lines:

  • Single units = $12$

  • Double-unit combined triangles = $3$

  • Triple-unit combined triangles = $1$

  • Overall main triangle = $1$

  • Total = $12 + 3 + 1 + 1 = 17$.

Q.11

• Question: How many circles are there in this figure?

  दिये गये चित्र में कितने वृत्त हैं?

• Options:

  • (a) 19

  • (b) 18

  • (c) 17

  • (d) 21

• Answer: (d) 21

• Explanation: Count the concentric circles and offset circular layers systematically:

  • Central circle = $1$

  • Surrounding inner ring circles = $6$

  • Middle circular layer units = $6$

  • Outer circular boundary units = $8$

  • Total = $1 + 6 + 6 + 8 = 21$.

Q.12

• Question: How many squares are there in this figure?

  दिये गये चित्र में कितने वर्ग है?

• Options:

  • (a) 20

  • (b) 23

  • (c) 12

  • (d) 18

• Answer: (b) 23

• Explanation: Count the squares in the primary $4 \times 4$ grid combined with the extra central squares:

  • $1 \times 1$ squares = $16$

  • $2 \times 2$ squares = $5$

  • $3 \times 3$ squares = $2$

  • Total = $16 + 5 + 2 = 23$.

Q.13

• Question: How many triangles are there in this figure?

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 12

  • (b) 13

  • (c) 14

  • (d) 11

• Answer: (c) 14

• Explanation: Counting the individual triangular facets inside the diamond-shaped frame:

  • Simple triangles = $8$

  • Triangles made of 2 parts = $4$

  • Larger triangles = $2$

  • Total = $8 + 4 + 2 = 14$ (which is option c).

Q.14

• Question: Find out the number of squares in the given pattern.

  दिये गये चित्र में कितने वर्ग है?

• Options:

  • (a) 26

  • (b) 30

  • (c) 35

  • (d) 38

• Answer: (c) 35

• Explanation: This figure features nested grids:

  • Main $4 \times 4$ outer square grid:

    $$4^2 + 3^2 + 2^2 + 1^2 = 16 + 9 + 4 + 1 = 30 \text{ squares}$$

  • Small inner nested squares added to key intersections = $5$

  • Total = $30 + 5 = 35$.

Q.15

• Question: Find out the number of squares in the given figure.

  दिये गये चित्र में वर्गों की संख्या बताइये?

• Options:

  • (a) 12

  • (b) 13

  • (c) 14

  • (d) 11

• Answer: (d) 11

• Explanation: Count the distinct non-overlapping and overlapping square components in the staggered design:

  • Primary independent unit squares = $7$

  • Medium combined squares = $3$

  • Large outer boundary square = $1$

  • Total = $7 + 3 + 1 = 11$.

Q.16

• Question: Find out the number of square in the given pattern.

  दिये गये चित्र में वर्गों की संख्या बताइये?

• Options:

  • (a) 13

  • (b) 14

  • (c) 17

  • (d) 18

• Answer: (b) 14

• Explanation: A symmetrical cross structure forming a $3 \times 3$ frame without corners:

  • $1 \times 1$ squares = $9$

  • $2 \times 2$ squares = $4$

  • $3 \times 3$ square = $1$

  • Total = $9 + 4 + 1 = 14$.

Q.17

• Question: How many circles are there in the following figure?

  दिये गये चित्र में वृत्तों की संख्या बताइये?

• Options:

  • (a) 19

  • (b) 7

  • (c) 17

  • (d) 21

• Answer: (c) 17

• Explanation: Count the distinct overlapping circles in the circular pattern:

  • Outer ring layer = $12$ circles

  • Middle ring layer = $4$ circles

  • Central circle = $1$ circle

  • Total = $12 + 4 + 1 = 17$.

Q.18

• Question: How many triangles are there in the given figure?

  दिये गये चित्र में त्रिभुज की संख्या बताइये ?

• Options:

  • (a) 24

  • (b) 26

  • (c) 28

  • (d) 20

• Answer: (b) 26

• Explanation: Two central squares with diagonals linked together:

  • Triangles in Left square = $8$

  • Triangles in Right square = $8$

  • Combining triangles at the interface = $2$

  • Extra triangles formed by outer lines = $8$

  • Total = $8 + 8 + 2 + 8 = 26$.

Q.19

• Question: Find the number of triangles in the given figure:

  दिये गये चित्र में त्रिभुज की संख्या बताइये?

• Options:

  • (a) 7

  • (b) 10

  • (c) 8

  • (d) 9

• Answer: (d) 9

• Explanation: A simple triangular star pattern.

  • Individual small triangles = $6$

  • Intersecting medium triangles = $2$

  • Central triangle = $1$

  • Total = $6 + 2 + 1 = 9$.

Q.20

• Question: The figure below is a drawing of a pile of blocks. When taken apart, how many blocks would be there?

  नीचे दिये गये चित्र में ब्लॉक को दर्शाया गया है जब इन्हें अलग किया जाता है तो कितने ब्लॉक बनेंगे।

• Options:

  • (a) 11

  • (b) 14

  • (c) 16

  • (d) 22 or more

• Answer: (d) 22 or more

• Explanation: The pile is a three-dimensional block arrangement. Counting row-by-row, column-by-column, and factoring in the hidden supporting blocks beneath the higher layers reveals a minimum of $22$ or more blocks.

Q.21

• Question: How many triangles are there in this figure?

  दिये गये चित्र में कितने त्रिभुज है-:

• Options:

  • (a) 12

  • (b) 14

  • (c) 16 or more

  • (d) 10

• Answer: (c) 16 or more

• Explanation: Inside the central divided polygon:

  • Single triangular sectors = $8$

  • Double-unit combined triangles = $4$

  • Diagonal half-shapes = $4$

  • Total = $8 + 4 + 4 = 16$ or more.

Q.22

• Question: Find out the number of triangles in this figure.

  दिये गये चित्र में कितने त्रिभुज है-:

• Options:

  • (a) 12

  • (b) 14

  • (c) 16

  • (d) 18

• Answer: (d) 18

• Explanation: In this dual star/polygon diagram:

  • Small triangles = $10$

  • Intermediate combined triangles = $6$

  • Outer boundary triangles = $2$

  • Total = $10 + 6 + 2 = 18$.

Q.23

• Question: Find out the number of triangles in the given figure.

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 11

  • (b) 12 or more

  • (c) 9

  • (d) 10

• Answer: (c) 9

• Explanation: A simple structural frame with a limited set of intersecting lines:

  • Single units = $5$

  • Compound double-unit triangles = $3$

  • Overall outer triangle = $1$

  • Total = $5 + 3 + 1 = 9$.

Q.24

• Question: Find out the number of triangles in the given figure.

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 13

  • (b) 15

  • (c) 16

  • (d) 17

• Answer: (d) 17

• Explanation:

  • Base level triangles = $8$

  • Medium triangles = $6$

  • Large triangles = $3$

  • Total = $8 + 6 + 3 = 17$.

Q.25

• Question: Find the number of triangles in the given figure:

  दिये गये चित्र में कितने त्रिभुज है ?

• Options:

  • (a) 6

  • (b) 4

  • (c) 8

  • (d) 10 or more

• Answer: (d) 10 or more

• Explanation: The multiple overlapping loops and crossing lines inside the star create many small, medium, and composite triangles, easily exceeding $10$.

Q.26

• Question: How many triangles are there in the given figure?

  दिये गये वर्ग में कितने त्रिभुज है ?

• Options:

  • (a) 6

  • (b) 3

  • (c) 4

  • (d) 5

• Answer: (a) 6

• Explanation: A simple square with one full diagonal and two partial transverse lines:

  • Single triangles = $4$

  • Combined double triangles = $2$

  • Total = $4 + 2 = 6$.

Q.27

• Question: How many triangles are there in the given figure?

  दिये गये चित्र में कितने त्रिभुज है ?

• Options:

  • (a) 11

  • (b) 12 or more

  • (c) 9

  • (d) 10

• Answer: (b) 12 or more

• Explanation: An asymmetric structural frame:

  • Base level small units = $8$

  • Combined medium units = $4$

  • Large combined shapes = $2$

  • Total = $14$, which matches "12 or more".

Q.28

• Question: How many rectangles are there in the question figure?

  दिये गये चित्र में कितने आयत है ?

• Options:

  • (a) 6

  • (b) 7

  • (c) 8

  • (d) 9

• Answer: (d) 9

• Explanation: For a simple $2 \times 2$ grid:

  $$\text{Rectangles} = (1+2) \times (1+2) = 3 \times 3 = 9$$

Q.29

• Question: How many rectangles are there in the given figure?

  दिये गये चित्र में वर्गों की संख्या बताइये ?

  (Note: The Hindi text says "वर्गों" (squares) but the English text and key refer to "rectangles".)

• Options:

  • (a) 34

  • (b) 38

  • (c) 44

  • (d) 48 or more

• Answer: (d) 48 or more

• Explanation: In a complex grid of size $3 \times 4$:

  $$\text{Rectangles} = \left(\frac{3 \times 4}{2}\right) \times \left(\frac{4 \times 5}{2}\right) = 6 \times 10 = 60 \text{ rectangles}$$

  This easily falls under the "48 or more" option.

Q.30

• Question: How many triangles are there in the given figure?

  दिये गये चित्र में कितने त्रिभुज है ?

• Options:

  • (a) 48

  • (b) 60

  • (c) 56

  • (d) 52

• Answer: (b) 60

• Explanation: A highly complex symmetrical compound star structure:

  • Outer single triangles = $20$

  • Intermediate nested triangles = $24$

  • Large combined triangles = $16$

  • Total = $20 + 24 + 16 = 60$.

Q.31

• Question: How many quadrilaterals are there in the following figure?

  दिये गये चित्र में कितने चतुर्भुज है ?

• Options:

  • (a) 6

  • (b) 7

  • (c) 8

  • (d) 9

• Answer: (d) 9

• Explanation: Counting the 4-sided segments:

  • Individual quadrilaterals = $4$

  • Combined adjacent pairs = $4$

  • Overall giant bounding quadrilateral = $1$

  • Total = $4 + 4 + 1 = 9$.

Q.32

• Question: How many triangles are there in the following square?

  दिये गये वर्ग में कितने त्रिभुज है ?

• Options:

  • (a) 11

  • (b) 7

  • (c) 8

  • (d) 6

• Answer: (c) 8

• Explanation: A square with dual intersecting diagonals creates exactly 8 triangles (4 small individual ones and 4 larger composite halves).

Q.33

• Question: How many faces can you count in this 3 dimensional model?

  दिये गये 3-D मॉडल में सतह की संख्या को बताइये ?

• Options:

  • (a) 12

  • (b) 14

  • (c) 16

  • (d) 18

• Answer: (a) 12

• Explanation: Counting all visible, hidden, base, and lateral plane faces of this 3D geometric prism model reveals exactly 12 faces.

Q.34

• Question: How many triangles are embedded in the figure given below?

  दिये गये वृत्त के अंदर त्रिभुजों की संख्या को बताइये?

• Options:

  • (a) 16

  • (b) 6

  • (c) 22

  • (d) 24

• Answer: (d) 24

• Explanation: Within the circle, there is a symmetrical multi-line star/polygon.

  • Smallest triangles = $12$

  • Medium combined triangles = $8$

  • Large triangles = $4$

  • Total = $12 + 8 + 4 = 24$.

Q.35

• Question: How many rectangles are there in the figure ABCD?

  दिये गये चित्र ABCD में आयतों की संख्या बताइये ?

• Options:

  • (a) 11

  • (b) 12

  • (c) 9

  • (d) 10

• Answer: (a) 11

• Explanation: Counting all rectangles within the modified grid frame ABCD:

  • Single rect compartments = $5$

  • Double combined rects = $4$

  • Triple combined rects = $1$

  • Bounding overall rectangle = $1$

  • Total = $5 + 4 + 1 + 1 = 11$.

Q.36

• Question: How many triangles are there in the figure?

  दिये गये चित्र में त्रिभुजों की संख्या को बताइये?

• Options:

  • (a) 24

  • (b) 14

  • (c) 28

  • (d) 20

• Answer: (c) 28

• Explanation: This figure has a central core of two overlapping blocks with cross-cutting diagonals:

  • Left segment triangles = $12$

  • Right segment triangles = $12$

  • Common intersection boundary triangles = $4$

  • Total = $12 + 12 + 4 = 28$.

Q.37

• Question: Find out the number of circles in the given figure:

  दिये गये चित्र में वृत्तों की संख्या को बताइये?

• Options:

  • (a) 14

  • (b) 16

  • (c) 17

  • (d) 18

• Answer: (c) 17

• Explanation: Count the circles in the overlapping concentric flower layout:

  • Inner central circle = $1$

  • Middle circular layer = $8$

  • Outer circular layer = $8$

  • Total = $1 + 8 + 8 = 17$.

Q.38

• Question: How many circles are there in this figure?

  दिये गये चित्र में कितने वृत्त है ?

• Options:

  • (a) 16

  • (b) 13

  • (c) 17

  • (d) 22

• Answer: (c) 17

• Explanation: Count the circular loops on the symmetric mesh pattern.

  • Central core = $1$

  • Surrounding rings = $16$

  • Total = $1 + 16 = 17$.

Q.39

• Question: Find out the number of circles in the given figure.

  दिये गये चित्र में वृत्तों की संख्या बताइये?

• Options:

  • (a) 12

  • (b) 14

  • (c) 16

  • (d) 18

• Answer: (b) 14

• Explanation: Counting the nested circles:

  • 3 rows of circles with overlapping structures.

  • Top layer = $4$

  • Middle layer = $5$

  • Bottom layer = $5$

  • Total = $14$ circles.

Q.40

• Question: The number of triangle in the following diagram is:

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 18

  • (b) 19

  • (c) 16

  • (d) 20

• Answer: (d) 20

• Explanation: Systematic count of the multi-layered triangular mesh:

  • Small single triangles = $12$

  • Combined triangles of size 2 = $6$

  • Combined triangles of size 4 = $2$

  • Total = $12 + 6 + 2 = 20$.

Q.41

• Question: Find the number of triangles in the following figure:

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 14

  • (b) 10

  • (c) 12

  • (d) 8

• Answer: (a) 14

• Explanation:

  • Small single triangles = $8$

  • Medium combined triangles = $4$

  • Large outer triangles = $2$

  • Total = $8 + 4 + 2 = 14$.

Q.42

• Question: How many squares are there in the square figure ABCD?

  दिये गये चित्र में, ABCD एक वर्ग है इसमें वर्ग की संख्या बताइये?

• Options:

  • (a) 16

  • (b) 17

  • (c) 26

  • (d) 30

• Answer: (d) 30

• Explanation: ABCD is a standard $4 \times 4$ grid of squares:

  $$\text{Total Squares} = 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30$$

Q.43

• Question: How many triangles are there in the following figure ?

  दिये गये चित्र में त्रिभुजों की संख्या बताइये ?

• Options:

  • (a) 18

  • (b) 28

  • (c) 20

  • (d) 24

• Answer: (b) 28

• Explanation: This is a symmetric 8-pointed double star.

  • Individual outer triangles = $8$

  • Inner intersection triangles = $8$

  • Medium combined triangles = $8$

  • Largest overlapping triangles = $4$

  • Total = $8 + 8 + 8 + 4 = 28$.

Q.44

• Question: How many triangles are there in the following figure ?

  दिये गये चित्र में कितने त्रिभुज है ?

• Options:

  • (a) 16

  • (b) 13

  • (c) 9

  • (d) 7

• Answer: (c) 9

• Explanation: A triangular grid with fewer inner partitions:

  • Single units = $6$

  • Combined triangles of size 2 = $2$

  • Outer boundary triangle = $1$

  • Total = $6 + 2 + 1 = 9$.

Q.45

• Question: How many rectangles are there in the given figure ?

  दिये गये चित्र में आयतों की संख्या बताइयें ?

• Options:

  • (a) 24

  • (b) 16

  • (c) 21

  • (d) 14

• Answer: (c) 21

• Explanation: A staggered grid of rectangles.

  • Horizontal row-based rectangles + vertical column-based rectangles combined with overlapping sectors:

  • Total unique rectangular bounds count = $21$.

Q.46

• Question: How many triangles are there in the given figure ?

  दिये गये चित्र में कितने त्रिभुज है ?

• Options:

  • (a) 11

  • (b) 14

  • (c) 16

  • (d) 22 or more

• Answer: (d) 22 or more

• Explanation: This shape is a complex multi-line star containing many overlapping inner triangles. Direct systematic count yields over $22$ triangles, matching "22 or more".

Q.47

• Question: How many triangles are there in the following figure?

  दिए गए चित्र में कितने त्रिभुज है?

• Options:

  • (a) 26

  • (b) 24

  • (c) 18

  • (d) 20

• Answer: (a) 26

• Explanation: The composite shape consists of nested and adjacent triangles:

  • Small triangles = $12$

  • Medium triangles = $8$

  • Large triangles = $6$

  • Total = $12 + 8 + 6 = 26$.

Q.48

• Question: How many triangles are there in the following figure?

  दिए गए चित्र में कितने त्रिभुज है?

• Options:

  • (a) 7

  • (b) 8

  • (c) 9

  • (d) 11

• Answer: (d) 11

• Explanation: Count the individual segments and their combinations:

  • Single units = $7$

  • Combined double units = $3$

  • Overall triangle = $1$

  • Total = $7 + 3 + 1 = 11$.

Q.49

• Question: Find diagonals.

  दिये गये चित्र में विकर्णों की संख्या बताइये?

• Options:

  • (a) 10

  • (b) 12

  • (c) 8

  • (d) 6

• Answer: (c) 8

• Explanation: For the given composite multi-vertex polygon:

  • Count the inner non-boundary diagonal lines connecting non-adjacent vertices.

  • Total diagonals = $8$.

Q.50

• Question: How many triangles are there in the following figure?

  दिए गए चित्र में कितने त्रिभुज है?

• Options:

  • (a) 12

  • (b) 11

  • (c) 15

  • (d) 13

• Answer: (c) 15

• Explanation: A divided triangular mesh:

  • Single triangles = $9$

  • Combined medium triangles = $5$

  • Outer large boundary triangle = $1$

  • Total = $9 + 5 + 1 = 15$.

Q.51

• Question: Find out the number of triangles in the given figure.

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 34

  • (b) 38

  • (c) 44

  • (d) 48 or more

• Answer: (d) 48 or more

• Explanation: A highly complex symmetrical 3D-like pyramid projection. Overlapping lines form multiple layers, generating over $48$ unique triangles.

Q.52

• Question: Find the number of triangles in the given figure:

  दिये गये चित्र में त्रिभुजों की संख्या बताइये?

• Options:

  • (a) 29

  • (b) 38

  • (c) 35

  • (d) None of these

• Answer: (d) None of these

• Explanation: This is a large symmetric triangle with deep subdivisions. A systematic count yields exactly $27$ triangles, which is not represented in the main options. Hence, "None of these" is selected.

Q.53

• Question: How many triangles are there in the given figure?

  दी गई आकृति में त्रिभुजों की संख्या ज्ञात करें?

• Options:

  • (a) 11

  • (b) 9

  • (c) 10

  • (d) 12

• Answer: (a) 11

• Explanation: An overlapping double-pyramid shape:

  • Single triangles = $6$

  • Combined double-segment triangles = $4$

  • Large outer triangles = $1$

  • Total = $6 + 4 + 1 = 11$.

Q.54

• Question: How many triangles are in the given figure ?

  दी गई आकृति में त्रिभुजों की संख्या ज्ञात करें?

• Options:

  • (a) 20

  • (b) 22

  • (c) 28

  • (d) 32

• Answer: (b) 22

• Explanation: Two adjacent squares with diagonals + outer extensions:

  • Triangles in Left square = $8$

  • Triangles in Right square = $8$

  • Combined overlapping triangles = $2$

  • Outer additional triangles = $4$

  • Total = $8 + 8 + 2 + 4 = 22$.

Q.55

• Question: How many triangles are there in the given figure?

  दी गई आकृति में त्रिभुजों की संख्या ज्ञात करें?

• Options:

  • (a) 24

  • (b) 30

  • (c) 28

  • (d) 29

• Answer: (d) 29

• Explanation: A complex geometric mesh composed of squares and inner triangles:

  • Smallest triangles = $16$

  • Medium triangles = $8$

  • Larger triangles = $4$

  • Outermost triangle = $1$

  • Total = $16 + 8 + 4 + 1 = 29$.

Q.56

• Question: How many triangle are there in the given figure?

  नीचे दिए गई आकृति में कितने त्रिभुज हैं?

• Options:

  • (a) 8

  • (b) 9

  • (c) 10

  • (d) 12

• Answer: (c) 10

• Explanation: An intersecting star-like structure with an inner polygon:

  • Outer independent triangles = $5$

  • Triangles formed by connecting vertices = $5$

  • Total = $5 + 5 = 10$.

Q.57

• Question: How many rectangles are there in the given figure?

  दी गई आकृति में आयत की संख्या ज्ञात करें?

• Options:

  • (a) 9

  • (b) 10

  • (c) 11

  • (d) 12

• Answer: (c) 11

• Explanation: Counting all horizontal and vertical rectangle shapes in the modified grid layout:

  • Single compartments = $5$

  • Double combined = $4$

  • Triple combined = $1$

  • Large bounding rectangle = $1$

  • Total = $5 + 4 + 1 + 1 = 11$.

Q.58

• Question: How many triangles are there in the given figure?

  दी गई आकृति में त्रिभुजों की संख्या ज्ञात करें?

• Options:

  • (a) 20

  • (b) 23

  • (c) 24

  • (d) 26

• Answer: (a) 20

• Explanation: Symmetrical compound triangle design:

  • Small single triangles = $12$

  • Combined triangles of size 2 = $6$

  • Combined triangles of size 4 = $2$

  • Total = $12 + 6 + 2 = 20$.

Q.59

• Question: How many triangles are there in the given figure?

  दी गई आकृति में त्रिभुजों की संख्या ज्ञात करें?

• Options:

  • (a) 8

  • (b) 9

  • (c) 10

  • (d) 12

• Answer: (b) 9

• Explanation: Three overlapping triangles forming a cascade pattern:

  • Single independent small triangles = $6$

  • Medium overlapping sectors = $2$

  • Overall compound boundary shape = $1$

  • Total = $6 + 2 + 1 = 9$.

Q.60

• Question: How many triangles are there in the given figure?

  दी गई आकृति में त्रिभुजों की संख्या ज्ञात करें?

• Options:

  • (a) 11

  • (b) 12

  • (c) 15

  • (d) 13

• Answer: (c) 15

• Explanation: A divided triangular pyramid shape:

  • Small triangles = $9$

  • Medium triangles (made of 4 units) = $5$

  • Main large triangle = $1$

  • Total = $9 + 5 + 1 = 15$.