Counting of figures– Railway Reasoning (part – 1)

Total Questions: 50

1. How many rectangles are there in the given figure? [NTPC CBT - I 30/12/2020 (Morning)]

Correct Answer: (a) 36
Solution: The short trick to find the total number of rectangles is to write the number of rows and columns as written in the above diagram, and then add them in both row-wise and column-wise and then multiply those two numbers.
Then number of total rectangles = value of column wise summation × value of row wise summation = 6 6 = 36

2. Find the number of triangles in the given figure. [NTPC CBT - I 28/01/2021 (Evening)]

Correct Answer: (d) 28
Solution:

8 + 8 + 8 + 4 = 28 triangles.

3. How many triangles are there in the following figure? [NTPC CBT - I 30/01/2021 (Evening) ]

Correct Answer: (c) 16
Solution:

16 trianglestriangles are :- AOB , AOH , COB , COD , EOD , EOF , GOF , GOH , AOC , COE , EOG , GOA , ACG , ACE , EGC , EGA .

4. How many triangles are there in the given figure? [RRB JE 25/05/2019 (Morning)]

Correct Answer: (c) 30
Solution:

Hence total triangles = 10 + 10 + 10 = 30

5. How many squares are there in the given figure? [RRB JE 31/05/2019 (Morning)]

Correct Answer: (c) 55
Solution: Tricks for finding squares :- first calculate number of rows and columns and then
(Cₙ × Rₙ ) +(Cₙ - 1 × Rₙ - 1 ) + ……….. (Cₙ -ₙ × Rₙ -ₙ)
In this figure rows = 5 and columns = 5 So total square = ( 5 × 5 ) + (4 × 4) + (3 × 3) + (2 × 2) + (1× 1
) = 25 + 16 + 9 + 4 + 1 = 55
Hence total number of square in this figure = 55

6. How many circles are there in the given figure? [RRB JE 26/06/2019 (Morning) ]

Correct Answer: (d) 13
Solution:

7. How many right angled triangles can be made from the given shape? [RPF S.I. 05/01/2019 (Morning)]

Correct Answer: (d) 6
Solution:

8. What is the minimum number of straight lines required to construct the given figure? [RRB ALP Tier - I 29/08/2018 (Morning)]

Correct Answer: (a) 17
Solution:

Minimum 17 lines are required namely :
AB, BC, CD, DA, DH, HG, GC, DE, FC, EH, FG, JM, JE, JF, IE, KF, IK

9. Find the number of triangles in the diagram given below. [RRB NTPC 28/12/2020 (Morning)]

Correct Answer: (a) 32
Solution:

From the above diagram if we consider the triangle , ∆ 𝐴𝐵𝐶
Number of triangles = 10
For triangle , ∆ 𝐶𝐷𝐸
Number of triangles = 10
For triangle ∆ 𝐵𝐸𝐹 ,
Number of triangles = 10
Also there are two more triangles ∆ 𝐴𝐷𝐹 and ∆ 𝐵𝐶𝐸
So, the total number of triangles in the above diagram = (10 + 10 + 10 + 2) = 32.

10. How many triangles are there in the following figure? [RRB NTPC 29/12/2020 (Evening)]

Correct Answer: (d) 10
Solution:

In the above diagram there are 10 triangles in total.