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Question

How many of squares are there in a given illustration?

This question was previously asked in
RRB NTPC 2019 CBT 1 Question Paper (8-Mar-2021) (Shift 2)
The correct answer is
30

To determine the total number of squares in the given illustration, we need to count all possible squares, including smaller squares within the larger square.

Let's break down the counting process step by step:

  1. 1x1 Squares: The grid has a total of 16 small squares (each 1x1). These are the smallest squares visible in the illustration.
  2. 2x2 Squares: A 2x2 square consists of 4 small squares. We can form these by choosing 2 adjacent squares along both the rows and columns. There are 3 possible positions along both dimensions, resulting in \(3 \times 3 = 9\) squares.
  3. 3x3 Squares: A 3x3 square consists of 9 small squares. These can be formed by choosing starting points for the 3 rows and 3 columns. We have 2 possible positions along both dimensions, resulting in \(2 \times 2 = 4\) squares.
  4. 4x4 Square: The entire grid itself is a 4x4 square. This gives us 1 big square.

Summing up all possible squares:

  • 1x1 Squares: 16
  • 2x2 Squares: 9
  • 3x3 Squares: 4
  • 4x4 Square: 1

Total number of squares = \(16 + 9 + 4 + 1 = 30\).

Therefore, the correct answer is 30.

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Similar Questions

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Important Questions from Figure Counting

  1. How many triangles are there in the given figure?

  2. How many squares are there in the given figure?

  3. How many squares are there in the figure shown below?

  4. How many triangles are there in the given figure?

  5. How many squares are there in the figure shown below?

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