Q 1. Figure Matrix
Consider the following three-dimensional figure:
How many triangles does the above figure have?
To determine the number of triangles in the three-dimensional figure, we must consider all possible triangular faces. This includes triangles formed by the vertices, edges, and faces of the figure. By systematically counting each triangular face, ensuring no repetition, we arrive at a total of 20 triangles. This count includes triangles on the surface as well as any internal triangular sections that may be formed by intersecting planes within the figure. Thus, the correct answer is Option B: 20.
Q 62. Figure Matrix
For a sports meet, a winners' stand comprising three wooden blocks is in the following form:
There are six different colours available to choose from and each of the three wooden blocks is to be painted such that no two of them has the same colour. In how many different ways can the winners' stand be painted?
To determine the number of ways to paint the winners' stand, we need to consider the choices for each block. There are six different colors available. For the first block, we have _6_ choices. Once the first block is painted, we have _5_ remaining colors for the second block. Finally, for the third block, we have _4_ colors left. Therefore, the total number of ways to paint the blocks is calculated by multiplying these choices: _6 × 5 × 4 = 120_. Thus, the correct answer is Option A: 120.
Q 25. Figure Matrix
Study the following figure: A person goes from A to B always moving to the right or downwards along the lines. How many different routes can he adopt?
Select the correct answer from the codes given below:
Technique 1: You can check all the routes manually and count the total number. Technique 2: Avoid technique 1 if the diagram has more boxes. Use logic. You can more from A to B in the given manner from point A node in two ways (right or downward). In each way there are 3 ways to go to B. Hence total 3+3 = 6. Technique 3: Use permutation & combination. Consider a p x q rectangular grid with top left corner A and bottom right corner B. The number of distinct paths available to traverse from A to B moving downward and rightward is p + q Cp or p + q Cq. We have a 2 X 2 rectangular grid in this case. So, the number of paths to traverse from A to B = 4 C2 = 6.
Q 26. Figure Matrix
Consider the following figure and answer the item that follows:
What is the total number of triangles in the above grid ?
The triangles given are equilateral triangles of different
lengths 1,2,3 and 4 units. The number of triangles of 1 unit length = 1 + 3 + 5
+ 3 = 12 The number of triangles of length 2 units = 1 + 2 + 3 = 6. Plus there
is one inverted triangle of length 2 units. So the number of triangles of
length 2 units = 7 The number of triangles of length 3 units = 1 + 2 = 3 The
number of triangles of length 4 units = 1 So, the total number of triangles =
12 + 7 + 3 + 1 = 23