If you are asked to draw the following four figures with the following constraints: They must be drawn in a single stroke (without lifting the pen from paper), and each line is drawn only once. Which of the options can't be drawn?
If you are asked to draw the following four figures with the following constraints: They must be drawn in a single stroke (without lifting the pen from paper), and each line is drawn only once. Which of the options can't be drawn?
Show Hint
- A
- B
- C
- D
The Correct Option is C, D
Solution and Explanation
Step 1: Understanding the Concept:
This problem is an application of graph theory, specifically related to Eulerian paths. A figure can be drawn in a single, continuous stroke without retracing lines if and only if its corresponding graph has either zero or exactly two vertices (nodes) of odd degree. The degree of a vertex is the number of lines meeting at that point.
Step 2: Detailed Explanation:
Let's analyze the degree of each vertex (represented by dots or line intersections) for all four figures.
Figure A: There are 9 vertices.
- The central vertex has 4 lines meeting (degree 4).
- The 4 vertices on the diagonals have 4 lines meeting (degree 4).
- The 4 vertices on the outer square have 4 lines meeting (degree 4).
All 9 vertices have an even degree. A graph with zero odd-degree vertices has an Eulerian circuit and can be drawn in a single stroke. Therefore, Figure A is drawable.
Figure B: There are 9 vertices.
- The central vertex has 4 lines meeting (degree 4).
- The 4 vertices on the corners of the inner square have 4 lines meeting (degree 4).
- The 4 outer vertices where the loops meet have 4 lines meeting (degree 4). All 9 vertices have an even degree. Therefore, Figure B is also drawable.
Figure C: There are 8 vertices to consider.
- The 4 vertices at the corners of the square (the black dots) each have 3 lines meeting (2 from the square, 1 from the loop). Their degree is 3 (odd).
- The 4 points where the loops cross the square sides are vertices of degree 4. Since there are four vertices of odd degree, this figure cannot be drawn in a single stroke.
Figure D: There are 9 vertices to consider.
- The 4 vertices at the corners of the square (the black dots) each have 5 lines meeting (2 from the square, 1 from the diagonal, 2 from the loop passing through). Their degree is 5 (odd).
- The central vertex has 4 lines meeting (degree 4).
- The 4 vertices where the diagonals intersect the loops have degree 4. Since there are four vertices of odd degree, this figure cannot be drawn in a single stroke.
Step 3: Final Answer:
The correct options are (C) and (D).
Top CEED Design Aptitude Questions
- A bank needs to upgrade its ATM kiosks to be wheel-chair accessible. An ATM kiosk entrance has four steps rising up to reach the floor level of the kiosk. Each step is 1000 mm in length, 300 mm in breadth, and 150 mm in height. The bank proposes to create a wheel-chair accessible ramp with a slope of 1:12, adjacent to the steps. What is the minimum horizontal length of the ramp in metre? \
- A system of frictionless and massless pulleys is being used to pull up a load of 2520 N. What is the minimum force (in Newtons) required at the end of the rope (shown in dashed lines)?
- Figure shows the plan of a one-way road passing next to a primary school. Which of the options can be the location(s) to set up a bus stop for the school bus in Indian context?
- Mobile sculptures are created by tying fish-shaped cut-outs of different colours using blue strings on brown sticks of negligible weight, as shown below. All the fish cut-outs are of the same size and weight. Which of the options will remain balanced after suspending from a ceiling?
- Which of the graphs shown below represent(s) the equation XY = 25?
Top CEED Data Interpretation Questions
Two water tanks A and B of equal square base of sides 3 feet are shown below. Water flows from tank A to tank B through a tube. What will be the volume (in cubic feet) of water in Tank A when the water stops flowing?
- In terms of calories, 20 jamuns and 3 bananas combined are equivalent to one mango and one papaya combined, and 2 mangoes and 5 bananas combined are equivalent to 4 papayas and 80 jamuns combined. Then 8 papayas and 2 mangoes are equivalent to how many bananas?
A designer has designed a logo. The form is shown on the left and its accompanying text is shown on the right. Which of the following statements about this logo is/are TRUE?
The pie chart shows proportions of income tax paid by a population of eight individuals. Each individual's tax share is shown in a different slice of the pie. Which of the statements can be derived from the chart shown below?
Four square table-tops of the same dimensions are shown below. Only the designs of their supports are different from each other. If a person stands upright on the red mark on each of the table, which of the tables will topple?
Top CEED Questions
- Solid 1, Solid 2 and Solid 3 are joined together to form a cuboid as shown in Figure 1. The cuboid is then painted from all the sides. How many surfaces are there without the paint when you separate all the three solids?
- An irregular solid is cut into seven pieces as shown. The pieces are neither rotated nor scaled, but are kept in a random sequence. Find the correct sequence to get the smooth form. The sequence should be written from left to right.
- What are the least number of lines required to generate a 3D form such that it creates shadows similar to the figure shown below?
- In the square ABCD, line XY is drawn parallel to the base as shown in the figure below. P and Q are any two arbitrary points on XY, forming triangles ABQ and CDP. What fraction of the area of the square is the total green shaded area?
- Five square pyramids are stacked as shown in the figure below with the bottom layer consisting of four pyramids in a 2 x 2 grid. If the bottom layer consists of pyramids in 6 x 7 grid, and they are stacked in a similar manner to its maximum height, how many pyramids will the formation contain?
