Q1: Which of the following is a key feature of a fractal?
(A) It has a well-defined smooth boundary.
(B) It has self-similarity across scales.
(C) It is always a 2-dimensional object.
(D) It can be described by a single polynomial equation.
Answer: (B) It has self-similarity across scales.
Q2: What is the dimension of a fractal known as?
(A) Topological dimension
(B) Euclidean dimension
(C) Fractal dimension
(D) Metric dimension
Answer: (C) Fractal dimension
Q3: In the context of fractals, what does the term “self-similarity” mean?
(A) A fractal is composed of a single distinct pattern.
(B) The structure of the fractal is identical at different scales.
(C) The fractal can only be described at the macroscopic level.
(D) The fractal has no repeating structures.
Answer: (B) The structure of the fractal is identical at different scales.
Q4: Which of the following is NOT an example of a fractal?
(A) Mandelbrot set
(B) Sierpinski triangle
(C) Euclidean circle
(D) Koch curve
Answer: (C) Euclidean circle
Q5: What is the fractal dimension of the Sierpinski triangle?
(A) 1
(B) 1.585
(C) 2
(D) 3
Answer: (B) 1.585
Q6: Which of the following is true about fractals?
(A) Fractals are always continuous but not differentiable.
(B) Fractals are always differentiable.
(C) Fractals are not continuous.
(D) Fractals are always discrete.
Answer: (A) Fractals are always continuous but not differentiable.
Q7: The box-counting method is commonly used to estimate what characteristic of a fractal?
(A) Fractal dimension
(B) Euclidean distance
(C) Area of the fractal
(D) Topological properties
Answer: (A) Fractal dimension
Q8: What is a key application of fractal geometry?
(A) Solving linear algebraic equations
(B) Modeling complex natural structures like coastlines and mountains.
(C) Predicting simple harmonic motion
(D) Optimizing linear regression models
Answer: (B) Modeling complex natural structures like coastlines and mountains.
Q9: In which of the following fields can fractal geometry be applied?
(A) Geography and meteorology
(B) Computer graphics and digital imaging
(C) Medical imaging and biology
(D) All of the above
Answer: (D) All of the above
Q10: What does the term “fractal” mean in geometry?
(A) A geometric shape that can be subdivided into parts, each of which is a reduced-scale copy of the whole.
(B) A geometric shape that does not repeat in any form.
(C) A simple shape that can be represented by a single equation.
(D) A geometric shape that is always smooth.
Answer: (A) A geometric shape that can be subdivided into parts, each of which is a reduced-scale copy of the whole.