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CTET Jan 2021 Paper 2 (Maths & Science) (English-I/ Hindi-II)
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- Intuition has no role in generating mathematical knowledge.
- Mathematical statements can be conditional.
- Mathematics consists of all the theorems proved in mathematics books.
- A person good in arithmetical computation is also good in Mathematics and vice-versa.
Answer (Detailed Solution Below)
Option 2 : Mathematical statements can be conditional.
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Mathematics is the study of numbers, shapes, quantities, and patterns. Mathematics is the ‘queen of all sciences’ and its presence is there in all the subjects. It acts as the basis and structure of other subjects. Some points to remember:
- On the basis of intuition, hypothesis are made in mathematics.
- A mathematics statement can be conditional. For example, a figure can not be said a 'rectangle' its opposite sides are not parallel and equal, and all angles are inclined at 90 degrees.
- Mathematics is not about theorems only. It contains other symbols, statements like axioms, and calculation.
- A person with good arithmetic computation does not guarantees that he is good in mathematics. Maybe he can lack in geometry or algebra.
Hence, a mathematics statement can be conditional.
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Answer
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Hint: There are four statements given. We will draw figures for each statement and then we will write arguments against the incorrect statements and in support of the right statement. Finally, we will be able to find the statement which is true.
Complete step by step solution:
We have been given four statements and we have to find the correct one. We find the right argument involving each statement and also draw their respective diagrams to find the conclusion.
We
know that an infinite number of lines can pass through one single point. These lines have one common point.
For the above line we can see that the lines are intersecting themselves at a single point A.
So, the first statement is wrong.
We know that two distinct points are required to get a particular line. This means there can be only one line going through two distinct points.
We can see that there exists only one line that goes through the points C and D. The second statement is wrong.
The fourth statement is also wrong as two circles with equal radii are called equal circles. Therefore, if two circles are equal, then their radii are equal.
For the above diagram the radii are equal which means $AB=CD$. They are equal circles.
If two lines have more than one common point then that means they are intersecting each other at more than one point. We know that two distinct points are required to get a particular line. This means there can be only one line going through two distinct points.
The third statement is right.
So, the correct answer is “Option C”.
Note: Equal circles are those whose diameters are equal, or whose radii are equal. They also can overlap each other. Two lines are distinct if they intersect at one and only one point or if they are parallel, that is there is no point of intersection between them. ... Any two adjacent sides of a triangle are also distinct lines.