Which of the following sets are finite?
- Set of all natural numbers
- Set of all prime numbers
- Set of months in a year
- None of these
The Correct Option is C
Solution and Explanation
Correct answer: Set of months in a year
Explanation:
A finite set is a set that has a countable number of elements.
- The set of all natural numbers is infinite, as natural numbers go on without end.
- The set of all prime numbers is also infinite, since there is no largest prime number.
- The set of months in a year has exactly 12 elements, so it is finite.
Therefore, the set of months in a year is the only finite set among the given options.
Top Questions on Prime and Composite Numbers
- Assertion (A) : For two prime numbers \(x\) and \(y\) (\(x<y\)), HCF\((x, y) = x\) and LCM\((x, y) = y\). Reason (R): HCF\((x, y) \leq \) LCM\((x, y)\), where \(x, y\) are any two natural numbers.
- CBSE Class X - 2025
- Mathematics
- Prime and Composite Numbers
Directions: In the Question, a statement of Assertion
(A) is followed by a statement of Reason (R).Choose the correct option from the following:
Assertion (A): For two odd prime numbers \(x\) and \(y\), \((x + y)\), \(\text{LCM}(2x,\ 4y) = 4xy\)
Reason (R):} \(\text{LCM}(x, y)\) is a multiple of \(\text{HCF}(x, y)\)- CBSE Class X - 2025
- Mathematics
- Prime and Composite Numbers
- A prime number \( p \) divides \( a^2 \) where \( a \) is a positive integer, then
- AP POLYCET - 2025
- Mathematics
- Prime and Composite Numbers
- Show that \(11 \times 19 \times 23 + 3 \times 11\) is not a prime number.
- CBSE Class X - 2024
- Mathematics
- Prime and Composite Numbers
- Show that \(11 \times 19 \times 23 + 3 \times 11\) is not a prime number.
- CBSE Class X - 2024
- Mathematics
- Prime and Composite Numbers
Questions Asked in AP POLYCET exam
- Area of a sector of a circle with radius 4 cm and angle 30° is (use \( \pi = 3.14 \)):
- The solution of \( x - 2y = 0 \) and \( 3x + 4y - 20 = 0 \) is:
- AP POLYCET - 2025
- Linear Equations
- If assumed mean of a data is 47.5, \( \sum f_i d_i = 435 \) and \( \sum f_i = 30 \), then mean of that data is:
- AP POLYCET - 2025
- Arithmetic Mean
- The points \( (1,5), (2,3) \) and \( (-2, -11) \) form a:
- A pair of linear equations \( a_1 x + b_1 y + c_1 = 0 \) and \( a_2 x + b_2 y + c_2 = 0 \) is such that \( \frac{a_1}{a_2} \neq \frac{b_1}{b_2} \), then they are:
- AP POLYCET - 2025
- Linear Equations