CBSE Class 11 Applied Mathematics — Flashcards

A: A prime number is a positive integer p > 1 that has exactly two positive divisors: 1 and p itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23. Note: 2 is the only even prime number.

A: Every positive integer n > 1 can be written as a product of primes, and this representation is unique up to the order of primes. Form: n = p₁^a₁ × p₂^a₂ × ... × pᵣ^aᵣ where p₁ < p₂ < ... < pᵣ are dist

A: If 1 were considered prime, it would violate the uniqueness part of the Fundamental Theorem of Arithmetic. For example, 10 = 2 × 5 = 1 × 2 × 5 = 1² × 2 × 5, giving multiple factorizations. Since 1 has

A: Average (Mean) = Sum of all observations / Total number of observations Average represents a calculated central value of given data and is a measure of central tendency. It lies between the maximum a

A: Weighted average considers that some elements carry more weight than others. Weighted Average (x̄w) = Σⁿᵢ₌₁ wᵢxᵢ / Σⁿᵢ₌₁ wᵢ where wᵢ = weight of iᵗʰ element, xᵢ = value of iᵗʰ element Example: Grad

A: Average Speed = Total distance travelled / Total time taken (direction independent) Average Velocity = Total displacement / Total time taken (direction dependent) Key difference: Average speed canno

A: An ordered pair is a pair of objects taken in a specific order, written as (a, b), where 'a' is the first member and 'b' is the second member. The order is significant. Unlike sets where {a, b} = {b,

A: Two ordered pairs (a, b) and (c, d) are equal if and only if a = c and b = d. Written as: (a, b) = (c, d) ⟺ a = c and b = d. Example: If (2x, y - 3) = (2, 1), then 2x = 2 and y - 3 = 1, giving x = 1 a

A: The Cartesian product of sets A and B, written as A × B, is the set of all ordered pairs (a, b) such that a ∈ A and b ∈ B. Formally: A × B = {(a, b) : a ∈ A, b ∈ B}. Example: If A = {1, 2} and B = {x,