general Flashcards
Product of n natural numbers
n!
Sum of first n natural numbers
n (n+1) / 2
sum of squares of the first n natural numbers
Sum of cubes of first n natural numbers
|x|< a
|x|< a then x∈(-a,a)
|x|>a
|x|>a then x∈(-∞,-a) U (a,∞)
One-to-One Mapping
A function f : A → B is one-to-one (injective) if:
f(a₁) = f(a₂) ⟹ a₁= a₂
No two different inputs have the same output.
What is the total number of mappings of a set with
n elements?
Totalnumberofmappings = mⁿ
n = Number of elements in the set being mapped
m = Number of elements in the set it is being mapped to.
[A->B
n = no. of elements of A , m = no. of elements of B]
Total number of one-to-one mappings
(both cases)
ᵐcₙ . n!
and n! if it is mapping to itself
Regular Hexagon
Regular hexagon means all sides are equal
Number of equilateral triangles in regular hexagon
Regular hexagon can have only 2 equilateral triangles
Numbers divisible by m and n number
Numbers that are divisible by both m and n number are the numbers which are divisible by LCM of m and n
Numbers divisible by 2 and 3
Numbers that are divisible by both 2 and 3 are the numbers divisible by 6
Numbers divisible by m or n are
Apply
mUn = m + n - m∩n
1/∞
1/∞ = 0
What does the graph of a line with a negative slope look like?
What does the graph of a line with a positive slope look like?
Graph of y=eˣ
Graph of y=x³
