A Quantity Index Number measures changes in the quantity or volume of goods over time or between places.
It focuses on physical amounts, not prices or values.
IQR measures the spread of the middle 50% of the data.
It is calculated as:
IQR = Q3 – Q1
Address consists of text (street, city, etc.).
It is non-numerical.
Marks, bank balance, and roll number are numerical values.
Let u = 5x, du/dx = 5, du = 5dx, dx = du/5
∫sin5xdx = (1/5)∫sinu du
= (1/5)(-cosu) + c
= -1/5cos5x + c
In a histogram, the Y-axis represents the frequencies (i.e., how many data points fall into each class).
The X-axis shows the class intervals (data ranges).
Two events A and B are independent if the occurrence of one does not affect the occurrence of the other.
This is mathematically defined as:
P(A ∩ B) = P(A) × P(B)
A relation from A to B is defined as a subset of A × B (the Cartesian product).
So, any subset of A × B is called a relation from A to B.
A matrix with m rows and n columns where m ≠ n is called a rectangular matrix.
A square matrix has m = n (same number of rows and columns).
A trivial solution to a system of homogeneous linear equations means all variables are zero.
So, the solution is (0, 0, 0).
Momentous means بہت اہم یا اہم ، خاص طور پر تاریخ میں
Historic means تاریخ میں بہت اہمیت کی بات ہے