Types of Linear Programming Problems | Class 12 Math Notes Study Material Download Free PDF
Linear programming or linear optimization is a process that takes into consideration certain linear relationships to obtain the best possible …
Maths Class 12
Linear Programming Problem LPP-Simplex & Graphical Method | Class 12 Math Notes Study Material Download Free PDF
Linear Programming Problems (LPP): Linear programming or linear optimization is a process which takes into consideration certain linear relationships to …
Linear Programming-Definition, Methods & Examples | Class 12 Math Notes Study Material Download Free PDF
Linear programming is a method of optimising operations with some constraints. The main objective of linear programming is to maximize …
Probability Bernoulli Trial & Binomial Distribution of Random Variables | Class 12 Math Notes Study Material Download Free PDF
Bernoulli Trials and Binomial Distribution are explained here in a brief manner. Bernoulli’s trial is also said to be a …
Probability Distribution | Definition, Types, Formula, Examples | Class 12 Math Notes Study Material Download Free PDF
In Statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. It provides the …
Bayes Theorem | Definition, Proof, Formula, Derivation & Solved Examples | Class 12 Math Notes Study Material Download Free PDF
Bayes’ theorem describes the probability of occurrence of an event related to any condition. It is also considered for the …
Independent & Mutually Exclusive Events in Probability-Definition, Venn Diagram & Solved Examples | Class 12 Math Notes Study Material Download Free PDF
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a …
Multiplication Rule of Probability | Proof & Solved Examples | Class 12 Math Notes Study Material Download Free PDF
The multiplication rule of probability explains the condition between two events. For two events A and B associated with a …
Conditional Probability, Solved Examples | Class 12 Math Notes Study Material Download Free PDF
Imagine a student who takes leave from school twice a week excluding Sunday. If it is known that he will …
Probability-Definition, Formula, Types, Problems & Solutions | Class 12 Math Notes Study Material Download Free PDF
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is …
Shortest Distance Between Two Lines in 3D Space, Solved Examples | Class 12 Math Notes Study Material Download Free PDF
The shortest distance between two lines in three-dimensional space is the length of the perpendicular segment drawn from a point …
Angles Between two Lines in 3D Space: Solved Examples | Class 12 Math Notes Study Material Download Free PDF
A line in mathematics and geometry is a fundamental concept representing a straight, one-dimensional figure that extends infinitely in both …
Equation of Line in Three Dimensions | Cartesian & vector Equation | Class 12 Math Notes Study Material Download Free PDF
Equation of a line is defined as y= mx+c, where c is the y-intercept and m is the slope. Vectors …
Direction Cosines & Direction Ratios – Definitions & Examples | Class 12 Math Notes Study Material Download Free PDF
Direction Cosines When a directed line OP passing through the origin makes \(\begin{array}{l}\alpha \end{array} \) , \(\begin{array}{l}\beta\end{array} \) and \(\begin{array}{l} …
Scalar or Dot Product Of Two Vectors | Projection of Vector | Definition, Properties, Formulas and Examples | Class 12 Math Notes Study Material Download Free PDF
Vector is a quantity that has both magnitude and direction. Some mathematical operations can be performed on vectors such as …
Multiplication Of Vectors by a Scalar Quantity with examples | Class 12 Math Notes Study Material Download Free PDF
A vector relates two given points. It is a mathematical quantity having both the Magnitude and the direction. Multiplication of …
Laws of Vector Addition- Parallelogram, Triangle Law, Vector Addition | Class 12 Math Notes Study Material Download Free PDF
Laws of Vector Addition A vector is a physical quantity which is represented both in direction and magnitude. In the …
Types of Vectors | Zero Vector, Unit Vector, Position Vector, Co-initial Vector, Like & Unlike Vectors, Co-planar Vectors, Collinear Vectors, Equal Vectors, Displacement Vector, Negative of a Vector
What is a vector? Vector is a physical quantity that has both direction and magnitude. In other words, the vectors …
Vectors in Maths-Unit Vector, Zero or null Vector, Magnitude of Vector, Operations on Vectors, Dot product of Vectors, Scalar Triple Product
Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented …
Separable Differential Equation-Solved Examples | Class 12 Math Notes Study Material Download Free PDF
A differential equation is an equation of the form \(\begin{array}{l}\frac{\mathrm{d} y}{\mathrm{d} x} = g(x),\;\;\;\; where\;\; y = f(x)\end{array} \). General …
