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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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} ...
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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 ...
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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 ...
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