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Definite Integral – Definition, Formulas, Properties and Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
An integral assigns numbers to functions in mathematics to define displacement, area, volume, and other notions that arise by connecting infinitesimal data. The process of finding integrals is called integration. Definite integrals are used when the limits are defined to generate a unique value. Indefinite integrals are implemented when the boundaries of the integrand are not specified. In case, the lower limit and upper limit of the independent variable of a function are specified, its integration is described using definite integrals. Also, we have several integral formulas to deal with various definite integral problems in maths.

An integral assigns numbers to functions in mathematics to define displacement, area, volume, and other notions that arise by connecting …

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Integration by Parts – Formula, ILATE Rule & Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 10, 2025 by Neeraj Anand, Param Anand
Integration by parts is a special technique of integration of two functions when they are multiplied. This method is also termed as partial integration. Another method to integrate a given function is integration by substitution method. These methods are used to make complicated integrations easy.

Integration by parts is a special technique of integration of two functions when they are multiplied. This method is also …

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Trigonometric Functions | NCERT Solutions | MCQs, Assertion & Reason Questions, Case Study, FAQs | Free PDF Download

September 9, 2025February 12, 2025 by Neeraj Anand, Param Anand
1. Find the radian measures corresponding to the following degree measures:

NCERT Solutions for Class 11 Maths Chapter Trigonometric Functions Exercise 3.1 1. Find the radian measures corresponding to the following …

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Inverse Relation Theorem(Class 11 Math)-Graph, Properties, Solved Examples, FAQs

September 9, 2025February 8, 2025 by Neeraj Anand, Param Anand
Inverse relation: an inverse relation is the opposite of a given relation obtained by interchanging or swapping the elements of each ordered pair. In simple terms, if (x, y) is a point in a relation r, then (y, x) is an element in the inverse relation.

Inverse Relation: An inverse relation is the opposite of a given relation obtained by interchanging or swapping the elements of …

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Partial Order Relation on a Set(Class 11 Math) Definition, Proof, Properties, Solved Examples, FAQs

September 9, 2025February 8, 2025 by Neeraj Anand, Param Anand
A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs of elements of the set it is defined on.

A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs …

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Equivalence Relations(Class 11 Math) Definition, Proof, Properties, Solved Examples, FAQs

September 9, 2025February 8, 2025 by Neeraj Anand, Param Anand
Equivalence relation is a type of relation that satisfies three fundamental properties: reflexivity, symmetry, and transitivity. These properties ensure that it defines a partition on a set, where elements are grouped into equivalence classes based on their similarity or equality. Equivalence relations are essential in various mathematical and theoretical contexts, including algebra, set theory, and graph theory, as they provide a structured way to compare and classify elements within a set.

Equivalence Relation is a type of relation that satisfies three fundamental properties: reflexivity, symmetry, and transitivity. These properties ensure that …

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Transitive Relations(Class 11 Math) Definition, Properties, Solved Examples, FAQs

September 9, 2025February 8, 2025 by Neeraj Anand, Param Anand
Transitive relation is one of the necessary conditions for equivalence relation, as for any relation to be that needs to to transitive at first. In transitive relation, if element a is related to element b and element b is related to element c, then there must also be a relationship between element a and element c, following the same rule or relation. In other words, if a relates to b and b relates to c, then a must relate to c.

Transitive Relation is one of the necessary conditions for equivalence relation, as for any relation to be that needs to …

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Antisymmetric Relation(Class 11 Math)-Definition, Formula, Types, Solved Examples, FAQs

September 27, 2025February 8, 2025 by Neeraj Anand, Param Anand
Antisymmetric relation is a type of binary relation on a set where any two distinct elements related to each other in one direction cannot be related in the opposite direction. For example, consider the relation "less than or equal to" (≤) on the set of integers. This relation is antisymmetric because if a ≤ b and b ≤ a, then a must be equal to b. This article deals with antisymmetric relation including their definition, examples, as well as properties.

Antisymmetric Relation is a type of binary relation on a set where any two distinct elements related to each other …

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Symmetric Relations-Definition, Formula, Types, Solved Examples | Class 11 Math Notes Study Material Download Free PDF

September 9, 2025February 7, 2025 by Neeraj Anand, Param Anand
Symmetric relation is a type binary relation in discrete mathematics defined on sets. Which satisfies that if arb exists then bra also exists for all pairs of a, b that belong to set s. Which means that if (a, b) belongs to r then (b, a) also belongs to relation r.

Symmetric relation is a type binary relation in discrete Mathematics defined on sets. Which satisfies that if aRb exists then …

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Reflexive Relations-Definition, Formula, Types, Examples | Class 11 Math Notes Study Material Download Free PDF

September 9, 2025February 7, 2025 by Neeraj Anand, Param Anand
Reflexive relation is a mathematical or set-theoretical relation in which every element is related to itself, meaning that for every element 'x' in the set, the pair (x, x) is a part of the relation. Other than reflexive, there are many types of relations such as symmetric, transitive, identity, etc. In maths, relation is a subset of the cartesian product of a set with another set where some well-defined rule relates the elements of two sets with each other.

Reflexive Relation is a mathematical or set-theoretical relation in which every element is related to itself, meaning that for every …

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Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Miscellaneous Exercise Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

NCERT Solutions Probability Miscellaneous Exercise Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

NCERT Solutions Probability Exercise 13.3 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.3 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.2 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.2 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.1 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.1 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Chapter 11 Three Dimensional Geometry from Anand Classes. Clear, step-by-step maths notes in PDF format.

Three Dimensional Geometry NCERT Solutions Miscellaneous Exercise Chapter-11 Class 12 Math Notes PDF Free Download

Download free NCERT Solutions for Class 12 Chapter 11 Three Dimensional Geometry from Anand Classes. Clear, step-by-step maths notes in PDF format.

Three Dimensional Geometry NCERT Solutions Exercise 11.2 Chapter-11 Class 12 Math Notes PDF Free Download (Set-2)

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