11th Maths Part 2 (Arts & Science) Solution (Digest) Chapters (Maharashtra State Board)

Select chapters

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Chapter 1 Complex Numbers

Exercise 1.1

Exercise 1.2

Exercise 1.3

Exercise 1.4

Miscellaneous Exercise 1

Chapter 2 Sequences and Series

Exercise 2.1

Exercise 2.2

Exercise 2.3

Exercise 2.4

Exercise 2.5

Exercise 2.6

Miscellaneous Exercise 2

Chapter 3 Permutations and Combination

Exercise 3.1

Exercise 3.2

Exercise 3.3

Exercise 3.4

Exercise 3.5

Exercise 3.6

Miscellaneous Exercise 3

Chapter 4 Methods of Induction and Binomial Theorem

Exercise 4.1

Exercise 4.2

Exercise 4.3

Exercise 4.4

Exercise 4.5

Exercise 4.6

Miscellaneous Exercise 4

Chapter 5 Sets and Relations

Exercise 5.1

Exercise 5.2

Miscellaneous Exercise 5

Chapter 6 Functions

Exercise 6.1

Exercise 6.2

Miscellaneous Exercise 6

Chapter 7 Limits

Exercise 7.1

Exercise 7.2

Exercise 7.3

Exercise 7.4

Exercise 7.5

Exercise 7.6

Exercise 7.7

Miscellaneous Exercise 7

Chapter 8 Continuity

Exercise 8.1

Exercise 8.2

Chapter 9 Differentiation

Exercise 9.1

Exercise 9.2

Miscellaneous Exercise 9

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Facts about Mathematics

The history of mathematics in India is rich and spans several millennia. Indian mathematics made significant contributions to various fields, including arithmetic, algebra, geometry, and trigonometry. Here's a brief overview of the key developments in the history of mathematics in India:

Indus Valley Civilization (3300–1300 BCE):

While not much is known about mathematical developments during this period, archaeological findings suggest that the Indus Valley Civilization had a sophisticated system of weights and measures.

Vedic Period (1500–500 BCE):

The earliest Indian mathematical texts are found in the Vedas, ancient religious texts of Hinduism. These texts contain mathematical concepts related to geometry, arithmetic, and astronomy.

Sulba Sutras (800–200 BCE):

The Sulba Sutras are a group of ancient Indian texts that deal with geometry and the construction of altars for Vedic rituals. They contain methods for constructing geometric shapes such as squares, rectangles, and circles.

Jaina Mathematics (5th century BCE onwards):

Jain mathematicians made significant contributions to number theory and algebra. Notable Jain mathematicians include Mahavira and Hemachandra, who worked on topics such as series expansions, factorization, and fractions.

Classical Period (5th century BCE–12th century CE):

The classical period saw the development of important mathematical texts, including the works of Aryabhata, Brahmagupta, and Bhaskara. Aryabhata's "Aryabhatiya" (5th century CE) contains astronomical and mathematical theories, including the concept of zero and the value of pi.

Brahmagupta's "Brahmasphutasiddhanta" (7th century CE) discusses arithmetic, algebra, and geometry. Bhaskara's "Lilavati" and "Bijaganita" (12th century CE) are treatises on arithmetic and algebra.

Kerala School of Mathematics (14th–16th centuries CE):

The Kerala School of Mathematics, centered around the city of Thrissur in Kerala, made significant contributions to calculus and infinite series. Notable mathematicians from this school include Madhava of Sangamagrama, Nilakantha Somayaji, and Jyeshtadeva.

Modern Period (18th century CE onwards):

In the modern period, Indian mathematicians continued to make advancements in various branches of mathematics. Notable figures include Srinivasa Ramanujan, who independently discovered many results in number theory and analysis, and Harish Chandra, known for his work in representation theory.

Throughout its history, Indian mathematics has had a profound influence on global mathematical development, particularly in the fields of algebra, arithmetic, and astronomy. Many mathematical concepts that originated in India, such as the decimal system and the concept of zero, are now fundamental to mathematics worldwide.