Showing posts with label class11-maths. Show all posts
Showing posts with label class11-maths. Show all posts

Sunday, 15 August 2021

Class 11 - Maths - Complex Numbers - Solved Problems - Part 1 (#class11Maths)(#eduvictors)(#cbsenotes)

Class 11 - Maths - Complex Numbers - Solved Problems - Part 1

Class 11 - Maths - Complex Numbers - Solved Problems - Part 1 (#class11Maths)(#eduvictors)(#cbsenotes)


Q1: What are imaginary numbers?


Answer: If the square of a given number is negative then such a number is called an imaginary number.


Q2: Name the mathematician who was the first to introduce the symbol i (iota) for square root of -1.


Answer: Euler.


Q3: Evaluate i⁹ + i¹⁹

Tuesday, 6 July 2021

CBSE Class 11 Maths - Relations - Domain, Range and Co-Domain (#class11Maths)(#eduvictors)(#cbse2021)

CBSE Class 11 Maths - Relations - Domain, Range and Co-Domain

CBSE Class 11 Maths - Relations - Domain, Range and Co-Domain (#class11Maths)(#eduvictors)(#cbse2021)


RELATION 

Let A and B be two nonempty sets. Then, a relation R from A to B is a subset of (A × B).

Thus, R is a relation from A to B ⇔ R ⊆ (A × B).


If (a, b) ∈ R then we say that ‘a is related to b‘ and we write, a R b. 


If (a, b) ∉ R then ‘a is not related to b‘ and we write, $a \not \mathrel{R} b$.



Q1: Let A = {-1, 2, 4} and B = {1, 3}. Show A × B as arrow diagram.

Thursday, 24 June 2021

CBSE Class 11 Maths - Cartesian Products of two sets (Important Points)- Relations and Function (#class11Maths)(#eduvictors)(#cbsenotes)

Class 11 Maths - Cartesian Products of Two sets (Important Points)

Chapter: Relations and Functions

CBSE Class 11 Maths - Cartesian Products of two sets (Important Points)- Relations and Function (#class11Maths)(#eduvictors)(#cbsenotes)


Let A and B be two nonempty sets. Then, the Cartesian product of A and B is the set denoted by (A×B), consisting of all ordered pairs (a, b) such that a ∈ A and b ∈ B.


∴ A × B = {(a, b): a ∈ A and b ∈ B }. 


② If A = ϕ or B = ϕ (empty sets), we define A × B = ϕ


③ B × A = {(b, a) : b ∈ B and a ∈ A} and A × A = {(a,b):a,b ∈ A}.

Wednesday, 2 June 2021

CBSE Class 11 Maths Chapter 2: Relations and Functions (1 Mark Based Questions with Answers) Part-1 (#Class11Maths)(#eduvictors)(#cbse2021)

CBSE Class 11 Maths Chapter 2: Relations and Functions (1 Mark Based Questions with Answers) Part-1

CBSE Class 11 Maths Chapter 2: Relations and Functions (1 Mark Based Questions with Answers) Part-1 (#Class11Maths)(#eduvictors)(#cbse2021)

Q1: What is an ordered pair?

Answer: An ordered pair is a pair of entries in the specified order.


Q2: What is ordered 2-tuple?

Answer: Another name of an ordered pair.


Q3: If A and B are any two sets, write to represent an ordered pair of elements of A and B? 

Answer: (a, b) : a ∈ A, b ∈ B


Q4: Is (a, b) = (b, a)?

Answer: No. a, b) ≠ (b, a) unless a = b

Sunday, 7 February 2021

Class 11 Maths Standard CBSE Preboard Sample Question Paper (Set-1) 2020-21 (#eduvictors)(#class11Maths)(#cbse2020_21)

Class 11 Maths Standard CBSE Preboard Sample Question Paper (Set-1) 2020-21

Class 11 Maths Standard CBSE Preboard Sample Question Paper (Set-1) 2020-21 (#eduvictors)(#class11Maths)(#cbse2020_21)

Learning is a continual process. To improve scores, the best way is to learn and practice. Solving question papers help students to evaluate their knowledge and familiarise with different types of question patterns being asked in the examination. 

Eduvictors provides CBSE Previous Year Papers, Study Notes and Sample Question Papers for Class 11 Maths, Physics, Accounts, English, Hindi, Business Studies and Physical Education with/without solutions to help students in their board exam preparation.

1. Buy Oswaal CBSE Sample Question Paper Class 11 Mathematics Book (Reduced Syllabus for 2021 Exam)


Here attached the Maths Preboard Sample Question Paper (2020-2021) for your practice.

Friday, 6 December 2019

CBSE Class 11 - Maths - Sets - NCERT Exercise 1.6 (#class11Maths)(#eduvictors)

Sets - NCERT Exercise 1.6 Answers 

Class 11 Maths
CBSE Class 11 - Maths - Sets - NCERT Exercise 1.6 (#class11Maths)(#eduvictors)

Q1: If X and Y are two sets such that n( X ) = 17, n( Y ) = 23 and n( X ∪ Y ) = 38, find n ( X ∩ Y ).

Answer: Given,
n( X ) = 17,
n( Y ) = 23 and
n( X ∪ Y ) = 38

We know that, n(X ∪ Y) = n(X)  + n(Y) - n (X ∩ Y)
∴  38 = 17 + 23  - n (X ∩ Y)
n (X ∩ Y) = 17 + 23 - 38 = 40 - 38 = 2
n (X ∩ Y) = 2.


Sunday, 1 December 2019

CBSE Class 11 Maths Sets - NCERT Exercise 1.5 Answers (#class11Maths)(#eduvictors)

Sets - NCERT Exercise 1.5 Answers 

CBSE Class 11 Maths 

CBSE Class 11 Maths Sets - NCERT Exercise 1.5 Answers  (#class11Maths)(#eduvictors)


Q1: Let U = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }, A = { 1, 2, 3, 4}, B = { 2, 4, 6, 8 } and C = { 3, 4, 5, 6 }. 
Find 
(i) A'
(ii) B'
(iii) (A ∪ C)'
(iv) (A ∪ B)'
(v) (A')'
(vi) (B – C)'


Answer:
(i) A' =  U - A = {5,6,7,8,9}

(ii) B'  = U - B = {1,3,5,7,9}

Thursday, 21 November 2019

CBSE Class 11 Maths Chapter Sets - NCERT Exercise 1.4 (Q 9 - Q 12) (#eduvictors)(#class11Maths)

Class 11  Maths Chapter Sets - NCERT Exercise 1.4 (Q 9 - Q 12)

NCERT Solutions
CBSE Class 11  Maths Chapter Sets - NCERT Exercise 1.4 (Q 9 - Q 12) (#eduvictors)(#class11Maths)


Q9: If A = {3, 6, 9, 12, 15, 18, 21}, 
  B = { 4, 8, 12, 16, 20 },
C = { 2, 4, 6, 8, 10, 12, 14, 16 }, 
D = {5, 10, 15, 20 }; 
find
(i) A – B 
(ii) A – C 
(iii) A – D 
(iv) B – A
(v) C – A 
(vi) D – A 
(vii) B – C 
(viii) B – D
(ix) C – B 
(x) D – B 
(xi) C – D 
(xii) D – C


Answer
(i) A – B    = {3, 6, 9, 15, 18, 21}

(ii) A – C  = {3, 9, 15, 18, 21}

(iii) A – D = {3, 6, 9, 12, 18, 21}

(iv) B – A  = {4, 8, 16, 20}

(v) C – A  = {2,4,8,10,14,16}

(vi) D – A = {5,10,20}

(vii) B – C = {20}

(viii) B – D = {4,8,12,16}

(ix) C – B = {2,6,10,14}

(x) D – B  = {5,10,15}

(xi) C – D = {2,4,6,8,12,14,16}

(xii) D – C = {5,15,20}


Friday, 15 November 2019

CBSE Class 11 Maths - Laws of Set Operations (#class11Maths)(#eduvictors)

Laws of Set Operations Class 11 Maths - Sets

CBSE Class 11 Maths - Laws of Set Operations  (#class11Maths)(#eduvictors)

Sets under the operations of union, intersection and complement satisfy various laws. These laws collectively called Algebra of sets.

Here follows few important Laws of Set Operations


1. Idempotent Laws:
(a) A ∪ A = A 
(b) A ∩ A = A

Wednesday, 13 November 2019

CBSE Class 11 Maths Chapter Sets - NCERT Exercise 1.4 (Q 6 - Q 8) (#eduvictors)(#class11)

Class 11  Maths Chapter Sets - NCERT Exercise 1.4 (Q 6 - Q 8)

NCERT Solutions
CBSE Class 11  Maths Chapter Sets - NCERT Exercise 1.4 (Q 6 - Q 8) (#eduvictors)(#class11)

Q6: If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find
(i) A ∩ B 
(ii) B ∩ C 
(iii) A ∩ C ∩ D
(iv) A ∩ C 
(v) B ∩ D 
(vi) A ∩ (B ∪ C)
(vii) A ∩ D 
(viii) A ∩ (B ∪ D) 
(ix) ( A ∩ B ) ∩ ( B ∪ C )
(x) ( A ∪ D) ∩ ( B ∪ C)

Answer:
(i) A ∩ B  = {7,9,11}

(ii) B ∩ C = {11, 13}

(iii) A ∩ C ∩ D = {A ∩ C} ∩ D  = {11} ∩ {15, 17} = φ

(iv) A ∩ C = {11}

(v) B ∩ D = {7, 9, 11, 13}  ∩ {15, 17} = φ

(vi) A ∩ (B ∪ C)
= {3, 5, 7, 9, 11}  ∩ ({7, 9, 11, 13} ∪ {11, 13, 15})
= {3, 5, 7, 9, 11}  ∩ {7, 9, 11, 13, 15}
= {7, 9, 11}

(vii) A ∩ D = φ

(viii) A ∩ (B ∪ D)
= {3, 5, 7, 9, 11}  ∩ ({7, 9, 11, 13} ∪ {15, 17})
= {3, 5, 7, 9, 11}  ∩ {7, 9, 11, 13, 15, 17}
= {7, 9, 11}

Friday, 8 November 2019

CBSE Class 11 Maths Sets - NCERT Exercise 1.4 Answers (Q1 - Q5) (#eduvictors)(#class11Maths)

CBSE Class 11 Maths Sets
NCERT Exercise 1.4 Answers 

(Q1 - Q5)

CBSE Class 11 Maths Sets - NCERT Exercise 1.4 Answers (Q1 - Q5) (#eduvictors)(#class11Maths)

Q1: Find the union of each of the following pairs of sets:
(i) X = {1,3,5} Y = {1,2,3}

(ii) A = {a,e,i,o,u}, B = {a,b,c}

(iii) A = {x : x is a natural number and multiple of 3}
       B = {x : x is a natural number less than 6}

(iv) A = {x : x is a natural number and 1 < x ≤ 6 }
      B = {x : x is a natural number and 6 < x < 10 }

(v) A = {1, 2, 3}, B = φ


Answers:
(i) X = {1,3,5} Y = {1,2,3}
     X ∪ Y = {1,2,3,5}

Wednesday, 6 November 2019

Class 11 - Maths - Chapter: Sets - Operations Of Sets (#class11Maths)(#eduvictors)

Sets - Operations Of Sets

Class 11 - Maths
Class 11 - Maths - Chapter: Sets - Operations Of Sets (#class11Maths)(#eduvictors)


COMPLEMENT OF A SET

If U  be the universal set and A is the subset of U, then the complement of A with respect to U, denoted by A',
A' is defined as
A' = {x : x ∈ U and x  ∉ A }

Saturday, 2 November 2019

Class 11 - Maths - Chapter: Sets - Venn Diagrams (#class11Maths)(#eduvictors)

Venn Diagrams

Chapter: Sets
Class 11 - Maths
Class 11 - Maths - Chapter: Sets - Venn Diagrams (#class11Maths)(#eduvictors)


Most of the relationship between sets can be represented by means of diagrams.

Figures representing sets in the form of an enclosed region in the plane are called Venn Digrams. In these diagrams, the universal set is usually represented by a rectangular region and its subsets by bounded regions inside the rectangular region.

VENN DIAGRAMS IN DIFFERENT SITUATIONS

Tuesday, 29 October 2019

CBSE Class 11 - Chapter Sets - NCERT Exercise 1.3(#class11Maths)(#eduvictors)

Mathematics - Sets 

CBSE Class 11 NCERT Exercise 1.3

CBSE Class 11 - Chapter Sets - NCERT Exercise 1.3(#class11Maths)(#eduvictors)


Q1: Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :

(i) { 2, 3, 4 } . . . { 1, 2, 3, 4,5 }

Answer: ⊂

(ii) { a, b, c } . . . { b, c, d }

Answer: ⊄


(iii) {x : x is a student of Class XI of your school}. . .{x : x student of your school}

Answer: ⊂


(iv) {x : x is a circle in the plane} . . .{x : x is a circle in the same plane with radius 1 unit}

Answer: ⊄


Wednesday, 23 October 2019

CBSE Class 11 - Mathematics - Sets - NCERT Exercise 1.2 (#class11Maths)(#eduvictors)

Mathematics - Sets 

CBSE Class 11

NCERT Exercise 1.2

CBSE Class 11 - Mathematics - Sets - NCERT Exercise 1.2 (#class11Maths)(#eduvictors)

Q1. Which of the following are examples of the null set
(i) Set of odd natural numbers divisible by 2

Answer: Yes

(ii) Set of even prime numbers

Answer: No

(iii) { x : x is a natural numbers, x < 5 and x > 7 }

Answer: Yes

(iv) { y : y is a point common to any two parallel lines}

Answer: Yes


Sunday, 26 May 2019

CBSE Class 11 - Maths - Chapter 1 - Different Types of Sets (#class11Maths)(#cbsenotes)(#eduvictors)

Different Types of Sets

Class 11 - Mathematics
CBSE Class 11 - Maths - Chapter 1 - Different Types of Sets  (#class11Maths)(#cbsenotes)(#eduvictors)


Empty Set: 
A set is said to be empty set if it does not have any element. It is denoted by Φ or {}. Empty set is also called a null set or void set.
For example, The set of all odd natural numbers divisible by 2 is an empty set because odd natural numbers are not divisible by 2.

Finite Set: 
A set which contains finite number of elements is called a finite set.
For example, The set {x: x ∈  N and x ≤ 10} is a finite set because number of elements in the set are countable.


Wednesday, 13 March 2019

CBSE Class 11 - Mathematics Annual Sample Question Paper (2018-19) (#cbsenotes)(#eduvictors)

CBSE Class 11 - Mathematics
 Annual Sample Question Paper
 (2018-19) 

CBSE Class 11 - Mathematics  Pre-Board Sample Question Paper  (2018-19) (#cbsenotes)(#eduvictors)

Getting good marks is very important for students of class 11. For this one must practice and attempt sample question papers within time limits.

Here follows a sample question paper on Mathematics subject to assess your knowledge about the subject.

For studying you may refer following books:


Thursday, 27 September 2018

Book For Serious Mathematics Readers - Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace

Must Read Book For Mathematics Students and Teachers
Book For Serious Mathematics Readers - Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace
Euclid's Window - Buy Ebook or Hard Copy


Through Euclid's Window Leonard Mlodinow brilliantly and delightfully leads us on a journey through five revolutions in geometry, from the Greek concept of parallel lines to the latest notions of hyperspace. Here is an altogether new, refreshing, alternative history of math revealing how simple questions anyone might ask about space in the living room or in some other galaxy have been the hidden engine of the highest achievements in science and technology.

Mlodinow reveals how geometry's first revolution began with a "little" scheme hatched by Pythagoras: the invention of a system of abstract rules that could model the universe. That modest idea was the basis of scientific civilization. But further advance was halted when the Western mind nodded off into the Dark Ages. Finally in the fourteenth century an obscure bishop in France invented the graph and heralded the next revolution: the marriage of geometry and number. Then, while intrepid mariners were sailing back and forth across the Atlantic to the New World, a fifteen-year-old genius realized that, like the earth's surface, space could be curved. Could parallel lines really meet? Could the angles of a triangle really add up to more or less than 180 degrees? The curved-space revolution reinvented both mathematics and physics; it also set the stage for a patent office clerk named Einstein to add time to the dimensions of space. His great geometric revolution ushered in the modern era of physics.

Friday, 24 August 2018

Divisibility Rules of Various Numbers - CBSE Class 6-12 - NTSE, Entrance Tests - Mathematics Tips (#cbsenotes)(#entrancetests)(#eduvictors)

Divisibility Rules of Various Numbers 

(2-25)
Divisibility Rules of Various Numbers  - CBSE Class 6-12 - NTSE, Entrance Tests - Mathematics Tips (#cbsenotes)(#entrancetests)(#eduvictors)

Divisibility by 2: 
A number is divisible by 2 if its unit’s digit is even or 0.

Divisibility by 3: 
A number is divisible by 3 if the sum of its digits are divisible by 3.

Divisibility by 4: 
A number is divisible by 4 if the last 2 digits are divisible by 4, or if the last two digits are 0’s.

Divisibility by 5: 
A number is divisible by 5 if its unit’s digit is 5 or 0.

Divisibility by 6: 
A number is divisible by 6 if it is simultaneously divisible by 2 and 3.

Thursday, 1 June 2017

CBSE Class 11 Mathematics -Syllabus (2017-18) (#cbseNotes)

Mathematics -Syllabus (2017-18)

CBSE Class 11 Mathematics -Syllabus (2017-18) (#cbseNotes)

CBSE Class 11 Mathematics


Here presents the prescribed syllabus for Class 11 Mathematics for the curriculum 2017-18.