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

Wednesday, 12 January 2022

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-7) Derivatives Using First Principle #class11Maths #limits #calculus #differentiation #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives Part-7

Derivatives Using First Principle

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-7)  Derivatives Using First Principle #class11Maths #limits #calculus #differentiation #eduvictors



In the previous post[Part-6], we learned about the Derivative of a function at a point. Let us focus on some important derivatives using the First Principle.


Theorem 1: From the first principle, we have 

Friday, 31 December 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-6) - Derivative of a Function At a Point #limits #class11Maths #calculus #eduvictors

Class 11 - Mathematics - Limits and Derivatives (Part-6) - Derivative of a Function At a Point 

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-6) - Derivative of a Function At a Point #limits #class11Maths #calculus #eduvictors



In the previous blog post Limits and derivatives Part-5, we learned about the limits. Let us understand the derivative of a function at a point.

Q1: What is the derivative of a function at a point?

Answer: Let y = f(x) is a continuous function. It means the value of y changes as the value of x changes.

At x = a, is a point in its domain of definittion. The derivative of f at a is defines as: 

Saturday, 25 December 2021

Class 11 and 12 Maths - Probability - Part 1 (Solved Questions) #probability #class11Maths #class12Maths #cbse202122 #eduvictors

Class 11 & 12 Maths - Probability - Part 1 (Solved Questions)

Class 11 and 12 Maths - Probability - Part 1 (Solved Questions) #probability #class11Maths #class12Maths #cbse202122 #eduvictors


Let us revisit the basic terminology used in probability.

Q1: Define probability. What can the probability never predict?

Answer: Probability gives us a measure of the likelihood that something will happen. However, probability can never predict the number of times that an occurrence actually happens.


Q2: Define experiment.

Answer: An action or operation resulting in two or more well-defined outcomes. 

e.g. tossing a coin, throwing a die, drawing a card from a pack of well-shuffled playing cards etc.

Wednesday, 22 December 2021

National Mathematics Day #mathematics #eduvictors

National Mathematics Day 

National Mathematics Day #mathematics #eduvictors

India celebrates National Mathematics Day on December 22 every year. The day marks the birth anniversary of famous mathematician Srinivasa Ramanujan.

*Typo in the graphic new = knew


Sunday, 19 December 2021

CBSE Class 11 - Mathematics - Limits and Derivatives Part-5 #class11Maths #eduvictors #limits #calculus

CBSE Class 11 - Mathematics - Limits and Derivatives Part-5

CBSE Class 11 - Mathematics - Limits and Derivatives Part-5 #class11Maths #eduvictors #limits #calculus


In the previous blog post Limits and derivatives Part-4, we learned about the  trigonometric limits. Let us solve other problems related to Limits

Wednesday, 1 December 2021

CBSE Class 11 - Mathematics - Limits and Derivatives Part-4- Limits of Trigonometric Functions #class11Maths #eduvictors #limits

CBSE Class 11 - Mathematics - Limits and Derivatives Part-4- Limits of Trigonometric Functions

CBSE Class 11 - Mathematics - Limits and Derivatives Part-4- Limits of Trigonometric Functions #class11Maths #eduvictors #limits



In the previous blog post Limits and derivatives Part-3, we learn about the algebra of limits. Now, let us study few theorems before we discuss about trignometric limits.


Theorem 1: Let f(x) and g(x) be two real valued functions with same domain such that f(x) ≤ g(x) for all x.
For some a, if $\lim_{x\rightarrow a} f(x)$ and $\lim_{x\rightarrow a} g(x)$ exist then $\lim_{x\rightarrow a} f(x) \leq  \lim_{x\rightarrow a} g(x)$

Theorem 2: Sandwich Theorem or Squeeze Theorem
Let f(x) and g(x) be two real valued functions with same domain such that f(x) ≤ g(x) ≤ h(x) for all x in common domain.
For some a, if $\lim_{x\rightarrow a} f(x) = l = \lim_{x\rightarrow a} h(x)$, then $\lim_{x\rightarrow a} g(x) = l$

Sunday, 14 November 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-3) Questions and Answers #class11Maths #Limits #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives 

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-3) Questions and Answers #class11Maths #Limits #eduvictors

Part-3  Algebra of Limits  

#class11Maths #Limits 

In the previous post Limits and derivatives Part-2, we get basic ideas of the algebra of limits and also learned about rules and properties of limits.


Let us try to solve few problems:


Q1: Evaluate the given limit $\lim_{r\rightarrow 1} \pi r^2$

Answer: $\lim_{r\rightarrow 1} \pi r^2 = \pi(1)^2 = \pi$


Wednesday, 10 November 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2) Questions and Answers #class11Maths #Limits #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2) 

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-2) Questions and Answers #class11Maths #Limits #eduvictors


Questions and Answers                                                                     #class11Maths #Limits 


In the previous blog post Limits and derivatives Part-1 , we learn


$\lim_{x\rightarrow a} f(x) = l$ and it is called limit of the function f(x)


The two ways x could approach a number an either from left or from right, i.e., all the values of x near a could be less than a or could be greater than a.


In this case the right and left hand limits are different, and hence we say that the limit of f(x) as x tends to zero does not exist (even though the function is defined at 0).

Saturday, 6 November 2021

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-1) Questions and Answers #class11Maths #Limits #eduvictors

CBSE Class 11 - Mathematics - Limits and Derivatives

Part-1 - Questions and Answers

CBSE Class 11 - Mathematics - Limits and Derivatives (Part-1) Questions and Answers #class11Maths #Limits #eduvictors

Q1: Define Calculus.

Answer: Calculus is that branch of mathematics that mainly deals with the study of change in the value of a function as the points in the domain change. 


👉Note: The chapter "Limits and Derivatives" is an introduction to Calculus.

👉Calculus is a Latin word meaning ‘pebble’. Ancient Romans used stones for counting.


Q2: Who are called pioneers of Calculus (who invented Calculus)?

Answer: Issac Newton (1642 - 1727) and G. W. Leibnitz(1646 - 1717).

Both of them were invented independently around the 17th century.



Q3: What is the meaning of 'x tends to a' or x → a?

Answer: When x tends to a (x  → a), x is nearly close to a but never equals to a.

e.g. x → 3 means the value of x maybe 2.99 or 2.999 or 2.999...9 is very close to 3 but not exactly equal to 3. Similarly, x may be 3.01, 3.001, 3.0001... from the right side and gets closer to 3.

Friday, 8 October 2021

CBSE Class 11 Maths Term 1 MCQs For Practice (#class11Maths)(#cbse2021)(#term1mcqs)(#eduvictors)

CBSE Class 11 Maths Term 1 MCQs For Practice 

CBSE Class 11 Maths Term 1 MCQs For Practice  (#class11Maths)(#cbse2021)(#term1mcqs)(#eduvictors)


No. of Questions: 15 

Time: 30 minutes

Chapters: Sets, Relations and Functions, Complex Numbers, Sequence and Series, Straight Lines, Limits and Statistics



Q1: The set {1, 2, 3, ...} is _______ set. Fill in the blank.

(a) null

(b) finite

(c) infinite

(d) singleton

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}