Gharoli Gharoli, Delhi, India - 110096
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Certified 16 yrs of Exp 
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1 Student 
UrbanPro Certified Tutor
For Pharmacy Tuition
Class Location
Online Classes (Video Call via UrbanPro LIVE)
Student's Home
Tutor's Home
Years of Experience in Pharmacy Tuition
16
Experience in School or College
I taught students in a degree college. Two years on a regular basis I taught and have a lot of experience in handling students in various ways. Practical knowledge was much more helpful in understanding the concepts. Weak students were able to come up and understand the concepts easily.
Taught in School or College
Yes
Teaching Experience in detail in Pharmacy Tuition
My industrial knowledge and experience were helpful in preparing students to face the real world after completing their studies. My teaching helped students to come out from difficult situations easily.
Class Location
Online Classes (Video Call via UrbanPro LIVE)
Student's Home
Tutor's Home
Years of Experience in Class 9 Tuition
16
Board
CBSE, NIOS, IGCSE, State, ICSE
Preferred class strength
One on one/ Private Tutions, Group Classes
Experience in School or College
It was a wonderful experience in teaching the students. My way of explaining the concepts is much liked by students.
Subjects taught
Mathematics, EVS, Chemistry, Physics, Environmental Management, History, Social Science, Home Science, Sanskrit, Science, Environmental Applications, Biology, Art, Geography
Taught in School or College
Yes
Teaching Experience in detail in Class 9 Tuition
My way of teaching attracts students. They feel comfortable in sharing their weaknesses, which helps me to make the concepts easily understandable. Even students can understand things easily. I create interest in the subject.
Class Location
Online Classes (Video Call via UrbanPro LIVE)
Student's Home
Tutor's Home
Years of Experience in Class 12 Tuition
16
Board
CBSE, ISC/ICSE, NIOS, State
Preferred class strength
One on one/ Private Tutions, Group Classes
Subjects taught
Entrepreneurship, Mathematics, Biology, Home Science, Physics, Applied Mathematics, Environmental science, Biotechnology, Chemistry, Environmental Management
Taught in School or College
Yes
Class Location
Online Classes (Video Call via UrbanPro LIVE)
Student's Home
Tutor's Home
Years of Experience in Class 10 Tuition
16
Board
CBSE, IGCSE, NIOS, State, ICSE
Preferred class strength
One on one/ Private Tutions, Group Classes
Subjects taught
Science, EVS, Social Science, Physics, Home Science, Biology, History and Civics, Environmental Applications, Chemistry, Mathematics, Geography, Environmental Management
Taught in School or College
Yes
Class Location
Online Classes (Video Call via UrbanPro LIVE)
Student's Home
Tutor's Home
Years of Experience in Class 11 Tuition
16
Board
CBSE, ISC/ICSE, NIOS, State
Preferred class strength
One on one/ Private Tutions, Group Classes
Subjects taught
Geography, Biology, Sociology, Psycology, Mathematics, Environmental science, Entrepreneurship, History, Social science, Environmental Management, Home Science, Physics, Biotechnology, EVS, Applied Mathematics, Chemistry
Taught in School or College
Yes
4.9 out of 5 18 reviews
Devyanshi
Class 9 Tuition Board of Education:CBSE Subjects:Biology,Chemistry,Mathematics,Physics
"I liked the class. The way ma'am explains and resolves the query is commendable, her patience and empathy towards the students create a comfort and encourages to ask questions easily. "
Rameshwar Kumar
Pharmacy Tuition
"Good way to teach mam. I am thankful to be your student. You are very supportive in every situation. And clear all doubts. Thanks again. "
Reply by Pranjali Saxena
Thankyou Rameshwar and all the best.
Ekta Sain
Pharmacy Tuition
"It was a wonderful expetience. I loved it a lot. Mam is very helpful. It gave me a lot of scope. Thank you so much mam. "
Reply by Pranjali Saxena
Thankyou Ekta and all the best.
Ayaz Chaudhary
Pharmacy Tuition
"Best teacher i have ever seen in my life. She's supportive and well knowledgeable, i'ill prefer pranjali ma'am "
Reply by Pranjali Saxena
Thankyou Ayaz and all the best.
Arun Bhandari
Pharmacy Tuition
"Pranjali mam is the best teacher and she's have fully knowledge of pharmacotherapeutic and community pharmacy and every student have good marks in this subjects we respect our pranjali mam thanks to teaching us 10/10. "
Reply by Pranjali Saxena
Thankyou Arun and all the best.
Himanshu Kumar siddharth
Pharmacy Tuition
"She's an exceptional educator! Her passion, patience, and dedication to her students are truly inspiring. She makes complex concepts easy to understand and has a gift for bringing out the best in her students. Her kindness, empathy, and enthusiasm create a supportive learning environment where everyone feels valued. She's not just a teacher; she's a mentor and a role model. I'm so grateful to have had the opportunity to learn from her . "
Reply by Pranjali Saxena
Thankyou Himanshu and all the best.
Aurangezeb
Pharmacy Tuition
"Pranjali Saxena mam is a dedicated and knowledgeable Community Pharmacy teacher. Her online classes are well-organized and easy to understand. She explains every topic clearly and connects theoretical knowledge with real-life pharmacy practice. Her teaching style is student-friendly, and she is always ready to clear doubts. I’m really benefiting from her sessions and feel more confident about the subject. "
Reply by Pranjali Saxena
Thankyou Aurangzeb and all the best to you.
Rahul Rai
Pharmacy Tuition
"Mam Explain in very easy language and easy to understand for me. Nature and behaviour of mam is very good. "
Reply by Pranjali Saxena
Thankyou Rahul and all the best.
Abhishek Kumar vishwakarma
Pharmacy Tuition
"She is the best teacher for ( Pharmacotherapeutics ) & ( Community pharmacy and management ) i genuinely appreciate here way of teaching and letting learn every single & important point for the semester and final examination she clear every single doubts such a nice and good teacher Thank you ma'am for being my Tutor for my Future. "
Reply by Pranjali Saxena
Thankyou Abhishek and all the best.
Aditya Kumar jha
Pharmacy Tuition
"Mam was my teacher for Community Pharmacy and Pharmacotheraputics in Diploma in Pharmacy. She is very sincere, dedicated, and always well-prepared for her classes. Her teaching style is clear and organized, which made it easier to understand complex topics in both subjects. She patiently explained difficult concepts and encouraged us to ask questions. Her sincerity and commitment to our learning truly made a difference in my academic journey. I’m grateful for her guidance and support. "
Reply by Pranjali Saxena
Thankyou Aditya and all the best.
Neha Prajapati
Pharmacy Tuition
"I have studied community pharmacy and pharmacotherapeutics from mam. Her way of teaching is very clear and understandable. She tries to make every student understand and clears doubts patiently. Sometimes topics are explained a little fast, but overall her dedication and sincerity are very commendable. If it is made a little more interactive, like group discussions or practical examples, then it can be even better. I thank her for her efforts. "
Reply by Pranjali Saxena
Thankyou Neha and all the best.
Abhishek Prajapati
"It's my honour to get educated from such a wonderful teacher like you . Great teacher , mentor and amazing teaching skills. "
Reply by Pranjali Saxena
Thankyou Abhishek and all the best.
Aastha
"Experience is good. Your explanation is very good nd easily to understand. Important ques, And your short notes is very helpful to cover exam. "
Reply by Pranjali Saxena
Thankyou Aastha and all the best.
Rohit Yadav
"Well experienced teacher ma’am she is very intelligent and knowledgeable teacher would like to say to continue for next sessions. "
Reply by Pranjali Saxena
Thankyou Rohit and all the best.
Saransh Diwakar
"Nice teaching method. Clear all doubts in simple way. Experience teacher. Great experience in field knowledge. "
Reply by Pranjali Saxena
Thankyou Saransh and all the best.
Answered 1 day ago Learn CBSE - Class 9/class 10 Tution
Answered on 05/12/2025 Learn Exam Coaching/Engineering Entrance Coaching/Mathematics for Engineering Entrance for Beginners to Advanced
A vector space is a basic concept in mathematics (especially algebra). Here is a simple and clear explanation:
⭐ What is a Vector Space? (Simple English)
A vector space is a collection (set) of objects called vectors.
These vectors can be added together and multiplied by numbers (called scalars).
And the important thing is: they follow certain rules.
⭐ Think of a Vector Space like a Playground
Imagine you have a playground where you can:
1. Add two things together (like joining two paths)
2. Stretch or shrink something using numbers
3. And the playground has some rules so things don’t become confusing.
The “things” you play with here are vectors.
The “numbers” used to stretch/shrink are called scalars.
These scalars are usually real numbers (like 1, 2.5, –3), but can also be complex numbers.
⭐ Examples of Vector Spaces (Simple)
1. Arrows in the plane (2D vectors)
Like (2, 3) or (–1, 4)
You can add them:
(2, 3) + (–1, 4) = (1, 7)
You can multiply by a number:
2 × (2, 3) = (4, 6)
2. Real numbers
The set of all real numbers is also a vector space.
3. Polynomials
Like:
2 + 3x
x² – 5x + 7
They can be added and multiplied by numbers.
⭐ Two Main Operations in a Vector Space
✔ 1. Vector Addition
You can add two vectors and get another vector in the same space.
✔ 2. Scalar Multiplication
You can multiply any vector by a number (scalar), and still stay inside the vector space.
⭐ Rules a Vector Space Must Follow
There are 10 rules, but here they are in simple language:
Rules for Addition
1. You can add any two vectors.
2. Addition does not change the space.
3. Order doesn’t matter:
u + v = v + u
4. Grouping doesn’t matter:
(u + v) + w = u + (v + w)
5. There is a special vector called zero vector which does nothing:
v + 0 = v
6. Every vector has an opposite (negative):
v + (–v) = 0
Rules for Scalar Multiplication
7. Multiply by 1 gives the same vector:
1 × v = v
8. Multiply a vector by one number, then another — order doesn’t matter:
a(bv) = (ab)v
9. You can distribute numbers over addition:
a(u + v) = au + av
10. You can distribute vectors over number addition:
(a + b)v = av + bv
⭐ Why are Vector Spaces Important?
Because they are used everywhere:
Physics (forces, velocity)
Engineering
Computer graphics
Machine learning
Data science
Economics
Robotics
Wherever there is a quantity that has direction or many values, vector spaces help describe and analyze them.
⭐ In Very Simple Words
A vector space is a set of objects that you can add and multiply by numbers, and they always follow the rules( like a well behaved system).
Answered on 13/06/2025 Learn 11th and 12th Biology, 8th,9th and10th Biology
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Shalimar Bagh, Delhi 
