## Monday, July 25, 2011

### Making Mathematics Simpler! NCERT TEXTBOOK SOLUTIONS - XII Mathematics

Dear Students Of Class XII
It is observed that many a times, after teachers have explained certain topics and have discussed certain questions from the related exercise, not all the questions of the exercise are being solved/attempted by the students. It is practically impossible and undesirable for the teacher to solve each and every question in the class itself. The remaining questions are supposed to be attempted by the student at home. However, it is very much possible that the student is unable to successfully solve all of them.
After discussing this issue with the students, I have decided to make the NCERT textbook solutions available at my blog. The solutions are taken from www.meritnation.com. You can directly visit this website but you will first need to register there and the solution of only one question can be seen at a time. This might be a cumbersome process while you are checking your answers. Therefore, to  save the student’s time and to make those solutions available to all the unregistered students as well, I have decided to upload the solutions here from time to time.
At the same time, I would want that the students do not check the solutions before they have tried the questions themselves. Hence, I’ll be uploading the solutions here only after the exercise has been covered in the class.
I’m also trying to upload the solutions of all the chapters which have been already covered in the school i.e. chapters 1-5.
Check this post frequently to get the latest updates and keep doing mathematics!
CHAPTER 1 (RELATIONS AND FUNCTIONS)

CHAPTER 2 (INVERSE TRIGONOMETRY)

CHAPTER 3 (MATRICES)

CHAPTER 4 (DETERMINANTS)
EX. 4.1     EX. 4.2       EX. 4.3      EX. 4.4
EX. 4.5     EX. 4.6       MISC. EX.
CHAPTER 5 (CONTINUITY AND DIFFERENTIABILITY)
EX 5.1        EX 5.2      EX. 5.3      EX. 5.4      EX. 5.5
EX. 5.6      EX. 5.7      EX. 5.8      MISC. EX.
CHAPTER 6 (APPLICATIONS OF DERIVATIVES)

EX 6.5 (Q1- Q12)   EX 6.5 (Q13 onward

CHAPTER 7 ( INTEGRALS)
EX. 7.5      EX. 7.6

EX. 7.7     EX. 7.8      EX. 7.9     EX. 7.10    EX. 7.11    MISC. EX.

CHAPTER 8 ( APPLICATION OF INTEGRALS)
EX 8.1     EX 8.2     MISC. EX.

CHAPTER 9 ( DIFFERENTIAL EQUATIONS)
EX. 9.1     EX. 9.2     EX. 9.3     EX. 9.4

CHAPTER 10 ( VECTOR ALGEBRA )

CHAPTER 11 ( THREE DIMENSIONAL GEOMETRY)

CHAPTER 12 ( LINEAR PROGRAMMING)

CHAPTER 13 ( PROBABILITY)

(Other Chapters will be uploaded soon.)

Happy learning...
All the best...
Amit Sir

## Friday, July 22, 2011

### Do you know today is a special day, Mathematically...

Dear All

Do you know what’s special about today,   22 July?
Well, today is Pi Approximation Day.

Pi Approximation Day celebrates the mathematical constant π (pi). It is observed on July 22, due to π being roughly equal to 22/7.
The fractional approximation of π ,227, resembles the date July 22 in the day/month format, where it is written 22/7. Pi Approximation Day is therefore celebrated on July 22.
In geometry, pi is defined as the ratio of a circle's circumference to its diameter. July 22, often written as 22/7, is an appropriate day to explore pi, since 22 divided by 7 is an approximation of pi.
Pi Approximation Day is celebrated in a number of ways, including contests to memorize pi to the most decimal places, solving math problems involving pi, discovering the history of pi, ruminating on how life would be different without pi and—of course—eating pie.
So, enjoy this mathematical day ...
Amit Sir

## Friday, July 15, 2011

### Class Test held in XII (All Sections)

Dear All,

Today a class test based on differentiation(class XII) was conducted. The demotivating factor was that 18 students were absent in XII A (Science students). All those who were absent today will give the test later.
Anyways, I was prepared with two different papers, one for XII A and other for XII B.
Here are the test papers along with solutions.
For class XII B and C

For class XII A

Here are the solutions:
It is hoped that students must have done well. Please check the methods and 'how to' give the answers.

All the Best...
Amit Sir

## Saturday, July 9, 2011

### Models of Platonic & Archimedean Solids

Dear All

Finally, I am done… I had been working for the last three weeks over my birthday gift for myself! I have finally completed making the three-dimensional models of Platonic and Archimedean Solids. Yet again! Surely, those forty-fifty hours while I was making them paid off well.
Although I had made these solids five years ago as well but the methodology and the type of paper used then was not the best way they could be. And I figured that out soon when I saw those models perishing. But of course, my past experience helped me a lot this time.
I got the nets of these solids printed out on 12”X18” photo paper and then used ‘half-cut’ method on paper to get the proper nets and hence the solids.

If you wish to make these solids for yourself, download this file and enjoy!
Good luck!
And yes, Happy Birthday to me J

Amit Sir

## Friday, July 1, 2011

### SO FAR, MY JOURNEY AS A TEACHER..

Dear All

July 2 – a very special and important day for me for this entire decade. I’m proud to share with all of you that I joined CRPF Public School as a Mathematics teacher on this very date exactly ten years back. This day marked the beginning of an absolutely delightful journey of my life.
Today, when I go down the memory lane, I can recall each and everything very distinctly. I see myself as a young, energetic and a passionate Mathematics teacher who wanted to impart the best Mathematics which exists to his students. And I honestly believe that I have kept that promise so far with utmost sincerity.
Like every other journey in life, this one has had its ups and downs too – there were times when I got really upset at the overall discouraging performance by some students and then there were times when I was simply proud of the fantastic achievements of my students in academics and other fields altogether. Someone has very rightly said that “Success is a journey, not a destination. The doing is often more important than the outcome.” Without any hesitation, I gladly admit that I have real satisfaction and contentment; not only just as a teacher elsewhere in the world, but as a teacher in this School.
It is surely the right time to thank my mentor and guide Sh. Suraj Prakash Sir for his guidance, motivation, affection, love, care and appreciation at every moment. He made me what I am today. He is the one who inspired me to work harder every day, with more dedication and sincerity; and that too not by mere preaching but by setting live examples.
Let me share one of my secrets. I was not good in Mathematics till class IX. In fact I scored almost less than half the marks I scored in my class X boards. And I believe that the only thing that is constant is, change. Though, how did that happen in just one year, that remains a mystery; yet I haven’t looked back once I started celebrating the real beauty of Mathematics. Mathematics is not only a subject for me; it’s my passion, love and perhaps my life.
I keep sharing it with everyone what someone shared with me that you might not get what you desire; but you will certainly get what you deserve. So, be a good, humble, kind and disciplined human being and bring yourself to level so that you may get everything ‘good’ you desire. I wish all the students a very successful and contented life.

### NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)

Dear all, Please do watch my latest video (dated 10-01-2021) on the topic “NUMBER OF TRAILING ZEROES IN A PRODUCT (PART -2)” VIDEO LINK HERE...