# Sandeep Bhardwaj's message-board.

Hello Brilliant !

You're most welcome to leave messages for me.

You can share your ideas, thoughts, complaints, suggestions, inspirations, and any other constructive stuffs for me.

Thanks a lot !

With love

Sandeep Bhardwaj

Note by Sandeep Bhardwaj
6 years, 6 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

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Note: you must add a full line of space before and after lists for them to show up correctly
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MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

!$\ddot\smile$. I guess You are Solving question of our community Brillaint.org in This Pic , ain't You ?

- 6 years, 6 months ago

Yeah, You're absolutely right. Doing so makes me feel alive. ! :P

- 6 years, 6 months ago

So True , It is Really Great Site , which offers Such an great Platform for Interacting with incredible Students and Awesome Professors Like You . I'am Proud To be member of This Family ! And Also Thank you for Your So much Contribution To our Community !

- 6 years, 6 months ago

How i increase my mathematical knowledge

- 6 years, 1 month ago

Sir I am predicting the future -

Yours and agnishom's messageboard will get atleast 100 reshares

- 6 years, 6 months ago

A lot of thanks for your wishes. @megh choksi

- 6 years, 6 months ago

How do you relate yourself with 'Po' the Panda in the movie Kungfu Panda? @Timon

- 6 years, 6 months ago

"I eat when I'm frustrated." this relates me with PO in that movie. And always remember, the people who love to eat are always the best people. :P @pumba $\ddot\smile$.

- 6 years, 6 months ago

& what about our tea @ ganesh?

- 6 years, 6 months ago

Po used to take soup, not tea. And I think thats what differs me from PO. Our tea @ganesh is just pain-relieving, that's one of my Awesome things.

- 6 years, 6 months ago

1. What is the worst way to teach mathematics?
2. What is the golden rule that every mathematics teacher should follow?

- 6 years, 6 months ago

According to me,

1. The worst way to teach mathematics is tell the students to use calculator in all algebra problems, to draw exact figure, then measure the lengths in geometry problems, to count all the cases in case of combinatorics problems. This will frustrate the students and they may have a tendency to hate Maths. This is the worst way, so it must be avoided. AND use of the word "obviously" on directly telling the result without answering the question of how and why will make it more weird.

2. I think that the golden rule that every mathematics teacher should follow that he/she should not tell only the solutions to the problems, but also the approach (matters most) and what stuffs made that approach stroke in his/her mind. On doing so, students will start thinking about the problems,then Maths won't look something magical or strange to them anymore. And this will enhance the interest of students in Mathematics. Being a JEE-Advanced Maths Faculty, this golden rule is subjected to the problem solving, as Maths is much more about computational approach than the conceptual one for JEE.

- 6 years, 6 months ago

- 6 years, 6 months ago

May be I could answer your first question - worst way would be to just read out the NCERT in the classroom with no more extra explanation.

- 6 years, 6 months ago

Staff - 6 years, 6 months ago

My keenness to learn Mathematics and share that knowledge, posting and solving problems on Brilliant, always having a desire to give my students the best of me : a lot of discussion, analysis, problem making, elegant approaches, how to face the exam, how to overcome some depressing moments in the exam, discussing Mathematical ideas and our future plans with my best friend @Sanjeet Raria, Always keep myself ready to face any challenge (any test, discussion, presentation, interview, lecture etc.), all these drive my ambition. @Calvin Lin

- 6 years, 6 months ago

Feeling great to talk directly to you!

- 6 years, 6 months ago

I am also feeling awesome. Nowadays, I am unable to give my time to the Brilliant. I will be very much active within a week, then I will add a lot of awesome problems of Sequence and Series. And off course, of many other topics too. You will definitely enjoy the problems. @megh choksi

- 6 years, 6 months ago

I can't thank you enough for how much of an inspiration you are to me along with all the others are Brilliant. I'm hopefully striving to reach your (and others) levels of math skills by the time I graduate from high school or by the time the school year here ends.

- 6 years, 6 months ago

All the best Mr. @tytan le nguyen Keep doing problems and keep learning from your mistakes. Always try to look all the given solutions to any problem and analyse each of those solutions, that will enhance your skills very rapidly. Great. Keep it up.

- 6 years, 6 months ago

$\huge \mathbb{HAPPY} \quad \mathbb{ BIRTHDAY} \quad \mathbb{ SIR!}$

- 6 years, 2 months ago

thank you very very much $\ddot \smile$ @Rajdeep Dhingra

- 6 years, 2 months ago

Lol the 2nd gif is so funny.

- 6 years, 2 months ago

On which topics did you write your thesis paper?

Oh.. I also have a doubt:

$\Huge Is\quad i>0,\quad where\quad { i }^{ 2 }=-1.\quad Why\quad Not?$

- 6 years, 6 months ago

Inequalities are not applicable in case of complex numbers. You can't even say that $2i>i$.

- 6 years, 6 months ago

Ok. Thanks.

I also wanted to know why?

- 6 years, 6 months ago

Because $i$ doesn't have any universally accepted significance in terms of its value. For eg $2>1$. But $-2<-1$. If I ask you why ? then probably you will have no meaningful answer to this why..!! Because these are the basic definitions, and these don't have any reason. There is a specific way of multiplication i.e. everyone knows the same way to multiply in the whole world, But if I ask you why is multiplication done only by this method, why not another one..? Probably you can't reply the answer to that why too?

So whole I want to say is that in Mathematics anything is accepted universally when it doesn't violate the laws of mathematics (it is conceptually true) and it has further applications. Probably there are not applications further associated with the inequalities in complex numbers or may be it violates some basic laws of maths when proceeded with this concept. @Math Philic

- 6 years, 6 months ago

Sorry, if I sounded rude. I have deleted that comment.

- 6 years, 6 months ago

It's ok dude. I disapprove of what you say, but I will defend to the death your right to say it. I replied to your comment with a hope that you will take my words in positive way. Read my comment again, may be there is something good that I wanted to convey.

- 6 years, 6 months ago

Ok @Sandeep Bhardwaj , I have revisited it and went through it again.

- 6 years, 6 months ago

Because complex numbers like i cannot be represented on the number line.Numbers like 1,2,3,-1,-2 can be represented on the number line and hence can be compared.

- 5 years, 4 months ago

(its simple) since i is a imaginary number then how can u compare it .

- 6 years, 4 months ago

Happy Birthday to you The sky is Blue No clouds  Sun shining bright for u!! HAPPY BIRTHDAY SIR!!

- 6 years, 2 months ago

Thank you very much $\ddot \smile$

- 6 years, 2 months ago

Super hero by night :P what do you mean :P xD

- 6 years, 6 months ago

The whole day moves on with learning and teaching. But life is not all about this, So all other stuffs (especially my interests, mentioned in my profile) left for the NIGHT, are to be accomplished like a SUPER-HERO. I would like to add here that the nights have the credit for making of the "real me".

- 6 years, 6 months ago

When do you sleep ? Are you a vampire ? :P :D

- 6 years, 1 month ago

It's not fixed when I sleep. I assume that I ain't an vampire :P :D But not too much sure I am !

- 6 years, 1 month ago

Solve the tic tac toe problems by me :P @Azhaghu Roopesh M

- 6 years, 1 month ago

Do you like carrots?

- 6 years, 6 months ago

Yeah I like carrots. Infact, I like everything to eat. $\ddot\smile$.

- 6 years, 6 months ago

How did you find Brilliant? :D

- 6 years, 6 months ago

My friend Sanjeet Raria told me about Brilliant, I signed up then on Brilliant, and I am doing it almost regularly since June 2014 (approx). @Marc Vince Casimiro

- 6 years, 6 months ago

From first day only i knew that you and @Sanjeet Raria must be friends/brothers because "sandeep" and "sanjeet" rhyme very nicely :P

- 6 years, 2 months ago

hahahaha, Nicely observed. :P

- 6 years, 2 months ago

- 6 years, 6 months ago

Hi sir , I just completed your set "Expected JEE-MAINS-2015" .

Marks obtained : 115 Time Taken : 1 h 27 minutes Questions Attempted : 30 Number of Guesses : 3

I enjoyed going through this set and am eagerly awaiting your next set that you have promised to @Cody Martin !!!!

- 6 years, 5 months ago

Your score is very good. Keep it up. You can get in top 10 All India Rank, if you perform like this in all the three subjects in JEE syllabus. Now in Maths, you need to reduce the time consumed. Ultimately, to increase your speed with accuracy. For that I will suggest you to memorize all the formulas instead of deriving those in the exam time, especially over co-ordinate geometry, for eg. equation of tangents, normals, parametric form, intercept-formulas etc. I wish you all the very best. Keep your efforts on and focus on more improvement.!! @Azhaghu Roopesh M

- 6 years, 5 months ago

You have read my mind perfectly sir !! Yes , I do derive certain formulae during exam time !!

I guess I have to start remembering the formulae then $\ddot\smile$

Thanks a lot sir for your best wishes $\ddot\smile$

- 6 years, 5 months ago

Yeah, you should start. On reading your reply, I realized that I've attained numerous priceless qualities of an Ideal teacher through one year experience of teaching JEE students. Thanks for making me this realization. Keep it up. @Azhaghu Roopesh M

- 6 years, 5 months ago

Sir , I have a suggestion . Seeing that you like to change your profile pic every 2-3 days , can you update the pic on this message board ?

This pic is from 2014 , please post one from 2015 :D

It's just a suggestion sir !!

- 6 years, 4 months ago

The limit of uploading your profile pics on Brilliant is $42$. My limit has reached. :P . What to do next ? How to update the pic on the message-board ?

Thanks for the suggestion.

- 6 years, 4 months ago

Haha , seriously ! The limit of 42 has been touched ! Btw I didn't know of that upper limit .

Well , there's one way . If the pic on this message board has been added using Markdown , then I guess you can add another one by simply deleting the previous code and uploading another pic , but if you have added the pic using the "Attach Image" , then I'm not too sure about it . Sorry sir .

- 6 years, 4 months ago

Okay.

I've attached the image there. I also don't know the way of resolving it.

$\ddot \smile$ Yeah , the sky has been touched.

I also want to delete some of the pics. But there is no such option there.

Btw if I upload the image on message-board, it's gonna buried deep after some time, as it was some days ago.

- 6 years, 4 months ago

$\huge \text{Happy Birthday sir !!}$

- 6 years, 2 months ago

Thank you very much $\ddot \smile$

- 6 years, 2 months ago

HAPPY BIRTHDAY SIR!!

- 6 years, 2 months ago

Thank you very much $\ddot \smile$ @Ninad Akolekar

- 6 years, 2 months ago

$\huge \mathbb {HAPPY BIRTHDAY} Sir!$

- 6 years, 2 months ago

thank you very much $\ddot \smile$ @Rohit Ner

- 6 years, 2 months ago

$\huge HAPPY BIRTHDAY SIR!$

Do you like carrots? :P

- 6 years, 2 months ago

Thank you very much $\ddot \smile$.

However, I don't want to comment about the mystery of Carrots right now. :P

- 6 years, 2 months ago

$\huge HAPPY BIRTHDAY SIR!$

May you live many years to celebrate your birthday, and educate people so that humanity reaches it's potential!

- 6 years, 2 months ago

Thanks a ton $\ddot \smile$ @Sravanth Chebrolu

- 6 years, 2 months ago

$HAPPY~BIRTHDAY ~SIR!$

- 6 years, 2 months ago

thanks a lot $\ddot \smile$ @Nishant Rai

- 6 years, 2 months ago

Belated

- 6 years, 2 months ago

thanks a lot $\ddot \smile$ @Soumo Mukherjee

- 6 years, 2 months ago

Umm , actually his B'day was yesterday :P

And as usual , your selection of pics is the best :D

- 6 years, 2 months ago

Lol...I didn't notice the time ...But I also wished him on Facebook. Perhaps he is busy enjoying. When I logged in here I found Sandeep's message board reshared, thought also to mention here. I didn't notice what's was the time.

- 6 years, 2 months ago

K . Fb huh ? Looks like I have to finally create an account there .

- 6 years, 2 months ago

- 6 years, 2 months ago

Yes I am . Here's the link to my profile .

- 6 years, 2 months ago

Mine is here

- 6 years, 2 months ago

I tried searching for your profile on G+ , but there are a lot of people who share their names with you , so no luck no my side .

And btw I don't have a mobile currently , so I'll wait till I buy one(probably next month b4 joining college) , to create an fb account .

- 6 years, 2 months ago

$\LARGE \color{#D61F06}{\text{H}} \color{#3D99F6}{\text{A}} \color{#CEBB00}{\text{P}} \color{cyan}{\text{P}}\color{#20A900}{\text{Y}}$
$\LARGE \color{#20A900}{\text{B}} \color{#D61F06}{\text{I}} \color{#624F41}{\text{R}} \color{magenta}{\text{T}} \color{#3D99F6}{\text{H}} \color{#CEBB00}{\text{D}} \color{cyan}{\text{A}} \color{#20A900}{\text{Y}}$

- 5 years, 2 months ago

Thanks, Ashish! :)

- 5 years, 2 months ago

Many many happy returns of the night XD, Am I right one to wish you :P

- 5 years, 2 months ago

I want to know how to solve calculus and algebra easily, can you help me ?

- 6 years, 6 months ago

Problem solving can be learnt only by solving the problems. Keep doing problems and learn from every problem. After some time, you will find that you've been leveled up and you can solve the problems more easily. All the best. @Anish Harsha

- 6 years, 6 months ago

I agree. I learned almost all Number Theory, Calculus and Combinatorics here at Brilliant!

- 6 years, 6 months ago

Thnx, I too learn like this. At start, I knew only little. But soon, I knew how to solve problems and soon level uped in many topics.

- 6 years, 6 months ago

Calm down ,there is lots of time left and all u have to do is just solve a lots of problems and find the reason behind why ur solving in a particular way , why not a easier step. And then whenever u learn a formula or get to see any results from problems then find how the formula was created and how the inventer or dicoverer would have reached to the result ; that is enough to take u to great heights; all the best

- 6 years, 6 months ago

In which college did you study sir ? Just, my curiosity's getting the better of me .

- 6 years, 6 months ago

Actually I didn't go to the college. :P @Azhaghu Roopesh M

- 6 years, 6 months ago

Can any one say wats the 5th dimension

- 6 years, 6 months ago

Such things are not universally accepted yet. These have a multiple issues. You can search wikipedia for that.

- 6 years, 6 months ago

Salutations Sir,

i have found brilliant to be an excellent source for enhancing problem solving skills and i have recommended it to many friends i am an engineering student in my freshmen year but i enjoy mathematics more my question is that how should i proceed going about learning the more rigorous kind of mathematics like analysis ,topology etc after i take the introductory courses like linear algebra differential equations etc as engineers in my university are not allowed to take these courses and unfortunately switching to math major is not a feasible option for me.

i understand this may not be the appropriate forum to ask these questions but any help would be much appreciated

Thank you

- 6 years, 6 months ago

My friend, there is no short way or short-trick to learn Mathematics. All you need to do is spend your time with Maths and very shortly, you will find yourself friendly with it. Just take good references, buy some good books and start studying, you will definitely get a way out. Take every factor into analysis while making some decision, It will escape you from a lot of regrets in the future. So take a look at every side of your situation and you will reach on the best option for you and then be completely devoted to that.

Every person in the world has 24 hours a day. But the thing that creates the difference is how you utilize that time.

All the best @Atif Farooq

- 6 years, 6 months ago

When you multiply 6 by an even number, they both end in the same digit.

Example: 6×2=12, 6×4=24, 6×6=36, etc

Why does this happen??

- 6 years, 6 months ago

It's just an observation. I think, at this level at which the question is, rules are made from the observations, that is theories are based on experiments(observations). It's just like asking $1$ comes after $0$, why ? So, there is no answer to this question. So whole I want to say is that such things just happen, It will be beneficial for you if you take it just as an observation and use it somewhere. @Harshvardhan Mehta

- 6 years, 6 months ago

In mathematics you do not understand things, you get used to them - John von Neumann

I agree with you! The why questions can probably never be answered.

However, the statement can be proven by induction

- 6 years, 6 months ago

I love this quote very much as posted by you ; "In mathematics you don't understand things, you get used to them. - By John von Newumann". @Agnishom Chattopadhyay

- 6 years, 6 months ago

- 6 years, 6 months ago

Your set on Expected JEE main 2015 has only 3 questions. But you say there are 30. Imgur

- 6 years, 5 months ago

I'm posting the questions, Please wait. It will be ready up to 6pm today. Please have a little patience. @Rajdeep Dhingra

- 6 years, 5 months ago

Please make 1 more set for jee mains

- 6 years, 5 months ago

Off course, So be ready. Expected JEE-Mains-2015-II coming soon...All the best !

- 6 years, 5 months ago

Check tis out!

- 6 years, 4 months ago

Sir please can you make one final set for jee mains 2015 Thanks :)

- 6 years, 4 months ago

I don't promise for that, but I will try. @Cody Martin

- 6 years, 4 months ago

Hello Sir,
I wanted to ask you for a suggestion.
Sir, I have just finished integration from RD Sharma class 12th. Could you suggest me what to do next $\ddot\smile$.

- 6 years, 4 months ago

Enhance the skills of integration from some other book whose level is higher than that of R.D. Sharma. You can go for the books recommended for JEE-Advanced. @Rajdeep Dhingra

- 6 years, 4 months ago

Any specific book ?

- 6 years, 4 months ago

sir i attempted EXPECTED JEE MAINS B i am getting only 25 marks in 2 and half an hour i got 10 questions correct and 15 questions wrong guessed only 2 problems but i learnt all the mistakes i did and i got 29 marks in the first set

- 6 years, 4 months ago

Sir could you help here

- 6 years, 3 months ago

Can you please post some more problems on Conic sections and binomial theorem??

- 6 years, 2 months ago

Sandeep Bhardwaj Sir . I wanted to to show you my approach to this problem . I have my work scanned . Should i post it here or do i mail it to you ? If so please tell me your id. Thanks ! $:)$

- 6 years, 2 months ago

Happy b'day sandeep sir

- 6 years, 2 months ago

thank you very much $\ddot \smile$ @Nishu sharma

- 6 years, 2 months ago

Hello sir need ur hlp its urgent sir

- 6 years, 1 month ago

Yeah, tell me..What help do you need ?

- 6 years, 1 month ago

friend how increase my mathematical knowldge

- 6 years, 1 month ago

Sir, I'm a student in class 11 at the moment, and plan on giving JEE in 2017. My coaching class starts day after tomorrow, and I had a question: How much sleep do you recommend? And from when to when? Others are free to comment too.

- 6 years, 1 month ago

Hello Sandeep Bhardwaj

During school days Math was not my favorite subject, I felt its difficult and it was not explained properly .
But Now its inverse, I joined Brilliant and realized that its interesting. This made me think what is fascinating me to solve Math problems?

1. I am dealing with Application of maths not just equations
2. Started visualizing and relate those to practical things.

Now i want to understand Maths properly and in depth. So i need your help for the same. I want to get trained by Maths experts like you. Please let me know how can i seek that?

- 6 years, 1 month ago

- 5 years, 12 months ago

Why don't you start posting problems for jee mains? Just like last year.

- 5 years, 4 months ago

Do you want me to post the problems for JEE this year too? @Aditya Kumar

- 5 years, 4 months ago

Yes. That will help JEE aspirants. :)

- 5 years, 4 months ago

Alright. I'll defnitely go for this one. Thanks!

- 5 years, 4 months ago

I should thank you :)

- 5 years, 4 months ago

hai

- 5 years, 4 months ago

Sir I 'm Atanu a COMMERCE student. Please help me to refer me some books. That will help me to be master means that will help me very much to understand the depth of COMMERCE(Accounts, Business study & Economics) & MATHEMATICS also. PLEASE HELP ME!

And i am very grateful to you that you have created this note. Please help me sir!

- 5 years, 4 months ago

Sir , I request you to make a new note of the JEE ADVANCED MATHEMATICS CONTEST-'16, as it is taking time to load the contents.

- 5 years, 3 months ago

Yeah, I already have this point in mind. But I'm waiting for the contest to grab 50 problems in the current note and then forward it to the new note. :)

- 5 years, 3 months ago

Sir a typo on this page shoukdnt it be 4 out of 5 people have trouble with fractions instead of 5 out of 4?

- 5 years, 2 months ago

It's intentional to make it funny. ;)

- 5 years, 2 months ago

It is intentional?!?! Oh my god!

- 5 years, 2 months ago

You teach math in which institution?

- 4 years, 1 month ago

https://brilliant.org/problems/how-to-make-a-triangle/?group=ZTtB5mdNQtMx&ref_id=539978

- 6 years, 6 months ago

Sir, where do you teach??

- 6 years, 6 months ago

I teach at an IIT-JEE institute named SAKSHAM IIT PMT, New Delhi. @Prashant Ramnani

- 6 years, 6 months ago

okay,thanks

- 6 years, 6 months ago

Sir, I would like to ask you how to find the no. of digits in the expansion of a given number when the power is not an integral multiple or power of 10.. For example we can use logarithms to find the no.of digits in $8^{1000}$

$10^{(x-1)}$ will have x digits and $10^{(x-1)}$ = $8^{1000}$

And by taking log on both sides, (x-1) = log $8^{1000}$ x-1 = 1000 \times log 8

And, x=904 (on Approximation)

But, Consider this question, If $x^{2}$ + x + 1 = 0 then the no.of digits if number $x^{3}$ + 1/$x^{3}$ the whole raised to 2014.... Please Solve it ...

- 6 years, 6 months ago

$x^2 + x + 1=0$

We can see x=0 will not be a factor of it, thus it is legal to divide it by x.

$\implies x + \dfrac{1}{x} = -1$

$-1^3 = x^3 + \dfrac{1}{x^3} + 3\times x\times \dfrac{1}{x}(x + \dfrac{1}{x})$

$x^3 + \dfrac{1}{x^3} = 2$

Now do the same as you proceeded for $8^{1000}$

Can you explain me why taking logarithms helps us to find the number of digits?

- 6 years, 6 months ago

You must have noticed that

• $10^{1} =$ The first appearance of a 2 digit number

• $10^{2} =$ The first appearance of a 3 digit number

. . . .

• $10^{x-1} =$ The first appearance of a x digit number .

So we basically equate the number of digits by taking log on both sides .

Hope this was satisfactory :)

- 6 years, 6 months ago

Nice logic +1

- 6 years, 6 months ago

@U Z I hope @Azhagu Roopesh M explained it already .... ( However It was me who was late :P ) Anyway Thanx for the solution bro _ /\ _ !

- 6 years, 6 months ago

@U Z Thanks @megh choksi @Azhaghu Roopesh M for your valuable responses to the problem.

- 6 years, 6 months ago

Nice one. Also $\omega$ is the root of the equation $x^2+x+1=0$ and $\omega^3=1$ $\implies x^3+\dfrac{1}{x^3}=2$.

- 6 years, 6 months ago

Check tis out!

- 6 years, 4 months ago

Hai All the best

- 6 years, 2 months ago

Sir m preparing for jee It's only about 6-7 months left of mains nd I hv to prepare for my 12 boards also Would you give me some suggestion on how should I study to balance both things? Thanks

- 6 years, 1 month ago