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**

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## Comments

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

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

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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 !

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Sir I am predicting the future -

Yours and agnishom's messageboard will get atleast 100 reshares

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A lot of thanks for your wishes. @megh choksi

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

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"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 \(\ddot\smile\).

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& what about our tea @ ganesh?

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According to me,

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.

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.

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Thanks for replying! :)

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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.

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What drives your ambition?

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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

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Feeling great to talk directly to you!

Sir please add more sequence and series problems.

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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

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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.

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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.

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\[\huge \mathbb{HAPPY} \quad \mathbb{ BIRTHDAY} \quad \mathbb{ SIR!}\]

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thank you very very much \(\ddot \smile\) @Rajdeep Dhingra

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Lol the 2nd gif is so funny.

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On which topics did you write your thesis paper?

Oh.. I also have a doubt:

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

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

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Ok. Thanks.

I also wanted to know why?

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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

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

OkThanks for replying.

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

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

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Thank you very much \(\ddot \smile\)

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

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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".

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

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@Azhaghu Roopesh M

Solve the tic tac toe problems by me :PLog in to reply

Do you like carrots?

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

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How did you find Brilliant? :D

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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

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

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please solve https://brilliant.org/problems/can-you-solve-it-9/?group=j4P7dyAoNhAb&ref_id=568173

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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 !!!!

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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

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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 \(\ddot\smile\)

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@Azhaghu Roopesh M

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.Log in to reply

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 !!

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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.

@Azhaghu Roopesh M

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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 .

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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.

@Azhaghu Roopesh M

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\[\huge \text{Happy Birthday sir !!} \]

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Thank you very much \(\ddot \smile\)

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HAPPY BIRTHDAY SIR!!

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Thank you very much \(\ddot \smile\) @Ninad Akolekar

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\(\huge \mathbb {HAPPY BIRTHDAY} Sir!\)

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thank you very much \(\ddot \smile\) @Rohit Ner

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\[ \huge HAPPY BIRTHDAY SIR! \]

Do you like carrots? :P

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Thank you very much \(\ddot \smile\).

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

@Nihar Mahajan

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\[\huge HAPPY BIRTHDAY SIR!\]

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

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Thanks a ton \(\ddot \smile\) @Sravanth Chebrolu

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\(HAPPY~BIRTHDAY ~SIR!\)

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thanks a lot \(\ddot \smile\) @Nishant Rai

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Belated

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thanks a lot \(\ddot \smile\) @Soumo Mukherjee

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Umm , actually his B'day was yesterday :P

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

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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.

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Here's the link to my profile .

Yes I am .Log in to reply

here

Mine isLog in to reply

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 .

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\[\LARGE \color{red}{\text{H}} \color{blue}{\text{A}} \color{yellow}{\text{P}} \color{cyan}{\text{P}}\color{green}{\text{Y}}\]

\[\LARGE \color{green}{\text{B}} \color{red}{\text{I}} \color{brown}{\text{R}} \color{magenta}{\text{T}} \color{blue}{\text{H}} \color{yellow}{\text{D}} \color{cyan}{\text{A}} \color{green}{\text{Y}}\]

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Thanks, Ashish! :)

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

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

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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

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

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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.

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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

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

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

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Can any one say wats the 5th dimension

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

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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

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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

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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??

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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

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I agree with you! The

whyquestions can probably never be answered.However, the statement can be proven by induction

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@Agnishom Chattopadhyay

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".Log in to reply

At Sandeep Bhardwaj : Thankyou your advice is invaluable

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

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

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Please make 1 more set for jee mains

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

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Check tis out!

Please participate and reshare.

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

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

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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 \(\ddot\smile\).

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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

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Any specific book ?

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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

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Sir could you help here

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

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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 ! \(:)\)

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Happy b'day sandeep sir

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thank you very much \(\ddot \smile\) @Nishu sharma

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Hello sir need ur hlp its urgent sir

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

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friend how increase my mathematical knowldge

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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.

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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?

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?

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https://brilliant.org/discussions/thread/doubt-5/?ref_id=898502

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

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

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Yes. That will help JEE aspirants. :)

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hai

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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!

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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.

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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. :)

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

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It's intentional to make it funny. ;)

BTW thanks for caring about this.

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It is intentional?!?! Oh my god!

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You teach math in which institution?

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

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Sir, where do you teach??

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

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okay,thanks

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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 ...

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\( x^2 + x + 1=0\)

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?

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You must have noticed that

\( 10^{1} = \) The first appearance of a 2 digit number

. . . .

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

Hope this was satisfactory :)

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

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

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Check tis out!

Please participate and reshare.

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Hai All the best

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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

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