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Showing posts from April, 2021

Ooo Vectors

I had to learn basic things about vectors. So thought why not write a blog post :P?  Also special thanks to papa 💫  So here we go.. PHYSICAL QUANTITY:- A quantity that can be measured and expressed in units. We have two types of Physical Quantity Scalar:- A physical quantity that has only magnitude. Example: Mass, speed. Vectors:- A physical quantity that has both magnitude and direction. Example: Displacement, velocity.  Now, what are vectors? VECTORS:- A physical quantity that has both magnitude and direction. In geometry, a vector is a directed line segment, whose length is the MAGNITUDE of the vector and the arrow indicating the DIRECTION. The MAGNITUDE of a vector $(\vec{A})$ is the absolute value of a vector and is indicated as $\boxed{|\vec{A}|}.$ REPRESENTATION OF VECTORS:- A vector pointing from $A$ to $B$ is written as $\vec{AB}.$ We usually define a single point $O$ as the ORIGIN. Then we associate every point $P$ with the vector $\vec{OP}$ or $\vec{P}$ MAGNITUDE OF VECTORS

Let's complex bash Part 1

I have to learn complex bash. And almost everyone knows that I am notes taking girl so thought why not make a post on complex bash ( so that I don't get emotionally demotivated lol).😇 There wasn't any need for learning complex bash, but it was in my dream checklist i.e " To learn a bash." And since I am not loaded with exams, I think it's high time to learn Bash and new topics.  Also if anyone from the "anti-bash" community is reading, sorry in advance and R.I.P.  Notes:- 1. Complex numbers are of the form $z=a+ib,$ where $a$ and $b$ are real numbers and $i^2=-1.$ 2. In polar form, $z=r(\cos \theta+~~i\sin\theta)=~~re^{i\theta},$ where $r=~~|z|=~~\sqrt{a^2+b^2},$ which is called the magnitude. 3. Here we used euler's formula i.e $\cos \theta+~~i\sin\theta=~~e^{i\theta}.$ 4. The $\theta $ is called the argument of $z,$ denored $\arg z.$ ( $\theta$ can be considered in $\mod 360$ and it is  measured anti-clockwise). 5. The complex conjugate of $z$ is

AA siblings..

This post is inspired by my brother.  I am not good at writing non-math posts, so please forgive me for that. Clickbait:P My family is... one word... weird. No really. We have my Papa, Mumma and my brother, Suhan. Now now, siblings. SIBLINGS. S.I.B.L.I.N.G.S. One of the worlds' most irritating "prani" (animal). I am the elder one, my brother is like 5 years younger than me. But no no no, we both are in fact treated equally :P ( Thanks Mumma papa).  Trust me.. Suhan is probably THE MOST PAMPERED KID OF ALL TIME. I am sure all the elder siblings go through this period. Arey Suhan is really pampered.. When Mumma and papa are out, and Suhan does something wrong, I get the scolding, in fact, I have got way more scolding than Suhan has got. And this is why he is so naughty -_-. But the evil happiness you get when your sibling gets scolding is just so good. Lemme share a story. A typical day, Suhan and me fighting. Mumma getting irritated. And then Mr Suhan said something in fro

Bio is Love..

Adios, everyone! Boards preparation at its peak :(  However, I am not able to study how I used to. Every time I try to study for boards, I just keep thinking much about a topic, stare at the book, jam a song or just start doing procrastination by bookmarking random cute problems in HSO. It's been more than a year I have studied like with a focus on a book. My lappy is being a big distraction tbh. So after INMO score come out, I will just give my lappy for repair and say papa to bring it back home after June 2.  Milk and Mocha I literally am taking 2 days to complete 1 bio chapter, some times even 3. The rate of my "slowness" is probably because I am like every 15 minutes checking discord to see if the INMO scores are out or not. So HBCSE, thank you for keeping me anxious.  Funfact:- we must be grateful that there is an organisation that is conducting these national Olys. There are some countries where no Olys are being conducted. ( Same dialogue which mumma uses, but in p

Some NMTC sub-junior level Problems

Well.. Many people don't know but I was a part of STEM's Horizon ( Now, I have left them due to boards etc.) BTW STEM's Horizons is really great! And anyone interested in Olympiad math should join it! More info about it in below (make sure to check it out!). So here are some problems I sent to them. They are fairly easy, and most of them are repetitive ideas. But they are my first sets of problems ( I know UMO was there but still..) The solutions will be posted in another blog posts. You guys can type out sols in the comments sections too :) Problems:- 1. What is maximum possible number dividing  $x^2+x+1$ and $x^5 +x^4 +x^3 + 3x^2 +2 x +4$ for all $x\in \Bbb{N}$ 2. Let $P$ be the sum of all $x$ and $y$ satisfying $45^x-2^x=2021^y.$ What is the last two digits of $p^2+p+1.$ 3. What is the greatest value of $r$ such that $3^r$ is factor of $10^{2022}-8^{674}$. 4. Find all possible tuples $ (x,y,l)$ such that $\frac{x}{100}=\frac{20}{y}=\frac{5}{l}.$ 5. Consider the following

Cute cats part 1 *not a clickbait*:-

 This post is dedicated to all those cat fans.  It's a collection of some of the cute cat pics I have, which I have saved on Pinterest. Again, the credits are given to the respective photographers :) Hope you like it!  This is just me when my teacher asks for Homework.. "Huh? which Homework?" Me asking papa for ice cream, even though Mumma said no "Papa you promised Nah"   Me and Suhan, after mumma enters our room in between our fight. "We are sweet kids u know? " My and Arpan Bhaiya's reaction to Anand saying "I am not pro". "Dramebaaz" Me when Rg complaining, how "mean" I am.. I am like" Here we go, not again please" So yeah! This was part 1. Did you guys enjoy it? Should I make a part 2 or so? If you liked it and want more content like this then do subscribe ('s okay if you don't want to :P ) Sunaina💜

Guess what? I will do class 8 geos ..

Obviously, I have become very rusted. So to unrust me ( oh god, is it unrust ?  I have become so bad in English). Okie wait.. "polish myself." I tried problems from ABJTOG 1.4. Easy ones TBH. Without further ado, here are the problems and solutions I tried. You guys can try too! I can assure you the difficulty is less than class 8. ( or class 7). I didn't try harder problems, because that would take me sometime. I did these in break :P . So yeah.. sorry for so easy  levels. Milk and Mocha  Problem 2 of ABJTOG:-  Let $ABC$ be a triangle and let $M$ be a point on the ray $AB$ beyond $B$ such that $\overline{BM} = \overline{BC}$. Prove that $MC$ is parallel to the angle bisector of $\angle ABC$. Solution :-  Note that$$\angle BMC=\frac{1}{2} \cdot (180-B)= \frac{B}{2}=\frac{1}{2}\angle ABC.$$ Problem 1 of ABJTOG :-  Let $C$ be a point on the line segment $AB$. Let $D$ be a point that doesn’t lie on the line $AB$. Let $M$ and $N$ be points on the angle bisectors of $\angle AC

Definition of Cute :O

Hey everyone, as I was going through my previous HSO Posts. I saw this beautiful problem which was given to me by Rege sir ( He teaches in IMOTC and INMOTC of Assam). I posted the solution in HSO on April 8 2020. And today I latexed the solution ( After like a year). The solution I got is pretty cute! Try it once! Problem:-  Determine the set A={$s(n^2)| n$ is a positive integer}. ($1 = s(1) = s(100),$ $ 4 = s(4) = s(121)$ belong to this set.)  Solution:- Let $A$={$s(n^2)| n$ is a positive integer}notice $n^2$ is always $0,1,4,7 \mod 9$ .by using the fact that $9| s(a) - a $ , $a$ is an integer  we get that  $9| s(n^2) - n^2$ which implies $s(n^2)$ is always  $0,1,4,7 \mod 9$ .  claim -  Any number of the form $0, 1, 4, 7 \mod 9$ belongs to set $A$ proof-  part 1- Notice that$$3^2=9,~~ 33^2 = 1089,~~ ,33^2=110889, ~~ 333^2=11108889 $$and the pattern continues (can be proved by induction )then notice that $s(3^2)=9,s(33^2)=18 , s(33^2)=27,s(33^2=)=36$, and so on . So any number of the