Search found 100 matches

by amlansaha
Sat Dec 10, 2011 12:25 pm
Forum: Higher Secondary Level
Topic: 3 problems of probability
Replies: 15
Views: 10539

3 problems of probability

1. if a student has passed all the 11 exams he attended before, what the probability of his passing the next exam? 2. if the student got 80%+ in his previous 11 exams, what is the probability of getting 80% marks in the next exam? 3. if the students would have passed in 10 out of 11 exams, what woul...
by amlansaha
Wed Dec 07, 2011 12:36 pm
Forum: Divisional Math Olympiad
Topic: Jessore 2007 HS prob 11
Replies: 9
Views: 3417

Re: Jessore 2007 HS prob 11

nafistiham wrote:এখানে তো $\angle DBA$ এর মানটা ধ্রুব থাকছে না । তাই না?
আমিও সেটাই বলছি :S
by amlansaha
Tue Dec 06, 2011 9:23 pm
Forum: Divisional Math Olympiad
Topic: Jessore 2007 HS prob 11
Replies: 9
Views: 3417

Re: Jessore 2007 HS prob 11

লাটেক্স ঠিক করছি। কিন্তু $90^{\circ}$ কেমনে হয়?? :? :? :?
by amlansaha
Tue Dec 06, 2011 7:46 pm
Forum: Divisional Math Olympiad
Topic: Jessore 2007 HS prob 11
Replies: 9
Views: 3417

Re: Jessore 2007 HS prob 11

আমার মাথায় একটা সলুশন আসছে। দেখ তো:
প্রদত্ত শর্ত অনুযায়ী, $B$ বিন্দুর অবস্থান নির্দিষ্ট না। তাই ,
$[0<\angle DBA< ( 180^{\circ} -\angle BAM) \ ]
$
by amlansaha
Tue Dec 06, 2011 5:13 pm
Forum: Divisional Math Olympiad
Topic: Kustia 2009 HS prob 7
Replies: 6
Views: 2236

Re: Kustia 2009 HS prob 7

At first I also thought that there were only 48. But look at these combos:: $ZXYZZXY$ and $XYZZXYZ$. In the same way they have 48 permutations. So the solution is $144$. hmm..... so there are total 3 combos, each having 48 permutations $XZYZXZY$ $ZYXZZYX$ $ZXYZZXT$ and the answer is 144 :D thanks L...
by amlansaha
Tue Dec 06, 2011 4:11 pm
Forum: Divisional Math Olympiad
Topic: Gopalgang higher hisec 2011 10
Replies: 4
Views: 1964

Re: Gopalgang higher hisec 2011 10

nafistiham wrote:but,amlan da
Euclid says,
the summations of two sides in a triangle is larger than the other side.

so, the rightmost $5$ combos are incorrect.
হায় হায়, এমন ভুল আমি কেমনে করলাম :oops: :oops: :oops: :oops:
thanx nafis :)
by amlansaha
Tue Dec 06, 2011 2:34 am
Forum: Divisional Math Olympiad
Topic: Kustia 2009 HS prob 7
Replies: 6
Views: 2236

Re: Kustia 2009 HS prob 7

nafistiham wrote: \[XZYZXZY\]
\[or\]
\[YZXZYZX\]

the number of $X,Y,Z$ are such $2,2,3$
so the number of combinations are
\[2\cdot2\cdot3!=24\]
nafis, as u have considered two situations(xzyzxzy & yzxzyzx) so you have to multiply $24$ with another $2$. so answer should be 48 :)
by amlansaha
Tue Dec 06, 2011 2:20 am
Forum: Divisional Math Olympiad
Topic: Jess-06-hisec-Q.10
Replies: 2
Views: 1743

Re: Jess-06-hisec-Q.10

let $x^2+xy+5x+m+5=(ax+by+c)(dx+e)=adx^2+bdxy+(cd+ae)x+bey+ce$
comparing the co efficiantes we get
$ad=1, bd=1, cd+ae=5, be=0, ce=m+5$
now, as $b\neq 0$ [bd=1] $e=0$. so $m+5=0$
so, $m=-5$ :D :D :D
by amlansaha
Tue Dec 06, 2011 1:45 am
Forum: Divisional Math Olympiad
Topic: Gopalgang higher hisec 2011 10
Replies: 4
Views: 1964

Re: Gopalgang higher hisec 2011 10

but i think the answer is $8$ .
let $a, a, b$ are the sides of the triangle. so
$2a+b=20$
$a=\frac{20-b}{2}$
there are $8$ possible results of $(a,b)$ [$(9,2),(8,4),(7,6),(6,8),(5,10),(4,12),(3,14),(2,16),(1,18))$]( whereas a, b are positive integers.
by amlansaha
Mon Dec 05, 2011 12:35 am
Forum: Divisional Math Olympiad
Topic: Gopalgang higher hisec 2011 08
Replies: 24
Views: 7187

Re: Gopalgang higher hisec 2011 08

no two member of X is a square less or equal to 21^2. তবে এখানে যদি sqare কথাটার পরে একটা ,(কমা) বসে, তবে ব্যাপারটা ভিন্ন হয়ে যাবে। তখন উত্তর সম্ভবত $১১৮$ হবে। এক্ষেত্রে বিষয়টা এরকমঃ আমরা যেই ২২১টা জিনিস নিয়ে $X$ তৈরি করেছি, তার যেকোনো ২টির যোগফল পূর্ণবর্গ হবে না। এখন যেকোনো ২টির যোগফল যেহেতু $>...