Search found 81 matches

Sat Jan 19, 2019 11:27 pm
Forum: Junior Level
Topic: করমর্দন
Replies: 2
Views: 4089

Re: করমর্দন

একটি অনুষ্ঠানে ছেলেরা কেবল মেয়েদের সাথে করমর্দন করে । অন্যদিকে প্রতিটি মেয়ে সবার সাথে করমর্দন করে । যদি মােট করমর্দনের সংখ্যা 40 হয় তবে অনুষ্ঠানে উপস্থিত ছেলেদের ও মেয়েদের সংখ্যা ( একের অধিক ) কত ? This problem was posted before. Have a look. http://matholympiad.org.bd/forum/viewtopic.php?f=13&...
Tue Jan 08, 2019 6:00 pm
Topic: BDMO 2018 National Olympiad: Problemsets
Replies: 3
Views: 3219

Re: BDMO 2018 National Olympiad: Problemsets

Bangladesh Mathematical Olympiad 2018: Higher Secondary Problem 1 Solve: $x^2(2-x)^2=1+2(1-x)^2$ Where $x$ is real number. http://matholympiad.org.bd/forum/viewtopic.php?f=13&t=4238 Problem 2 $AB$ is a diameter of a circle and $AD$ & $BC$ are two tangents of that circle.$AC$ & $BD$ intersect on a p...
Tue Jan 08, 2019 5:55 pm
Topic: BDMO National Higher Secondary 2018/7
Replies: 2
Views: 1731

BDMO National Higher Secondary 2018/7

Evaluate

$\int^{\pi/2}_0 \frac{\cos^4x + \sin x \cos^3 x + \sin^2x\cos^2x + \sin^3x\cos x}{\sin^4x + \cos^4x + 2\ sinx\cos^3x + 2\sin^2x\cos^2x + 2\sin^3x\cos x} dx$
Tue Jan 08, 2019 5:21 pm
Topic: BDMO 2018 National Olympiad: Problemsets
Replies: 3
Views: 3219

Re: BDMO 2018 National Olympiad: Problemsets

Bangladesh Mathematical Olympiad 2018: Secondary Problem 1 Solve: $x^2(2-x)^2=1+2(1-x)^2$ Where $x$ is real number. http://matholympiad.org.bd/forum/viewtopic.php?f=13&t=4238 Problem 2 $AB$ is a diameter of a circle and $AD$ & $BC$ are two tangents of that circle.$AC$ & $BD$ intersect on a point of...
Tue Jan 08, 2019 4:59 pm
Topic: BDMO 2018 National Olympiad: Problemsets
Replies: 3
Views: 3219

Re: BDMO 2018 National Olympiad: Problemsets

Bangladesh Mathematical Olympiad 2018: Junior Problem 1 The area of a rectangle is $240$. All the lengths of the sides of this rectangle are integer, what can be the lowest possible perimeter of this rectangle? http://matholympiad.org.bd/forum/viewtopic.php?f=13&t=5366 Problem 2 If the average of f...
Tue Jan 08, 2019 4:43 pm
Topic: BDMO 2018 National Olympiad: Problemsets
Replies: 3
Views: 3219

Bangladesh Mathematical Olympiad 2018 : Primary problem 1 The average age of the $5$ people in a Room is $30$. The average age of the $10$ people in another Room is $24$. If the two groups are combined, what is the average age of all the people? http://matholympiad.org.bd/forum/viewtopic.php?f=13&t...
Tue Jan 08, 2019 2:01 pm
Topic: BDMO National Junior 2018/9
Replies: 1
Views: 1223

BDMO National Junior 2018/9

Find the number of positive integers that are divisors of at least one of $10^{10}$, $12^{12}$, $15^{15}$.
Tue Jan 08, 2019 1:59 pm
Topic: BDMO National Junior 2018/8
Replies: 1
Views: 1323

BDMO National Junior 2018/8

In triangle $\triangle ABC$, $AB=10$, $CA=12$. The bisector of $\angle B$ intersects $CA$ at $E$, and the bisector of $\angle C$ intersects $AB$ at $D$. $AM$ and $AN$ are the perpendiculars to $CD$ and $BE$ respectively. If $MN=4$, then find $BC$.
Tue Jan 08, 2019 1:53 pm
Topic: BDMO National Junior 2018/7
Replies: 3
Views: 1420

BDMO National Junior 2018/7

All possible $4$ digit numbers are created using $5,6,7,8$ and then sorted from smallest to largest. In the same manner, all possible $4$ digit numbers are created using $3,4,5,6$ and then sorted from smallest to largest. Then first number of the second type is subtract from first number of the firs...
Tue Jan 08, 2019 1:50 pm
From $1$ to $6$ nodes, one can go only right side and downward. From $7$ to $11$ nodes, one can go right side or along the diagonal. If you start from $1$, in how many ways can you reach $12$ ?