Problem 1.
Which least integer do you need to multiply with $240$ to make it a perfect square?
Problem 2.
In $ABCD$ parallelogram $E, F, G,$ and $H$ are the midpoints of $AB, BC, CD,$ and $DA$ respectively. Area of $ABCD$ is$ 25$ sq. unit. Find the area of $PQRS$.
Problem 3.
In triangle $ABC$. $D,E,F$ are three points on $BC,CA,AB$ respectively such that $AE:EC=1:3$, $DC:DB=2:1$,$ BF:FA=3:2$, after attaching $D,E,F$ with "shirshobindu" of opposite side, there creates another triangle $HIG$ in the middle. what is the area of triangle $HIG$?
Problem 4.
$3$ non negative integers $(x,y,z)$ satisfies $34x+51y=6z$ If $y$ and $z$ are primes what is $x+(y×z)$?
Problem 5.
$10$ people are seating on chairs around a circular table. These chairs are marked $ 0,1,2,3,...,9$ in a clockwise manner.There is a ball on the man's hand who is seated on $0$ marked chair, and the ball will be passed from one man to another in clockwise manner. In first step, the ball goes to $1$ marked chair with $1^1$ turn. In second step, from there, the ball goes to $5$ marked chair with $2^2$ turns. In third step, the ball goes to $2$ marked chair by $3^3$ turns from $5$ marked chair. By this means, in which chair the ball will be in $2018^{th}$ step?
Problem 6.
$x$ is a positive integer such that its digits can only be $3,4,5,6$. $x$ contains at least one copy of each of these four digits. The sum of the digits of $x$ is $900$ and the sum of the digits of $2x$ is also $900$. How many digits are there in the minimum value of $x$?
Problem 7
$abc$ and $cba$ are two three-digit numbers such that, their sum is divisible by . (Here $a\neq c$, ). Find the remainder when the number $c1b2a$ is divided by $9$ . ($1,b,2,a,c$ are individual digits of the number)
Problem 8.
$AC$ is the inner bisector of $\angle{DAB}$.$DP$ is the tangent .$DP=15$.$CD$ can be expressed as $\dfrac{15\sqrt a}{\sqrt b}$.$AD=12$,$AB=14$ and $a,b$ are co-prime.$a+b=$?
Problem 9
$1+2^{4-3m^2-n^2}=2^{k+4-4m^2}+2^{n^2+k-m^2}$
Here, $m,n$ are positive integers. $k$ is an odd integer and $0<k<95$. How many values of $k$ are there for each of which there are two solution pairs$(m,n)$?
Problem 10.
$A={1,2,3,... ... ... ,2014,2015,2016}$
S is a set whose elements are the subset of A such that one element of S cannot be a subset of another element. Let, S has maximum possible number of elements. In this case, what is the number of elements of S?
Mymensingh secondary 2017 Problemset
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.