Mymensingh secondary 2017 Problemset

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samiul_samin
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Mymensingh secondary 2017 Problemset

Unread post by samiul_samin » Sun Feb 17, 2019 7:50 pm

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 $PQRS$.
Screenshot_2019-02-17-15-19-37-2.png

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 $HIG$?
Screenshot_2019-02-17-15-19-37-1.png
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.
Screenshot_2019-02-17-15-13-15-3.png
$AC$ 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?

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