Problem 1 .

The sum of the age of Nonte and Fonte is $25$ and the sum of the age of Nut and Boltu is $40$ . If Nut is at least $2$ years elder than Nonte then Boltu is at least how many years elder then Fonte?

Problem 2

The product of the digits of a $3$ digit number is also a three digit number . Find the smallest number having this properties.

Problem 3

In triangle $ABC$ , $H$ is orthocenter . $CD$ is perpendicular to $AB$ . The midpoint of $AH$ is $M$ and the midpoint of $BC$ is $N$ . Find the value of $\angle {MND}$.

Problem 4

$9^x-3^{x+1}=k$ this equation has one or more real roots . Then the values of $k$ can be write as $[c,b)$ . Find $c$.

Problem 5

Two points $D$ and $E$ are taken inside the triangle $ABC$ such as$\angle{ABD}=\angle{EBC}$ From the point $D$ two perpendicular lines $DF$ and $DG$ are drawn to $AB$ and $BC$ respectively . From the point E two perpendicular lines $EH$ and $EI$ are drawn to $AB$ and $BC$ respectively .$ DF=8,DG=9,EI=17, EH=$?

Problem 6

Infinity Roy made an stadium with infinite number of seats. Where all the seats are numbered as $1,2,3………$ For a special guest stadium committee take the decision to transfer the spectators from $n^{th}$ numbered seat to $n+1^{th}$ numbered seat For this they refund him{$\dfrac{1}{n}-\dfrac{1}{n+1}$ } tk . How many taka stadium committee needs to transfer seat by this process?

Problem 7

Sneha has some chocolates. Each day she divides the chocolate in two equal halves. Then she eats one half and remains another half for the next day. If she can not divide in tow equal halves the she gives one chocolate to her cat. At the $11^{th}$ day all the chocolate has over and she gave chocolate to her cat in first two days and the $5^{th}$ days. How many chocolates she had?

Problem 8

$ABCD$ is a trapezium with $AB\parallel CD$ and $\angle{ADC}=90^{\circ}$ . $E$ is a point on $CD$ that $BE\perp CD$. $F$ is a point on the extension of $CB$ that $DF\perp CF$.$DF$ and $EB$ intersects at the point $K$.$\angle {EAB}=47^{\circ}$,then$\angle {KCE}=$?

Problem 9

For a function $f:R\rightarrow R,f(xy+1)=f(x)f(y)-f(y)-x+2$ and $f(0)=1$

$f(2013)+f(2012)=$?

Problem 10

The elements of a set $S$ is those set that the $LCM$ of them is $12$ .Such as ${1,2}$ and ${4,6}$ are two elements of set $S$. Find the number of total elements of set $S$.

## Mymensingh higher secondary 2013 Problemset

**Forum rules**

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.

- samiul_samin
**Posts:**999**Joined:**Sat Dec 09, 2017 1:32 pm