Suppose Elina bought a pen at $10$ taka. She then sold it to Himu at $20$. Himu then sold it to Rifat at $40$ taka. Rifat again sold it to Elina at $80$ taka. How much profit Himu will get?
Problem 2.
A triangle is inscribed in a circle with radius of $6$ units such a way that one side of the triangle becomes the diameter of the circle. What is the maximum area of thetriangle?
Problem 3.
In the picture, gear $1$ has $8$ teeth, gear $2$ has $24$ teeth, and gear $3$ has $16$ teeth. If gear $1$ rotates $24$ times, how many times will gear $3$ rotate?
Problem 4
Let $S=1^1+2^2+3^3+4^4+...+2016^{2016}$.
What is the remainder when $S$ is divided by $2$?
Problem 5
How many divisors of $2016$ is not a mutiple of $7$?
Problem 6
What is the lowest value of $(x^2-8x)(x^2-8x+10)$?
Problem 7.
In the planet 'hoyto' every question has three answers.Yes,No or May be.In the planet 'Shokto' every question has two answers. Yes or No. If you ask $2018$ questions, what is the difference between number of all possible way of answering?
Problem 8.
Two integers will be taken from $1$ to $100$, where at least one of them should be a square number and sum of them should also be a square number. How many different pair like this can be found?
Problem 9.
In triangle $ABC$,$\angle ABC=90^{\circ}$, $D$ is the midpoint of line $BC$. Point $P$ is on $AD$ line. $PM$ & $PN$ are respectively perpendicular on $AB$ & $AC$. $PM = 2PN$, $AB = 5$, $BC =a\sqrt b$ , where $a, b$ are positive integers. $a-b=$?
Problem 10
There are $20$ boxes on a table.There are $2$ balls in the $1$st box,$3$ balls in the $2$nd box,$4$ balls in the $3$rd box,.........,$21$ balls in the $20$th box.Bijoy wants to pick $2$ balls from any particular box. In how many ways he can do this work?
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