Recent questions tagged cmi2024-datascience-part-b

 Each round of a TV game show consists of ten questions. Before each round the host takes ten boxes and places prizes in nine of them, leaving one empty. The host then sh...

Find values of $x$ and $y$ that satisfy both the following equations:\[\begin{aligned}\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}} & =\frac{5}{2} \\\frac{x}{\sqrt{y}}+\frac{y}{\...

Let $F$ be the set of points on the plane with coordinates $(x, y)$ such that $\| x|-|y||+|x|+|y|=4$. What is the number of points in $F$ with integer coordinates?

Let $\alpha$ be a fixed real number and let $f$ be a function from $\mathbb{R}^{2}$ to $\mathbb{R}^{2}$ defined as\[f(x, y)=(x \cos \alpha-y \sin \alpha, x \sin \alpha+y ...

"I've defeated more than $10$ FIDE masters," a chess player boasted. "Surely, it must be fewer than $10$," said the referee. "Well, I suppose it was at least one," said t...

In a farmer's stable three animals, a donkey, a cow and a horse had to share two types of feed bags, one containing hay and the other containing grain, as follows:If the ...

There are $7$ elevators in a large shopping mall, each stopping at ground floor and at most six other floors. If at least $3$ elevators stop at each floor and if it is po...

Consider the following expression\[\sqrt{x+2 \sqrt{x-1}}+\sqrt{x-2 \sqrt{x-1}}\]Find two real numbers $a, b$ such that the above expression is constant for $a \leq x \leq...

Does there exist a polynomial $q(x)$ with integer coefficients such that $q(1)=2$ and $q(3)=5$ ? Given an example if there is one. Justify, if there is not.

Find the number of all $4$-digit natural numbers formed with exactly two distinct digits.

In June $2017$, a cyberattack named NotPetya spread all over the world. Big companies like Marex, Merck, and FedEx's TNT Express lost a lot of money because of this attac...