Recent questions tagged descriptive

Let $M$ be an $n \times n$ matrix. We define an elementary row operation on $M$ to be one of the following:Interchanging some two rows of $M$.Multiplying a row in $M$ by ...

There are $18$ chocolates in a bag, of which $7$ are green, $6$ are blue, and $5$ are red. We pick chocolates one at a time from the bag without replacement.What is the p...

$15$ balls are placed independently and uniformly at random into $15$ bins numbered from $1$ to $15.$ The probability that a ball ends up in a particular bin is $\frac{1}...

A toy company currently sells $1,000$ toys each month at a price of ₹$500$ per toy. To increase their sales, the company is considering to lower the price. Market researc...

The snakes and ladders game is played on a board with $100$ squares, numbered $1$ to $100.$ There are some ladders and some snakes. Each ladder stands on some square and ...

The snakes and ladders game is played on a board with $100$ squares, numbered $1$ to $100.$ There are some ladders and some snakes. Each ladder stands on some square and ...

We have an array $A$ of $n$ numbers, where $n$ is a power of $2$.We build a full binary tree on top of the array $A.$ The elements of the array are leaves of the tree, nu...

We have an array $A$ of $n$ numbers, where $n$ is a power of $2$.We build a full binary tree on top of the array $A.$ The elements of the array are leaves of the tree, nu...

Let $S$ be a nonempty set and $P$ the set of all subsets of $S$. Let $f: P \rightarrow P$ be a function satisfying the following property: if $X \subseteq Y$, then $f(X) ...

Consider the language $L=\left\{1^{x} O^{y} 1^{z} \mid x>0, y \geqslant 0, z>0\right\}$ over the alphabet $\Sigma=\{0,1\}.$ Construct a $3$-state $\text{NFA }$ for $L$ an...

A toy company currently sells $1,000$ toys each month at a price of ₹$500$ per toy. To increase their sales, the company is considering to lower the price. Market researc...

$15$ balls are placed independently and uniformly at random into $15$ bins numbered from $1$ to $15.$ The probability that a ball ends up in a particular bin is $\frac{1}...

There are $18$ chocolates in a bag, of which $7$ are green, $6$ are blue, and $5$ are red. We pick chocolates one at a time from the bag without replacement.What is the p...

Let $M$ be an $n \times n$ matrix. We define an elementary row operation on $M$ to be one of the following:Interchanging some two rows of $M$.Multiplying a row in $M$ by ...

Three hostel friends Amar, Prem and Raj are suspected of breaking a window. They made the following statements when questioned by the warden:$\text{Amar:}$ $\textit {I di...

A cloth bag labeled $X$ contains two apples, bag $Y$ contains two oranges and bag $Z$ one apple and one orange. You pick a bag at random and then remove one fruit from th...

Five executives of a company namely $\text {CEO}$ (chief executive officer), $\text {CFO}$ (chief financial officer), $\text {COO}$ (chief operating officer), $\text {CTO...

Evaluate the following limit:$$ \lim _{x \rightarrow 0} \frac{e^{2 x}-2 x-\cos x}{x \sin x} $$

Find the determinant of the following matrix:$$ A=\left[\begin{array}{cccc}1 & 1 & 4 & 3 \\5 & 8 & 26 & 21 \\2 & 3 & 10 & 8 \\3 & 5 & 16 & 13\end{array}\right]$$

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function which is twice differentiable everywhere and suppose that $f^{\prime}(q)=0$ for every rational number $q.$ Find t...

Consider the following $2 \times 2$ matrix$$ B=\left[\begin{array}{cc}0 & r \\-1 & 0\end{array}\right],$$where $r$ is a nonzero real number. Find $B^{2025},$ i.e., the ma...

Read the following description carefully and answer the questions that follow. Use all the information provided. Clearly show all your calculations.Description:NorthCool ...

Construct a finite automaton for the language $L$ consisting of all binary strings with equal number of occurrences of $01$ and $10$.

We have an array $A$ of $n$ numbers, where $n$ is a power of $2$.We build a full binary tree on top of the array $A.$ The elements of the array are leaves of the tree, nu...

The snakes and ladders game is played on a board with $100$ squares, numbered $1$ to $100.$ There are some ladders and some snakes. Each ladder stands on some square and ...