Comments by Kiyoshi

Consider a square sheet of side $1$ unit. The sheet is first folded along the main diagonal. This is followed by a fold along its line of symmetry. The resulting folded s...

The product of three integers $X$, $Y$ and $Z$ is $192$. $Z$ is equal to $4$ and $P$ is equal to the average of $X$ and $Y$. What is the minimum possible value of $P$?$6$...

The value of the expression $\dfrac{1}{1+ \log_u \: vw} + \dfrac{1}{1+ \log_v \: wu} + \dfrac{1}{1+\log_w uv}$ is _______$-1$$0$$1$$3$

In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature $10^{\circ} C$) and a...

In the graph below, the concentration of a particular pollutant in a lake is plotted over (alternate) days of a month in winter (average temperature $10^{\circ} C$) and a...

Let $S_{1}$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x - 1 \mid \leq 2$ and $ \mid y+2 \mid \leq 3$. Let $S_{2}$ be the plan...

A right-angled cone (with base radius $5$ cm and height $12$ cm), as shown in the figure below, is rolled on the ground keeping the point $P$ fixed until the point $Q$ (a...

Which of the following curves represents the function $ln(|e^{[|\sin(|x|)]}|)$ for $\mid x\mid< 2\pi$? Here, $x$ represents the abscissa and $y$ represents the ordinate.

Five teams have to compete in a league, with every team playing every other team exactly once, before going to the next round. How many matches will have to held to compl...

$M$ and $N$ had four children $P$, $Q$, $R$ and $S$. Of them, only $P$ and $R$ were married. They had children $X$ and $Y$ respectively. If $Y$ is a legitimate child of $...

Ms. $X$ came out of a building through its front door to find her shadow due to the morning sun failing to her right side with the building to her back. From this, it can...