PRACTICE QUESTIONS COMPETITION WING

If $\sqrt[3]{x}+\frac{1}{\sqrt[3]{x}}=\frac{325}{18}$, then find the value(s) of $x$?

In an Atlas, a map occupies $\frac{1}{5}th$ of a page with dimensions $25 cm and 30 cm$, respectively. If the real area of the map is $194,400 m^2$, then the scale to which the map is drawn is_____

The volume of a spherical ball is given by the formula $V=\frac{4}{3}{\mathrm{\pi r}}^3$, where $V$ is the volume and $r$ is the radius. Find the diameter of the sphere whose volume is $\frac{117128}{21} m^3$

If $a$ is any natural number, then $a^3-\frac{1}{a^3}$ will always be greater than or equal to _____

In a four-digit perfect cube number $5a3b, a>b$ and $a=b^3$. Then the difference between the number and its cube root is _____

In a school, there are as many children in each room as thrice the number of rooms in the school. For a charity, each child contributed an average amount of $₹5\frac{1}{3}$. If the total money contributed was $₹25,600$, then find the number of children in each room of the school.

Find how many three-digit perfect cubes are there whose sum of the digits is a perfect square.

If $x and y$ are whole numbers such that $y^x=19,683$ and $y>x$ and $1<x<4$, then $\sqrt[x]{y}$ is _____