RK JHA Solutions for Chapter: Data Interpretation and Quantitative Ability, Exercise 18: Crack XAT 3

If $x \& y$ are natural numbers such that ${\left(\frac{1}{x}\right)}^{\frac{1}{y}}=0.\overline{3}$, then the value of $xy$ is _____

The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius $r \mathrm{cm}$ is _____.

A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of second square is -

The cost of fencing an equilateral triangular park and a square park is the same. If the area of the triangular park is $16\sqrt{3}{ \mathrm{m}}^2$, the length of the diagonal of the square park is:

A closed aquarium of dimensions $30 \mathrm{cm}\times 25 \mathrm{cm}\times 20 \mathrm{cm}$ is made up entirely of glass plates held together with tapes. The total length of tape required to hold the plates together (ignore the overlapping tapes) is: 

Three boys are standing on a circular boundary of a fountain. They are at an equal distance from each other. If the radius of the boundary is $5 \mathrm{m}$, the shortest distance between any two boys is:

Rita and Meeta both are having lunch boxes of cuboidal shape. The length and breadth of Rita's lunch box are $10\%$ more than that of Meeta's lunch box, but the depth of Rita's lunch box is $20\%$ less than that of Meeta's lunch box. The ratio of the capacity of Rita's lunch box to that of Meeta's lunch box is:

The sum of digits of a natural number $\left({10}^n-1\right)$ is $4707$, where $n$ is a natural number. The value of $n$ is ____