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A cube of side length $a=10$ and a sphere of radius $R = 7.5$ have the same center. Find the volume of the sphere that lies …

Brilly the ant stands at point $A$, in a distance of $25$ cm from a cylindrical glass beaker. At point C inside the far side of the beaker and $6$ …

Above figure consists of $\color{#3D99F6}{\infty \text{ circles}}$ inscribed in an $\color{#3D99F6}{\text{Equilateral Triangle}}$ in a pattern as shown above. Let $\color{#3D99F6}{\text{Area of Infinite circles} = A_1}$$(\text{dotted region})$ and ...

$S(k)= \sum_{n=1}^\infty \dfrac{n^k}{e^{2\pi n}-1}$

Define $S(k)$ as above, find $\dfrac{1}{S(5)}+\dfrac{1}{S(9)}+\dfrac{1}{S(13)}$.

The function $f$ defined by $f(x)= \frac{ax+b}{cx+d}$, where $a$,$b$,$c$ and $d$ are nonzero real numbers, has the properties $f(19)=19$, $f(97)=97$ and $f(f(x))=x$ for all values except $\frac{-d}{c}$. Find the unique …

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