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We have a triangular uniformly charged plate of charge density \(\sigma\).

We take a point just above a vertex of the triangular plate at a distance \(d\) perpendicular to the ...

\[\large \lim_{n \to \infty} \left(\frac{\binom{3n}{n} }{\binom{2n}{n} }\right) ^{\frac{1}{n}} = \frac{a}{b} \]

The equation above holds true for coprime integers \(a\) and ...

Say we have the following compound

\[\ce{(Si7O17)(OH)4K2Fe^{II}_{x}Fe^{III}_{y}}\]

Now take the value of \(x \times y\).

Which of these is/are ...

A massive circular ring of unit radius is centered on the origin within the \(xy\) plane. The ring parameters and mass density are given below:

...

\[\large \displaystyle \int_{-\pi}^{\pi} \dfrac{1}{3 \cos^2 x + 1} \,dx \]

Evaluate the integral above up to 2 places of decimal.

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