List of top Mathematics Questions on sequences asked in BITSAT

The coefficient of \(x^3\) in the expansion of
\[ \left(x - \frac{1}{x}\right)^7 \]
is:
The value of \[ \frac34+\frac{15}{16}+\frac{63}{64}+\cdots \text{ up to } n \text{ terms is} \]
If arithmetic means are inserted between 1 and 31 so that the ratio of the 7th and (m-1)th means is 5:9, then find the value of m.