List of top Mathematics Questions on general and middle terms asked in MET

The coefficient of the middle term in the binomial expansion in powers of \( x \) of \( (1 + \alpha x)^4 \) and \( (1 - \alpha x)^6 \) is the same, if \( \alpha \) is equal to

The middle term of \(\left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)^6\) is

The term independent of \( x \) in the expansion of \( \left( 2x^4 - \frac{1}{x^2} \right)^{12} \) is

The middle term in the expansion of \( \left(x - \frac{1}{2y}\right)^{10} \) is

If the term free from \( x \) in the expansion of \( \left(\sqrt{x} - \frac{k}{x^2}\right)^{10} \) is 405, then the value of \( k \) is

Middle term in the expansion of $\left(x^2 + \frac{1}{x^2} + 2\right)^n$ is

The term independent of \( x \) in the expansion of \( \left(x + \frac{1}{x}\right)^{2n} \) is: