List of top Mathematics Questions asked in AP EAMCET

$\lim_{n \to\infty} n^{-nk} \left\{\left(n+1\right) \left(n+ \frac{1}{2}\right) \left(n + \frac{1}{2^{2}}\right) ...\left(n + \frac{1}{2^{k-1}}\right)\right\}^{n} = $
Let $z = x + iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z - 1}{z + i}$ is 1. then a point that lies on the locus of $P$ is
If $z_{1} = 1 -2i ; z_{2} = 1 + i$ and $z_{3 } = 3 + 4i,$ then $ \left( \frac{1}{z_{1}} + \frac{3}{z_{2}}\right) \frac{z_{3}}{z_{2}} = $
If $1 , \omega , \omega^2$ are the cube roots of unity, then $\frac{1}{1+2\omega} + \frac{1}{2+\omega } - \frac{1}{1+\omega } = $
If A and B are the two real values of k for which the system of equations $x + 2y + z = 1,x + 3y + 4r = k.x + 5v + 10z = k^2 $ is consistent, then $A + B = $
The number of rational terms in the binomial expansion of $\left(\sqrt[4]{5} + \sqrt[5]{4}\right)^{100} $ is
If a circle touches the lines $3x - 4y - 10 = 0$ and $3x - 4y + 30 = 0$ and its centre lies on the line $x + 2y = 0$ then the equation of the equation of the circle is