The equation of a curve passing through $(1,0)$ and having slope of tangent at any point $(x, y)$ of the curve as $\frac{y-1}{x^2+x}$ is

A box contains 8 red and $x$ number of green balls. 3 balls are drawn at random, if the probability that 3 balls being red is $\frac{7}{15}$, then number of green balls is…

The number of ways in which a team of 11 players can be formed out of 25 players, if 6 out of them are always to be included and 5 of them are always to be excluded, is

$$ \mathop {\lim }\limits_{x \to \infty } \frac{(2 x+1)^{50}+(2 x+2)^{50}+(2 x+3)^{50}+\cdots+(2 x+100)^{50}}{(2 x)^{50}+(10)^{50}}= $$