Consider the following series:

(i) $\sum\limits_{n=1}^{\infty} \frac{1}{\sqrt{n}}$

(ii) $ \sum\limits_{n=1}^{\infty} \frac{1}{n(n+1)}$

(iii) $\sum\limits_{n=1}^{\infty} \frac{1}{n!}$

A pot contains two red balls and two blue balls. Two balls are drawn from this pot randomly without replacement.

What is the probability that the two balls drawn have different colours?

Consider the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined as

$$ f(x)=2 x^3-3 x^2-12 x+1 $$

Which of the following statements is/are correct?

(Here, $\mathbb{R}$ is the set of real numbers.)

The function $y(t)$ satisfies

$$ t^2 y^{\prime \prime}(t)-2 t y^{\prime}(t)+2 y(t)=0 $$

where $y^{\prime}(t)$ and $y^{\prime \prime}(t)$ denote the first and second derivatives of $y(t)$, respectively. Given $y^{\prime}(0)=1$ and $y^{\prime}(1)=-1$, the maximum value of $y(t)$ over $[0,1]$ is ___________ (rounded off to two decimal places).