Consider the differential equation given below. Using the Euler method with the step size (h) of 0.5 , the value of $y$ at $x=1.0$ is equal to _________ (rounded off to 1 decimal place).

$$ \frac{d y}{d x}=y+2 x-x^2 ; y(0)=1 \quad(0 \leq x<\infty) $$

A one-way, single lane road has traffic that consists of $30 \%$ trucks and $70 \%$ cars. The speed of trucks (in km/h) is a uniform random variable on the interval ( 30,60 ), and the speed of cars (in km/h) is a uniform random variable on the interval $(40,80)$. The speed limit on the road is $50 \mathrm{~km} / \mathrm{h}$. The percentage of vehicles that exceed the speed limit is ________ (rounded off to 1 decimal place).

Note: $X$ is a uniform random variable on the interval ( $\alpha, \beta$ ), if its probability density function is given by

$$ f(x)= \begin{cases}\frac{1}{\beta-\alpha} & \alpha < x < \beta \\ 0 & \text { otherwise }\end{cases} $$

Fecal Coliform (FC) concentration in river water was measured as 10780 cfu/100 ml. The FC concentration after the conventional water treatment, but before chlorination, was measured as $23 \mathrm{cfu} / 100 \mathrm{ml}$. The 'Log Kill' (inactivation) of FC due to the conventional water treatment is closest to

A hydrocarbon $\left(\mathrm{C}_n \mathrm{H}_m\right)$ is burnt in air $\left(\mathrm{O}_2+3.78 \mathrm{~N}_2\right)$. The stoichiometric fuel to air mass ratio for this process is

Note: Atomic Weight: $\mathrm{C}(12), \mathrm{H}(1)$

Effective Molecular Weight: Air(28.8)

Ignore any conversion of N 2 in air to the oxides of nitrogen $\left(\mathrm{NO}_{\mathrm{x}}\right)$