1
GATE CE 2025 Set 1
Numerical
+2
-0

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

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

Your input ____
2
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33

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
4.00
B
2.50
C
2.67
D
3.00
3
GATE CE 2025 Set 1
MCQ (Single Correct Answer)
+1
-0.33

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 $\left(\mathrm{NO}_{\mathrm{x}}\right)$

A
$0.0291 \frac{(4 n+m)}{(12 n+m)}$
B
$34.42 \frac{(12 n+m)}{(4 n+m)}$
C
$34.42 \frac{(4 n+m)}{(12 n+m)}$
D
$0.0291 \frac{(12 n+m)}{(4 n+m)}$
4
GATE CE 2025 Set 1
MCQ (More than One Correct Answer)
+1
-0
The Surface Overflow Rate (SOR) in a rectangular sedimentation tank is $45 \mathrm{~m}^3 / \mathrm{m}^2 / \mathrm{d}$. Minimum diameters of spherical inorganic and organic particles expected to be completely removed in this tank are calculated. Assume that Stoke's law is applicable. Which of the following options is/are correct: Specific gravity of inorganic particles $=2.65$ Specific gravity of organic particles $=1.20$ Acceleration due to gravity $(\mathrm{g})=9.81 \mathrm{~m} / \mathrm{s}^2$ Kinematic viscosity $(v)=1 \times 10^{-6} \mathrm{~m}^2 / \mathrm{s}$
A
Minimum diameter of inorganic particles is $24 \mu \mathrm{~m}$
B
Minimum diameter of organic particles is $69 \mu \mathrm{~m}$
C
Minimum diameter of inorganic particles is $15 \mu \mathrm{~m}$
D
Minimum diameter of organic particles is $55 \mu \mathrm{~m}$
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