1
GATE CE 2017 Set 2
Numerical
+1
-0
The divergence of the vector field $$\,V = {x^2}i + 2{y^3}j + {z^4}k\,\,$$ at $$x=1, y=2, z=3$$ is ________.
2
GATE CE 2017 Set 2
Numerical
+1
-0
A two-faced fair coin has its faces designated as head $$(H)$$ and tail $$(T)$$. This coin is tossed three times in succession to record the following outcomes: $$H, H,H.$$ If the coin is tossed one more time, the probability (up to one decimal place ) of obtaining $$H$$ again, given the previous realizations of $$H, H$$ and $$H$$, would be _____.
3
GATE CE 2017 Set 2
Numerical
+2
-0
The analysis of a water sample produces the following results: The total hardness (in mg/L as $${\mathrm{CaCO}}_3$$) of the water sample is ______.
4
GATE CE 2017 Set 2
Numerical
+2
-0
The figure shows a U-tube having a 5 mm × 5 mm square cross-section filled with mercury (specific gravity = 13.6) up to a height of 20 cm in each limb (open to the atmosphere). If 5cm3 of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be______

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