1
GATE CE 2010
+1
-0.3
The partial differential equation that can be formed from $$z=ax+by+ab$$ has the form $$\,\,\left( {p = {{\partial z} \over {\partial x}},q = {{\partial z} \over {\partial y}}} \right)\,\,$$
A
$$z=px+qy$$
B
$$z=px-qy$$
C
$$z=px+qy+pq$$
D
$$z=qy+pq$$
2
GATE CE 2010
+2
-0.6
The table below gives values of a function $$f(x)$$ obtained for values of $$x$$ at intervals of $$0.25$$

The value of the integral of the function between the limits $$0$$ to $$1,$$ using Simpson's rule is

A
$$0.7854$$
B
$$2.3562$$
C
$$3.1416$$
D
$$7.5000$$
3
GATE CE 2010
+1
-0.3
The modulus of the complex number $${{3 + 4\,i} \over {1 - 2\,i}}$$ is
A
$$5$$
B
$$\sqrt 5$$
C
$${1 \over {\sqrt 5 }}$$
D
$${1 \over 5}$$
4
GATE CE 2010
+2
-0.6
Ion concentrations obtained for a groundwater sample (having pH=8.1) are given below.
Ion $$Ca^{2+}$$ $$Mg^{2+}$$ $$Na^+$$ $$HCO_3^-$$ $$SO_4^{2-}$$ $$Cl^{-}$$
Ionconcentration(mg/L) 100 6 15 250 45 39
Atomic Weight Ca=40 Mg=24 Na=23 H=1,C=12,O=16 S=32,O=16 Cl=35.5

Total hardness (mg/L as $$CaCO_3$$) present in the above water sample is
A
205
B
250
C
275
D
308
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