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Chemical Engineering (CH) 2017
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The value of lim as x→0 of (tan(x)/x) is ______.
The real part of 6e^(iπ/3) is ______.
The number of positive roots of the function f(x) shown below in the range 0 < x < 6 is ______.

Let i and j be the unit vectors in the x and y directions, respectively. For the function F(x, y) = x3 + y2, the gradient of the function, i.e., ∇F is given by
The marks obtained by a set of students are: 38, 84, 45, 70, 75, 60, 48. The mean and median marks, respectively, are
The volumetric properties of two gases M and N are described by the generalized compressibility chart which expresses the compressibility factor (Z) as a function of reduced pressure and reduced temperature only. The operating pressure (P) and temperature (T) of two gases M and N along with their critical properties (Pn, Tn) are given in the table below.
| Gas | P (bar) | T (K) | Pn (bar) | Tn (K) |
|---|---|---|---|---|
| M | 25 | 300 | 75 | 150 |
| N | 75 | 1000 | 225 | 500 |
Zm and Zn are the compressibility factor of the gases M and N under the given operating conditions, respectively. The relation between Zm and Zn is