List of top Questions asked in GATE CH

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be coloured such that any two corners that are connected by an edge must be of different colours. The minimum number of colours required to achieve this is

For the equipment sizing problem described under the given operating and design conditions, the required diameter of the equipment is ______ mm (rounded off to one decimal place).

In a double pipe cocurrent heat exchanger, operating at steady state, oil (specific heat capacity = \(2100\ \mathrm{J\,kg^{-1}\,^\circ C^{-1}}\)) entering at \(7\ \mathrm{kg\,s^{-1}}\) at \(100^\circ\mathrm{C}\) is used to heat water (specific heat capacity = \(4200\ \mathrm{J\,kg^{-1}\,^\circ C^{-1}}\)) flowing at \(3.5\ \mathrm{kg\,s^{-1}}\) from \(20^\circ\mathrm{C}\) to \(50^\circ\mathrm{C}\). If the overall heat transfer coefficient is \(291\ \mathrm{W\,m^{-2}\,^\circ C^{-1}}\), the required heat transfer area (in \(\mathrm{m^2}\)) is ______ (rounded off to one decimal place).

As shown in the figure, circle C1 with center O1 and radius r1 touches the square VWXY at points P and Q while circle C2 with center O2 and radius r2 touches the square VWXY at points R and S. The two circles touch each other at T.
Given r1 = 1 cm and VY = VW = 4 cm, r2 = cm.

Consider a non-reactive binary mixture of two ideal gases A and B in an isothermal horizontal closed tube. Due to the concentration difference at the two ends of the tube, equimolal counterdiffusion occurs along the axial direction. No concentration gradients exist in the radial direction. The profile for partial pressure of component A (\(p_A\)) as a function of axial distance \(z\) is shown in the figure. The partial pressure of component B (\(p_B\)) approaches zero at \(z = 0.8\) m. At a location \(z = z_1\) the partial pressures of the components A and B are equal. The value of \(z_1\) (in m) is ______ (rounded off to two decimal places).

A school has 100 students distributed among 1st to 10th standards.

Based on this, which one of the following statements is always correct?

A flooding velocity curves for two different structured packings are considered. Under the design operating conditions given for the packed absorption column, the process temperature at which the operation reaches its target condition is ______ K (rounded off to one decimal place).

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to the cubes shown in Panel II, which one of the options is correct?

The flooding velocity curves for two different structured packings are shown in the figure. The ratio of mass velocities of liquid (\(G_x\)) to that of the gas (\(G_y\)) is 1.27. The density of the liquid (\(\rho_x\)) is 1200 kg m^-3 and that of the gas (\(\rho_y\)) is 1.2 kg m^-3. For both the packings, the allowable superficial vapor velocity is 60% of the flooding velocity (\(u_{0,F}\)). The ratio of the allowable mass velocity of the vapor in packing P to that in packing Q is ______ (rounded off to one decimal place).

Which one of the following is the pair of eigenvalues of the matrix \( \begin{bmatrix} -3 & 4 \\ 4 & 3 \end{bmatrix} \)?

Which one of the following ratios does Grashof number represent?

Which one of the following is the value of \( \displaystyle\lim_{x \to 0} \frac{e^{x} - x - 1}{\cos x - 1} \)?

Consider a closed system of one mole of an ideal gas undergoing a polytropic process. The process follows \( PV^n = \text{constant} \), where P is the pressure, V is the volume and n is a constant. If the process is isobaric, which one of the following is the value of n?

The data given in the table are fitted to the equation \(y = mx\) using the method of least squares. The value of \(m\) is ______ (rounded off to one decimal place).

x	1	2	3	4
y	2	6	7	10

Methanol is formed by the following gas phase homogeneous reaction:

\[ \mathrm{CO(g) + 2H_2(g) \rightleftharpoons CH_3OH(g)} \]

The standard Gibbs free energies of formation at \(298\ \mathrm{K}\) for CO and \(\mathrm{CH_3OH}\) are \(-137\ \mathrm{kJ\,mol^{-1}}\) and \(-162\ \mathrm{kJ\,mol^{-1}}\), respectively. The value of the universal gas constant is \(8.314\ \mathrm{J\,mol^{-1}\,K^{-1}}\). The equilibrium constant for the given reaction at \(298\ \mathrm{K}\) is ______ \(\times 10^4\) (rounded off to one decimal place).

For the given heat exchange/power process operating under the stated conditions, the net power requirement of the process is ______ kW (rounded off to one decimal place).

For the given separation process operating under the stated conditions, the percentage recovery of the target component is ______ % (rounded off to one decimal place).

Consider the following curve in polar coordinates.
\[ r = 2 - 2\sin\theta \]
Which one of the following is the area enclosed by the curve for \(0 \le \theta \le 2\pi\)?

Water is discharged from the vertical side of a tank through a circular orifice of diameter 2 cm under laminar flow conditions. The water surface in the tank is maintained at a constant level above the center of the orifice. If the fluid jet has a diameter of 1.6 cm at its vena contracta, then the coefficient of contraction is ______ (rounded off to two decimal places).

Consider two successive screen sizes in the Tyler standard screen scale, viz. 150 meshes per inch and 200 meshes per inch. Their linear sizes of the openings are L150 and L200, respectively. If the value of L200 is \(2.9 \times 10^{-3}\) inch, then the value of L150 (in inch) is \(\times 10^{-3}\) (rounded off to one decimal place).

Consider the following homogeneous isothermal liquid-phase parallel reactions carried out in three reactor configurations (having identical volumes and same operating temperatures), as shown in the figure.
\[ A + B \rightarrow D \qquad \text{Rate of formation of D: } r_D = k_1 C_A C_B \]\[ A + B \rightarrow U \qquad \text{Rate of formation of U: } r_U = k_2 C_A^2 C_B \]
where D is the desired product and U is the undesired product. The inlet concentrations of A and B are the same in all three configurations (\(C_{A0}=C_{B0}=1\ \text{mol L}^{-1}\)). The total molar feed flow rate of A (\(F_{A0}\)) and that of B (\(F_{B0}\)) are the same in all three configurations (\(F_{A0}=F_{B0}=10\ \text{mol min}^{-1}\)). In configuration I, \(F_{A0}\) is equally distributed among all the inlets. Similarly, in configuration III, \(F_{B0}\) is equally distributed among all the inlets. Assuming plug flow behavior, at steady state, which one of the following statements is CORRECT?