List of top Questions asked in GATE CH

The value of $ (1 + i)^{12} $, where $ i = \sqrt{-1} $, is

Given matrix $ A = \left[\begin{matrix} x & 1 & 3 \\ y & 2 & 6 \\ 3 & 5 & 7 \end{matrix}\right] $, the ordered pair $ (x, y) $ for which $ \text{det}(A) = 0 $ is

Let $ f(x) = e^{-|x|} $, where $ x $ is real. The value of $ \dfrac{df}{dx} \text{ at } x = -1 \text{ is} $

The value of the real variable $ x \geq 0 $, which maximizes the function $ f(x) = x e^x e^{-x} $ is

For a single component system at vapor-liquid equilibrium, the extensive variables A, V, S and N denote the Helmholtz free energy, volume, entropy, and number of moles, respectively, in a given phase. If superscripts $ (\nu) $ and $ (\ell) $ denote the vapor and liquid phase, respectively, the relation that is NOT CORRECT is

Catalytic reforming is commonly used in the petroleum industry to improve fuel quality. The undesirable reaction in the catalytic reforming of naphtha is

A control system on the jacket side of a reactor is shown in the figure. Pressurized water flows through the jacket to cool the reactor. The heated water flashes in the boiler. The exothermic reaction heat thus generates steam. Fresh boiler feed water (BFW) is added to make-up for the loss of water as steam. Assume that all control valves are air-to-open. The controller action, 'direct' or 'reverse', is defined with respect to the controller. Select the option that correctly specifies the action of the controllers.

Liquid flowing through a heat exchanger (HX) is heated. A bypass stream is provided to control the temperature of the heated exit stream. From the given plumbing options, the one that provides the most effective temperature control for large disturbances while avoiding vaporization in the heat exchanger is

The appropriate feedforward compensator, $G_{ff}$, in the shown block diagram is

Choose the option that correctly pairs the given measurement devices with the quantities they measure.
\[ \begin{array}{c c c c} \underline{S\ No} & \underline{\text{Measurement Device}} & \underline{S\ No} & \underline{\text{Measured Quantity}} \\ \text{I} & \text{Bourdon Gauge} & \text{A} & \text{Temperature} \\ \text{II} & \text{Orifice Plate meter} & \text{B} & \text{Concentration} \\ \text{III} & \text{Pyrometer} & \text{C} & \text{Pressure} \\ \text{IV} & \text{Colorimeter} & \text{D} & \text{Flow rate} \\ \text{V} & \text{Pirani Gauge} & \text{E} & \text{Liquid level} \\ \end{array} \]

A simple distillation column is designed to separate an ideal binary mixture to specified distillate and bottoms purities at a given column pressure. If RR$_{\min}$ is the minimum reflux ratio for this separation, select the statement that is NOT CORRECT with regard to the variation in the total annualized cost (TAC) of the column with reflux ratio (RR).

In an enzymatic reaction, an inhibitor (I) competes with the substrate (S) to bind with the enzyme (E), thereby reducing the rate of product (P) formation. The competitive inhibition follows the reaction mechanism shown below. Let [S] and [I] be the concentration of S and I, respectively, and $r_s$ be the rate of consumption of S. Assuming pseudo-steady state, the correct plot of $\frac{1}{-r_s}$ vs $\frac{1}{[S]}$ is

The area of a circular field is 25 m$^2$. The radius, r, is to be determined using the Newton-Raphson iterative method. For an initial guess of r = 2.500 m, the revised estimate of r after one iteration is $\underline{\hspace{2cm}}$ m (rounded off to three decimal places).

5 moles of liquid benzene, 8 moles of liquid toluene and 7 moles of liquid xylene are mixed at 25$^\circ$C and 1 bar. Assuming the formation of an ideal solution and using the universal gas constant $R = 8.314$ J mol$^{-1}$ K$^{-1}$, the total entropy change is $\underline{\hspace{2cm}}$ J K$^{-1}$ (rounded off to one decimal place).

A perfectly insulated double pipe heat exchanger is operating at steady state. Saturated steam enters the inner pipe at 100 °C and leaves as saturated water at 100 °C. Cooling water enters the outer pipe at 75 °C and exits at 95 °C. The overall heat transfer coefficient is 1 kW m$^{-2}$ K$^{-1}$ and the heat transfer area is 1 m$^{2}$. The average specific heat capacity of water is 4.2 kJ kg$^{-1}$ K$^{-1}$. The required cooling water flow rate is $\underline{\hspace{2cm}}$ kg s$^{-1}$ (rounded off to two decimal places).

Consider steady-state diffusion in a binary A-B liquid at constant temperature and pressure. The mole-fraction of A at two different locations is 0.8 and 0.1. Let $N_{A1}$ be the diffusive flux of A calculated assuming B to be non-diffusing, and $N_{A2}$ be the diffusive flux of A calculated assuming equimolar counter-diffusion. The quantity $\frac{(N_{A1} - N_{A2})}{N_{A1}} \times 100$ is $\underline{\hspace{2cm}}$ (rounded off to one decimal place).

Consider interphase mass transfer of a species S between two immiscible liquids A and B. The interfacial mass transfer coefficient of S in liquid A is twice of that in liquid B. The equilibrium distribution of S between the liquids is given by $y_S^A = 0.5 y_S^B$, where $y_S^A$ and $y_S^B$ are the mole-fractions of S in A and B, respectively. The bulk phase mole-fraction of S in A and B is 0.10 and 0.02, respectively. If the steady-state flux of S is estimated to be 10 kmol h$^{-1}$ m$^{-2}$, the mass transfer coefficient of S in A is $\underline{\hspace{2cm}}$ kmol h$^{-1}$ m$^{-2}$ (rounded off to one decimal place).

A wet solid containing 20% (w/w) moisture (based on mass of bone-dry solid) is dried in a tray-dryer. The critical moisture content of the solid is 10% (w/w). The drying rate (kg m$^{-2}$ s$^{-1}$) is constant for the first 4 hours, and then decreases linearly to half the initial value in the next 1 hour. At the end of 5 hours of drying, the percentage moisture content of the solid is $\underline{\hspace{2cm}}$ % (w/w) (rounded off to one decimal place).

A compressor with a life of 10 years costs Rs 10 lakhs. Its yearly operating cost is Rs 0.5 lakh. If the annual compound interest rate is 8%, the amount needed at present to fund perpetual operation of the compressor is Rs $\underline{\hspace{2cm}}$ lakhs (rounded to first decimal place).

Consider a bare long copper wire of 1 mm diameter. Its surface temperature is $T_s$ and the ambient temperature is $T_a$ ($T_s > T_a$). The wire is to be coated with a 2 mm thick insulation. The convective heat transfer coefficient is 20 W m$^{-2}$ K$^{-1}$. Assume that $T_s$ and $T_a$ remain unchanged. To reduce heat loss from the wire, the maximum allowed thermal conductivity of the insulating material, in W m$^{-1}$ K$^{-1}$, rounded off to two decimal places, is

N moles of an ideal gas undergo a two-step process as shown in the figure. Let $ P, V, T $ denote the pressure, volume and temperature of the gas. The gas, initially at state-1 $ (P_1, V_1, T_1) $, undergoes an isochoric (constant volume) process to reach state-A, and then undergoes an isobaric (constant pressure) expansion to reach state-2 $ (P_2, V_2, T_2) $. For an ideal gas, $ C_P - C_V = NR $, where $ C_P $ and $ C_V $ are heat capacities at constant pressure and volume. The heat gained by the gas in the two-step process is given by

A horizontal cylindrical water jet of diameter $D_1 = 2 \text{ cm}$ strikes a vertical solid plate with a hole of diameter $D_2 = 1 \text{ cm}$, as shown in the figure. A part of the jet passes through the hole and the rest is deflected along the plate. The density of water is $1000\ \text{kg m}^{-3}$. If the jet speed is $20\ \text{m s}^{-1}$, the magnitude of the horizontal force required to hold the plate stationary is

Consider a horizontal rod of radius $aR$ ($a < 1$) in a stationary pipe of radius $R$. The rod is pulled coaxially at a constant velocity $V$ as shown in the figure. The annular region is filled with a Newtonian incompressible fluid of viscosity $\mu$. The steady–state fully–developed axial velocity profile in the fluid is \[ u(r) = V\frac{\ln(r/R)}{\ln(a)}, \] where $r$ is the radial coordinate. Ignoring end effects, the magnitude of the pulling force per unit rod length is

Match the product in Group-1 with the manufacturing process in Group-2. The correct combination is

The directional derivative of $f(x,y,z)=4x^{2}+2y^{2}+z^{2}$ at the point (1,1,1) in the direction of the vector $\vec{v}=\hat{i}-\hat{k}$ is $\underline{\hspace{2cm}}$ (rounded off to two decimal places).