List of practice Questions

The sum of the components of the force due to pressure and shear at the solid-fluid boundary of a solid body in the direction normal to the flow is:

In industrial heat exchanger design, the overall heat transfer coefficient $ U $ is estimated from the equation: \[ \frac{1}{U} = \frac{1}{h_i} + \frac{1}{h_o} \] where $ h_i $ and $ h_o $ are the convective heat transfer coefficients on the inner and outer side of the tube, respectively. This is valid for (i) tube of (ii) thermal conductivity.
Which one of the following is the CORRECT option to fill in the gaps (i) and (ii)?

The boundary of a system does not allow exchange of either mass or energy (in the form of heat and/or work) with the surroundings. The system is termed

A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is

Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors $\hat{i}, \hat{j}$, and $\hat{k}$. Let vector $\mathbf{a} = \sqrt{2}\hat{i} + \frac{1}{\sqrt{2}}\hat{k}$, and vector $\mathbf{b} = \frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j} - \hat{k}$. The inner product of these vectors ($\mathbf{a} \cdot \mathbf{b}$) is:

To manufacture paper from ______(i) _______, the ________ (ii) _______ must be freed from the binding matrix of ________(iii) ________ in the pulping step. Which one of the following is the CORRECT option to fill in the gaps (i), (ii) and (iii)?

The block diagram of a series cascade control system (with time in minutes) is shown in the figure. For $ \tau_1 = 8 $ min and $ K_s^c = 1 $, the maximum value of $ K_m^c $, below which the cascade control system is stable, is \_\_\_\_ (rounded off to the nearest integer).
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A zero-order gas phase reaction $A \to B$ with rate $(-r_A) = k = 100$ mol/(L min) is carried out in a mixed flow reactor of volume 1 L. Pure $A$ is fed to the reactor at a rate of 1 mol/min. At time $t = 0$, the outlet flow is stopped while the inlet flow rate and reactor temperature remain unchanged. Assume that the reactor was operating under steady state before the flow was stopped ($t<0$). The rate of consumption of $A$, $-\frac{dC_A}{dt}$, in mol/(L min), at $t = 1$ min is:

Consider a Cartesian coordinate system with orthogonal unit basis vectors $ \hat{i}, \hat{j} $ defined over a domain: $ x, y \in [0,1] $. Choose the condition for which the divergence of the vector field $ \mathbf{v} = ax\hat{i} - by\hat{j} $ is zero.

Choose the CORRECT ordering of the diameter $ d $ of the different types of pores in a solid catalyst.

Consider two complex numbers $ z_1 = 1 - i $ and $ z_2 = i $. The argument of $ z_1z_2 $ is:

Given the equation: $$ 3^{x^2} = 27 \times 9^x $$ Find the value of: $$ \frac{2^{x^2}}{(2^x)^2} $$

The figure shows a circular portion of radius $ \frac{R}{2} $ removed from a disc of mass $ m $ and radius $ R $. The moment of inertia about an axis passing through the centre of mass of the disc and perpendicular to the plane is:

How many dehydrogenation reactions in Krebs cycle?

How many time needed for PCR?

What is the primary function of Bowman’s capsule in nephron?

Disorder caused due to accumulation of amyloid proteins in CNS.

If the square of the shortest distance between the lines $$ \frac{x-2}{1} = \frac{y-1}{2} = \frac{z+3}{-3} \quad \text{and} \quad \frac{x+1}{2} = \frac{y+3}{4} = \frac{z+5}{-5}, $$ is $ \frac{m}{n} $, where $m, n$ are coprime numbers, then $m+n$ is equal to:

A single-stage axial compressor, with a 50 % degree of reaction, runs at a mean blade speed of 250 m/s. The overall pressure ratio developed is 1.3. Inlet pressure and temperature are 1 bar and 300 K, respectively. Axial velocity is 200 m/s. Specific heat at constant pressure, $ C_p = 1005 \, {J/kg/K} $ and specific heat ratio, $ \gamma = 1.4 $. The rotor blade angle at the outlet is __________ degrees (rounded off to two decimal places).

An ideal ramjet with an optimally expanded exhaust is travelling at Mach 3. The ambient temperature and pressure are 260 K and 60 kPa, respectively. The inlet air mass flow rate is 50 kg/s. Exit temperature of the exhaust gases is 700 K. Fuel mass flow rate is negligible compared to air mass flow rate. Gas constant is $ R = 287 \, {J/kg/K} $, and specific heat ratio is $ \gamma = 1.4 $. The thrust generated by the engine is __________ kN (rounded off to one decimal place).

A monopropellant liquid rocket engine has 800 injectors of diameter 4 mm each, and with a discharge coefficient of 0.65. The liquid propellant of density 1000 kg/m³ flows through the injectors. There is a pressure difference of 10 bar across the injectors. The specific impulse of the rocket is 1500 m/s. The thrust generated by the rocket is __________ kN (rounded off to one decimal place).

Air at temperature 300 K is compressed isentropically from a pressure of 1 bar to 10 bar in a compressor. Eighty percent of the compressed air is supplied to a combustor. In the combustor, 0.88 MJ of heat is added per kg of air. The specific heat at constant pressure is $ C_p = 1005 \, {J/kg/K} $ and the specific heat ratio is $ \gamma = 1.4 $. The temperature of the air leaving the combustor is _______ K (rounded off to one decimal place).

An ideal turbofan with a bypass ratio of 5 has core mass flow rate, $ \dot{m}_a,c = 100 \, {kg/s} $. The core and the fan exhausts are separate and optimally expanded. The core exhaust speed is 600 m/s and the fan exhaust speed is 120 m/s. If the fuel mass flow rate is negligible in comparison to $ \dot{m}_a,c $, the static specific thrust ($ \frac{T}{\dot{m}_a,c} $) developed by the engine is _________ Ns/kg (rounded off to the nearest integer).

Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is ________ (rounded off to two decimal places).

A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is ____________ (rounded off to two decimal places).