List of practice Questions

In a single–spool aviation turbojet engine, which of the following is the correct relationship between the total work output \(W_t\) of a 2-stage axial turbine and the total work required \(W_c\) by a 6-stage axial compressor, neglecting losses?

A two–dimensional potential–flow solution for flow past an airfoil has the streamline pattern shown. Which additional condition is required to satisfy the Kutta condition? \begin{center} \includegraphics[width=0.5\textwidth]{03.jpeg} \end{center}

Consider the Blasius solution for the incompressible laminar flat–plate boundary layer. Among the options, select the correct relation for the development of the momentum thickness \(\theta\) with distance \(x\) from the leading edge along the plate.

Which of the following shapes can be used to tile (completely cover by repeating) a flat plane infinitely in all directions, without leaving gaps or overlaps?

The direction in which a scalar field \(\phi(x,y,z)\) has the largest rate of change is along:

If a monotonic and continuous function \(y=f(x)\) has exactly one root in the interval \(x_1<x<x_2\), then:

Consider the one–dimensional wave (advection) equation \[ \frac{\partial u}{\partial t}+\frac{\partial u}{\partial x}=0, -\infty<x<\infty,\ t\ge 0. \] For the initial condition \(u(x,0)=e^{-x^{2}}\), the solution at \(t=1\) is:

The World Bank has declared it will not offer new financing to Sri Lanka until an adequate macroeconomic policy framework is in place. It says Sri Lanka needs structural reforms focusing on economic stabilisation and tackling the root causes of its crisis. The crisis has starved the country of foreign exchange and led to shortages of food, fuel, and medicines. The Bank is repurposing existing loans to help with essentials. Based only on this passage, which statement can be inferred with certainty?

Find the coefficient of \(x^4\) in \((x-1)^3(x-2)^3\).

References : ............. : : Guidelines : Implement (By word meaning)

In the given figure, \(PQRS\) is a parallelogram with \(PS = 7\text{ cm}\), \(PT = 4\text{ cm}\) and \(PV = 5\text{ cm}\). What is the length of \(RS\) (in cm)? (The diagram is representative.) \begin{center} \includegraphics[width=0.5\textwidth]{01.jpeg} \end{center}

In 2022, June Huh was awarded the Fields medal (the highest prize in Mathematics). When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. \medskip Based only on the above information, which of the following statements can be logically inferred with certainty?

A line of symmetry divides a figure into two parts that are mirror images. The given figure consists of 16 unit squares. Three are already black. What is the minimum number of additional squares that must be coloured black so that both \(PQ\) (vertical midline) and \(MN\) (diagonal) are lines of symmetry? \begin{center} \includegraphics[width=0.5\textwidth]{02.jpeg} \end{center}

In an imagined world: - Some creatures are cruel. - Humans are one kind of creature. - It is given that the statement "Some human beings are not cruel creatures" is FALSE. Which statements can be logically inferred with certainty? (i) All human beings are cruel creatures. (ii) Some human beings are cruel creatures. (iii) Some creatures that are cruel are human beings. (iv) No human beings are cruel creatures.

Sand and cement are mixed in the ratio \(3:1\). Cost ratio of sand to cement is \(1:2\). Total cost of sand and cement is \(\,1000\) rupees. Find the cost of cement used.

"You are delaying the completion of the task. Send ............. contributions at the earliest."

A copper ball and a steel ball having diameters \(d_1\) and \(d_2\), respectively, are initially at 200°C. Both are cooled to ambient 30°C. If both reach 120°C in equal duration, find ratio \(d_1/d_2\). Assume Biot < 0.1.

Two cylindrical reservoirs 'A' and 'B' are connected by a 30 m long pipe of 250 mm internal diameter as shown. Darcy friction factor for the pipe is 0.025. Initially reservoir 'A' was full and reservoir 'B' was empty. Neglecting entrance and exit losses, find the time required to empty reservoir 'A' in hours (rounded off to 3 decimal places). \begin{center} \includegraphics[width=0.5\textwidth]{03.jpeg} \end{center}

A homogenous anisotropic earthen dam of height 52 m with a free board of 2 m is constructed on an impermeable foundation. The horizontal and vertical hydraulic conductivities of soil are \(K_h = 4.5 \times 10^{-8} \, m/s\) and \(K_v = 2.0 \times 10^{-8} \, m/s\). There are 6 flow channels and 25 equipotential drops in a square flownet drawn in the transformed dam section. If the downstream dam side is dry, the quantity of seepage per unit length through the dam in m\(^3\)/day/m is \underline{\hspace{3cm}}.

A salt affected crop field is to be leached with irrigation water having salt concentration of 3.5 meq/L. Salt concentration in saturation extract of soil is 15.2 meq/L. Leaching efficiency of field = 55%. In March, ET\(_0\) = 150 mm, effective rainfall = 75 mm, crop coefficient = 1.05. Find leaching requirement for the month in mm.

A 10 m pipe carries peak discharge = 1 m\(^3\)/s, head = 4 m, entrance loss coefficient = 0.5, friction loss coefficient = 0.02. Find neutral slope of water level in %.

Discharge from centrifugal pump at 1000 rpm with head = 30 m is 300 L/min. Efficiency = 65%. If speed increases to 1200 rpm, find power required.

A 0.30 m well penetrates an unconfined aquifer (saturated depth = 40 m). Pumping 0.03 m\(^3\)/s for 8 hours. Drawdowns in two observation wells: 3 m at 20 m, 2 m at 50 m. Find drawdown in pumping well in m.

The apparent wall shear stress in a 0.6 m long pipe line carrying refined oil is 12.5 Pa. If the pressure drop along the length is 300 Pa and flow rate is 0.25 m\(^3\)/s, the absolute viscosity of oil in \(10^{-3}\) Pa·s is \underline{\hspace{3cm}}.