List of top Questions asked in GATE AE

The figure shows schematic of a set-up for visualization of non-uniform density field in the test section of a supersonic wind tunnel. This technique of visualization of high speed flows is known as: 

Which of the following statement(s) is/are true about the function defined as \( f(x)= e^{-x} \lvert \cos x \rvert \) for \( x>0 \)?
 

An aircraft with twin jet engines has: 
Thrust per engine = 8000 N 
Spanwise distance between engines = 10 m 
Wing area = 50 m\(^2\), Wing span = 10 m 
Rudder effectiveness: \( C_{n_{\delta r}} = -0.002/\text{deg} \) 
Air density at sea level: \( \rho = 1.225 \, \text{kg/m}^3 \) 
The rudder deflection, in degrees, required to maintain zero sideslip at 100 m/s in steady and level flight at sea level with a non-functional right engine is ________ (round off to two decimal places).

A free vortex filament (oriented along Z–axis) of strength \(K = 5 \, \text{m}^2/\text{s}\) is placed at the origin. The circulation around the closed loop ABCDEFA is \(\underline{\hspace{1cm}}\). 

A rigid massless rod pinned at one end has a mass $m$ attached to its other end. The rod is supported by a linear spring of stiffness $k$ as shown in the figure. The natural frequency of this system is: 

The figure shows three glasses P, Q and R with water and floating ice cube. Glass P has a solid ice cube, glass Q has an ice cube with a small solid steel ball embedded in it and glass R has an ice cube with an air bubble. After the ice cube melts, the level of water in glasses P, Q and R, respectively:

\[ \lim_{x \to 0} \left( \frac{1}{\sin x} - \frac{1}{x} \right) = \underline{\hspace{2cm}} \text{ (round off to nearest integer).} \]

Which of the following statement(s) is/are true across an oblique shock (in adiabatic conditions) over a wedge shown below? 

$C_m - \alpha$ variation for a certain aircraft is shown in the figure. Which one of the following statements is true for this aircraft? 

Let $V_{TAS}$ be the true airspeed of an aircraft flying at a certain altitude where the density of air is $\rho$, and $V_{EAS}$ be the equivalent airspeed. If $\rho_0$ is the density of air at sea-level, what is the ratio $\frac{V_{TAS}}{V_{EAS}}$ equal to?
 

For the state of stress as shown in the figure, what is the orientation of the plane with maximum shear stress with respect to the x-axis? 

Uniaxial tension test (see the figure) is conducted on two different samples prepared with homogeneous, isotropic materials. One of the materials is brittle, whereas the other is ductile.

Assuming that there is no stress concentration at loading points, the failurewould initiate:

The figure shows schematics of wave patterns at the exit of nozzles A and B operating at different pressure ratios.

Nozzles A and B, respectively, are said to be operating in: 

\(u (x,y)\) is governed by the following equation \[ \frac{\partial^{2}u}{\partial x^{2}} - 4\frac{\partial^{2}u}{\partial x \partial y} + 6\frac{\partial^{2}u}{\partial y^{2}} = x + 2y \] The nature of this equation is: 
 

Consider the differential equation \[ \frac{d^{2}y}{dx^{2}} + 8\frac{dy}{dx} + 16y = 0 \] and the boundary conditions \( y(0) = 1 \) and \( \frac{dy}{dx}(0) = 0 \). The solution to this equation is:
A jet aircraft weighs 10,000 kg, has an elliptic wing of span 10 m and area 30 m\(^2\). The zero-lift drag coefficient is \(C_{D0} = 0.025\). The maximum steady level-flight speed at sea level is 100 m/s. Density of air is 1.225 kg/m\(^3\), and \(g = 10\ \text{m/s}^2\). Determine the maximum thrust developed by the engine (round off to two decimals).
A jet transport airplane has the following data:
Lift-curve slope of wing-body: \(\frac{\partial C_{Lwb}}{\partial \alpha_{wb}} = 0.1/\deg\)
Lift-curve slope of tail: \(\frac{\partial C_{Lt}}{\partial \alpha_t} = 0.068/\deg\)
Tail area \(S_t = 80\ \text{m}^2\), wing area \(S = 350\ \text{m}^2\)
Tail moment arm \(\ell_t = 28\ \text{m}\)
Mean aerodynamic chord \(\bar{c} = 9\ \text{m}\)
Downwash: \(\epsilon = 0.4\alpha\)
Wing-body aerodynamic center: \(x_{ac}/\bar{c} = 0.25\)
CG location: \(x_{cg}/\bar{c} = 0.3\)
Determine the pitching-moment coefficient slope \(C_{m_\alpha}\) (round off to three decimals).
An aircraft with a turbojet engine flies at 270 m/s. Enthalpies:
Incoming air: 260 kJ/kg, Exit gas: 912 kJ/kg.
Fuel–air mass-flow ratio: 0.019.
Fuel heating value: 44.5 MJ/kg.
Heat loss: 25 kJ/kg of air.
Find the exhaust jet velocity (round off to 2 decimals).
Hot gases at 2100 K and 14 MPa expand ideally to 0.1 MPa through a rocket nozzle.
Molecular mass = 22 kg/kmol, heat-capacity ratio $\gamma = 1.32$,
Universal gas constant = 8314 J/kmol-K, \(g = 9.8\,\text{m/s}^2\).
Throat area = \(0.1\ \text{m}^2\). Find the specific impulse (round off to 2 decimals).
A twin-spool turbofan engine at sea level (\(P_a = 1\ \text{bar},\ T_a = 288\ \text{K}\)) has separate cold and hot nozzles. During static thrust test, the total air mass flow rate is 100 kg/s and the cold exhaust temperature is 288 K. Given:
Fan pressure ratio = 1.6
Overall pressure ratio = 20
Bypass ratio = 3.0
Turbine entry temperature = 1800 K
\(C_p = 1.005\ \text{kJ/kg-K}\), \(\gamma = 1.4\).
Find the static thrust from the cold nozzle (ideal fan and ideal expansion), in kN (round to two decimals).
A single-stage axial turbine has a mean blade speed of 340 m/s. Rotor inlet and exit blade angles are 21° and 55°, respectively. Density at rotor inlet is 0.9 kg/m³, annulus area = 0.08 m², degree of reaction = 0.4. Find the mass flow rate (round off to 2 decimals).
Air flow rate = 100 kg/s. Stagnation temperatures:
\(T_{t1} = 600\ \text{K}\), \(T_{t2} = 1200\ \text{K}\).
Burner efficiency = 0.9. Fuel heating value = 40 MJ/kg.
Specific heats: \(C_{p,a} = 1000\), \(C_{p,g} = 1200\ \text{J/kg·K}\).
Find the fuel flow rate (round off to 2 decimals).
Evaluate \(\int_{1}^{5} x^2 dx\) using 4 equal intervals by trapezoidal rule and Simpson's 1/3 rule, and compute the absolute difference (round to 2 decimals).
For a beam with deflection
\[ y = \frac{w}{48EI} (2x^4 - 3lx^3 + l^3x) \] find the non-dimensional location \(x/l\) at which deflection is maximum (round to 2 decimals).
A finite wing of elliptic planform with aspect ratio 10 and symmetric airfoil operates at \(5^\circ\) angle of attack in uniform flow. The induced drag coefficient is \(\underline{\hspace{1cm}}\) (round off to three decimal places).