List of top Questions asked in GATE AE

Consider a circulation distribution over a finite wing given by the equation below.
\[ \Gamma(y) = \begin{cases} \Gamma_0 \left(1 - \frac{2y}{b}\right) & \text{if } 0 \leq y \leq \frac{b}{2}, \\ \Gamma_0 \left(1 + \frac{2y}{b}\right) & \text{if } -\frac{b}{2} \leq y \leq 0, \end{cases} \] The wingspan \( b \) is 10 m, the maximum circulation \( \Gamma_0 \) is 20 m\(^2\)/s, density of air is 1.2 kg/m\(^3\), and the free stream speed is 80 m/s.
The lift over the wing is _________ N (rounded off to the nearest integer).

A rocket operates at an absolute chamber pressure of 20 bar to produce thrust \(F_1\). The hot exhaust is optimally expanded to 1 bar (absolute pressure) using a convergent-divergent nozzle with exit to throat area ratio \(\left(\frac{A_e}{A_t}\right)\) of 3.5 and thrust coefficient, \(C_{F,1} = 1.42\). The same rocket when operated at an absolute chamber pressure of 50 bar produces thrust \(F_2\) and the thrust coefficient is \(C_{F,2}\). Which of the following statement(s) is/are correct?

The vector field \( \vec{v} = x^3 \hat{i} + y^3 \hat{j} + z^3 \hat{k} \) is a vector field where \( \hat{i}, \hat{j}, \hat{k} \) are the base vectors of a Cartesian coordinate system.
Using the Gauss divergence theorem, the value of the outward flux of the vector field over the surface of a sphere of unit radius centered at the origin is _________ (rounded off to one decimal place).

The largest eigenvalue of the given matrix is: \[ \begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{bmatrix} \]

For a conventional airplane in straight, level, constant velocity flight condition, which of the following condition(s) is/are possible on Euler angles (\(\phi, \theta, \psi\)), angle of attack (\(\alpha\)) and the sideslip angle (\(\beta\))?

A horizontal load \(F\) is applied at point R on a two-member truss, as shown in the figure. Both the members are prismatic with cross-sectional area \(A_0\), and made of the same material with Young's modulus \(E\). The horizontal displacement of point R is:

Which of the following is NOT always true for a combustion process taking place in a closed system?

A convergent nozzle fed from a constant pressure, constant temperature reservoir, is discharging air to atmosphere at 1 bar (absolute) with choked flow at the exit (marked as \(Q\)).
Flow through the nozzle can be assumed to be isentropic.
If the exit area of the nozzle is increased while all the reservoir parameters and ambient conditions remain the same, then at steady state

A cylindrical object of diameter 900 mm is designed to move axially in air at 60 m/s. Its drag is estimated on a geometrically half-scaled model in water, assuming flow similarity. Co-efficients of dynamic viscosity and densities for air and water are \(1.86 \times 10^{-5}\) Pa-s, 1.2 kg/m\(^3\) and \(1.01 \times 10^{-3}\) Pa-s, 1000 kg/m\(^3\) respectively. Drag measured for the model is 2280 N. Drag experienced by the full-scale object is ___ N (rounded off to the nearest integer).

The real function \( y = \sin^2(|x|) \) is

Consider a conventional subsonic fixed-wing airplane. \(e\) is the Oswald efficiency factor and \(AR\) is the aspect ratio. Corresponding to the minimum \(\left(\frac{C_D}{C_L^{3/2}}\right)\), which of the following relations is true?

An unpowered glider is flying at a glide angle of 10 degrees. Its lift-to-drag ratio is _________ (round off to two decimal places).

The two-dimensional plane-stress state at a point is: \[ \sigma_{xx} = 110\,\text{MPa},\quad \sigma_{yy} = 30\,\text{MPa},\quad \tau_{xy} = 40\,\text{MPa}. \] The normal stress $\sigma_n$ on a plane inclined at $45^\circ$ as shown is (round off to the nearest integer).

In a static test, a turbofan engine with bypass ratio of 9 has core hot exhaust speed 1.5 times that of fan exhaust speed. The engine is operated at a fuel–air ratio of $f=0.03$. Both the fan and the core streams have no pressure thrust. The ratio of fan thrust to thrust from the core engine is (round off to one decimal place).

In a single stage turbine, the hot gases come out of stator/nozzle at a speed of 500 m/s and at an angle of 70 degrees with the turbine axis as shown. The design speed of the rotor blade is 250 m/s at the mean blade radius. The rotor blade angle, \( \beta \), at the leading edge is _________ degrees (round off to one decimal place).

Consider the differential equation \(\frac{d^2y}{dx^2} - 2 \frac{dy}{dx} + y = 0\). The boundary conditions are \(y = 0\) and \(\frac{dy}{dx} = 1\) at \(x = 0\). Then the value of \(y\) at \(x = \frac{1}{2}\) is

Consider the partial differential equation \(\frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} = 0\) where \(x, y\) are real. If \(f(x, y) = a(x)b(y)\), where \(a(x)\) and \(b(y)\) are real functions, which one of the following statements can be true?

The height of a right circular cone of maximum volume that can be enclosed within a hollow sphere of radius \(R\) is

For International Standard Atmosphere (ISA) up to 11 km, which of the following statement(s) is/are true?

Let \(\sigma\) and \(\tau\) represent the normal stress and shear stress on a plane, respectively. The Mohr circle(s) that may possibly represent the state of stress at points in a beam of rectangular cross-section under \textit{pure bending} is/are:

An isotropic linear elastic material point under plane strain condition in the x–y plane always obeys:

Across an oblique shock wave in a calorifically perfect gas,

A high-pressure-ratio multistage axial compressor encounters an extreme loading mismatch during starting. Which of the following technique(s) can be used to alleviate this problem?

The arc length of the parametric curve: \( x=\cos\theta,\; y=\sin\theta,\; z=\theta \) from \( \theta=0 \) to \( \theta=2\pi \) is equal to _________ (round off to one decimal place).

NACA 2412 airfoil has