List of top Questions asked in GATE AE

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?

NACA 2412 airfoil has

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).

The service ceiling of an airplane is the altitude

Regarding the horizontal tail of a conventional airplane, which one of the following statements is true?

A three-member truss is simply supported at Q and R, and loaded at P by a horizontal force \( F \) as shown. The force in QR is

A beam with a symmetrical T-shaped cross-section, as shown in the figure, is subjected to pure bending. The maximum magnitude of the normal stress is realised:

The closed thin-walled rectangular channel shown in figure (i) is opened by introducing a sharp cut at the center of the bottom edge, as shown in figure (ii). Which one of the following statements is correct?

The region of highest static temperature in a rocket engine and the region of highest heat flux are _______, respectively.

If $\hat{a}, \hat{b}, \hat{c}$ are three mutually perpendicular unit vectors, then $\hat{a} \cdot (\hat{b} \times \hat{c})$ can take the value(s):

The equation of the straight line representing the tangent to the curve \(y = x^2\) at the point (1, 1) is

Consider steady, two-dimensional, incompressible flow over a non-porous flat plate as shown in the figure. For the control volume PQRS, the speed \(u_{\infty}\) at section PQ is uniform and the speed at section RS is given by \(u(y)=A_0\left(\frac{y}{h}\right)^n\), where \(n\) is a positive integer. The value of \(A_0\) for which the flow through section PS will vanish is:

Consider the velocity distribution $u(y)$ shown in the figure. For two adjacent fluid layers L1 and L2, the viscous force exerted by L1 on L2 is _________.

The point of maximum entropy on a Fanno-curve in a Temperature–Entropy (T–s) diagram represents the

Let \(\hat{i}, \hat{j}, \hat{k}\) be the unit vectors in the x, y, and z directions, respectively. If the vector \(\hat{i} + \hat{j}\) is rotated about positive \(\hat{k}\) by \(135^\circ\), one gets