List of top Questions asked in GATE AE

The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is \_\_\_\_ m\(^2\)/s (rounded off to two decimal places).
In a centrifugal compressor, the eye tip diameter is 10 cm. For a shaft rotational speed of 490 rotations per second, the tangential speed at the inducer tip is \_\_\_ m/s (rounded off to one decimal place).
A lifting surface has a spanwise circulation distribution of \( \Gamma(\theta) = A \sin 3\theta \) (where \( A \neq 0 \)) over its span \( -\frac{b}{2} \leq y \leq \frac{b}{2} \), and \( y = -\frac{b}{2} \cos \theta \) is the spanwise coordinate. Furthermore, the downwash varies along the span as \( w(\theta) = V_\infty \left( \frac{3A \sin 3\theta}{\sin \theta} \right) \), where \( V_\infty \) is the freestream velocity. Which one of the following options represents the total lift \( L \) and induced drag \( D_i \)?
For a homogeneous, isotropic material, the relation between the shear modulus (\( G \)), Young’s modulus (\( E \)), and Poisson’s ratio (\( \nu \)) is \_\_\_\_?
A simply supported horizontal beam is subjected to a distributed transverse load varying linearly from \( q_0 \) at A to zero at B, as shown in the figure. Which one of the following options is correct?
\includegraphics[width=0.5\linewidth]{27.png}
A stress field is given by \( \sigma_{xx} = \sigma_{zz} = C_1 y \); \( \sigma_{yy} = C_2 y \); \( \tau_{xy} = \tau_{yz} = \tau_{zx} = 0 \), where \( C_1 \) and \( C_2 \) are non-zero constants. If the stress field satisfies equilibrium, which one of the following options is correct?
A uniform symmetric cross-section cantilever beam of length \( L \) is subjected to a transverse force \( P \) at the free end, as shown in the figure. The Young’s modulus of the material is \( E \) and the moment of inertia is \( I \). Ignoring the contributions due to transverse shear, the strain energy stored in the beam is \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{29.png}
In the given figure, plate ABCD in its undeformed configuration (solid line) is a rhombus with all the internal angles being 90°. The lengths of the undeformed diagonals are 20 cm. ABCD deforms as shown by the dotted lines. Upon deformation, diagonal AC reduces to 19.96 cm and BD increases to 20.04 cm. In the given x-y coordinate system, the engineering shear strain \( \gamma_{xy} \) is equal to \_\_\_\_\_.
\includegraphics[width=0.5\linewidth]{30.png}
\( \delta Q \) and \( \delta W \) are the heat and work interactions of a system with its surroundings, and \( dU \) is the change in the internal energy of the system. For an adiabatic process in a closed, constant pressure combustor, which one of the following options is correct?
Consider a pair of point vortices with clockwise circulation \( \Gamma \) each. The distance between their centers is \( a \), as shown in the figure. Assume two-dimensional, incompressible, inviscid flow. Which one of the following options is correct?
\includegraphics[width=0.5\linewidth]{20.png}
In a fluid flow, Mach number is an estimate of \_\_\_\_\_.
A general aviation airplane is in steady and level flight. The airplane is prone to adverse yaw. Which one of the following options best describes the deflections of aileron and rudder to achieve a coordinated right turn?
For a general aviation airplane, which one of the following has a destabilizing effect on its static roll stability?
A general aviation airplane is flying at an altitude of 5000 m. The indicated airspeed is 250 km/h. Assume that there are no instrument errors and position errors. Neglecting compressibility effects, which one of the following options is FALSE?
To achieve longitudinal static stability of a general aviation airplane, which one of the following conditions should be satisfied?
The eigenvalues of the matrix \[ \begin{bmatrix} 1 & 2
0 & 3 \end{bmatrix} \] are \_\_\_\_\_ .
The partial differential equation \[ \frac{\partial^2 u}{\partial x^2} + 4 \frac{\partial^2 u}{\partial x \partial y} + 2 \frac{\partial^2 u}{\partial y^2} = 0 \] is \_\_\_\_\_\_.
Let the function \( f(x) \) be defined as: \[ f(x) = \begin{cases} A + x, & {if } x<2
1 + x^2, & {if } x \geq 2 \end{cases} \] If the function \( f(x) \) is continuous at \( x = 2 \), the value of \( A \) is \_\_\_\_\_.
If \( i = \sqrt{-1} \), \[ \frac{(i+1)^3}{i-1} = \_\_\_\_\_\_\_\_. \]
For a two-dimensional incompressible flow over a flat plate, the laminar boundary layer thickness at a distance \( x \) from the leading edge is \( \delta \). If \( Re_x \) is the Reynolds number defined based on length scale \( x \), \[ \frac{\delta}{x} \propto \_\_\_\_\_\_. \]
For a NACA 4415 airfoil, the location of maximum camber, as a fraction of the chord length from the leading edge, is \_\_\_\_\_\_.
A positively cambered airfoil is placed in a uniform flow (velocity, \( U_\infty \)) at its zero-lift angle of attack. \( M \) is the corresponding pitching moment. Which one of the following representations accurately describes this scenario?
Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let \( a_1 \) and \( a_2 \) (in years) denote the ages of the brothers and \( a_1<a_2 \). Which one of the following statements is correct about their age on the day when they attain the same weight?
A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius \( r \) cm as shown in the figure. The side of the dodecagon is \( d \) cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side \( r \) cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are:
\includegraphics[width=0.5\linewidth]{8.png}
If a real variable \(x\) satisfies \(3^{x^2} = 27 \times 9^x\), then the value of \(\frac{2^{x^2}}{(2^x)^2\) is:}