List of top Questions asked in GATE Aerospace Engineering

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:}

The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is \({\rupee} 1000(X - 0.2)\), what is the average amount (in \rupee) she has earned per shift in the past 100 shifts?
\includegraphics[width=0.5\linewidth]{10.png}

Solve the system of equations: \[ 2x + 3y + z = 0 \] \[ x + y = 0 \] \[ y + z = 0 \] The given system of equations has:

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}

A 4 × 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with \( U \leq 4 \) is:
\includegraphics[width=0.5\linewidth]{3.png}

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?
\includegraphics[width=0.5\linewidth]{4.png}

We \_\_\_\_\_\_\_ tennis in the lawn when it suddenly started to rain.
Select the most appropriate option to complete the above sentence.

A rectangle has a length \(L\) and a width \(W\), where \(L>W\). If the width, \(W\), is increased by 10%, which one of the following statements is correct for all values of \(L\) and \(W\)?
Select the most appropriate option to complete the above sentence.

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.
\includegraphics[width=0.5\linewidth]{6.png}

Courage : Bravery :: Yearning :
Select the most appropriate option to complete the analogy.

A single-stage axial compressor, with a 50 % degree of reaction, runs at a mean blade speed of 250 m/s. The overall pressure ratio developed is 1.3. Inlet pressure and temperature are 1 bar and 300 K, respectively. Axial velocity is 200 m/s. Specific heat at constant pressure, \( C_p = 1005 \, {J/kg/K} \) and specific heat ratio, \( \gamma = 1.4 \). The rotor blade angle at the outlet is \_\_\_\_\_\_\_ degrees (rounded off to two decimal places).

A prismatic vertical column of cross-section \( a \times 0.5a \) and length \( l \) is rigidly fixed at the bottom and free at the top. A compressive force \( P \) is applied along the centroidal axis at the top surface. The Young’s modulus of the material is 200 GPa and the uniaxial yield stress is 400 MPa. If the critical value of \( P \) for yielding and for buckling of the column are equal, the value of \( \frac{l}{a} \) is \_\_\_\_ (rounded off to one decimal place).
\includegraphics[width=0.5\linewidth]{58.png}

A thin flat plate is subjected to the following stresses: \[ \sigma_{xx} = 160 \, {MPa}; \, \sigma_{yy} = 40 \, {MPa}; \, \tau_{xy} = 80 \, {MPa}. \] Factor of safety is defined as the ratio of the yield stress to the applied stress. The yield stress of the material under uniaxial tensile load is 250 MPa. The factor of safety for the plate assuming that material failure is governed by the von Mises criterion is \_\_\_\_\_\_\_ (rounded off to two decimal places).
\includegraphics[width=0.5\linewidth]{59.png}

Two designs A and B, shown in the figure, are proposed for a thin-walled closed section that is expected to carry only torque. Both A and B have a semi-circular nose, and are made of the same material with a wall thickness of 1 mm. With strength as the only criterion for failure, the ratio of maximum torque that B can support to the maximum torque that A can support is \_\_\ (rounded off to two decimal places).
\includegraphics[width=0.5\linewidth]{60.png}

An ideal turbofan with a bypass ratio of 5 has core mass flow rate, \( \dot{m}_a,c = 100 \, {kg/s} \). The core and the fan exhausts are separate and optimally expanded. The core exhaust speed is 600 m/s and the fan exhaust speed is 120 m/s. If the fuel mass flow rate is negligible in comparison to \( \dot{m}_a,c \), the static specific thrust (\( \frac{T}{\dot{m}_a,c} \)) developed by the engine is \_\_\_\_\_\_\_ Ns/kg (rounded off to the nearest integer).

F and G denote two points on a spacecraft’s orbit around a planet, as indicated in the figure. O is the center of the planet, P is the periapsis, and the angles are as indicated in the figure. If \( OF = 8000 \, {km} \), \( OG = 10000 \, {km} \), \( \theta_F = 0^\circ \), and \( \theta_G = 60^\circ \), the eccentricity of the spacecraft's orbit is \_\_\_\_\_\_\_\_ (rounded off to two decimal places).
\begin{figure} \centering \includegraphics[width=0.5\linewidth]{53.png} \end{figure}

For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is \_\_\_\_ N (answer in integer).
\includegraphics[width=0.5\linewidth]{56.png}

A uniform rigid bar of mass 3 kg is hinged at point F, and supported by a spring of stiffness \( k = 100 \, {N/m} \), as shown in the figure. The natural frequency of free vibration of the system is \_\_\_\_\_\_ rad/s (answer in integer).
\includegraphics[width=0.5\linewidth]{57.png}

A perfect gas flows through a frictionless constant-area duct with heat addition. The inlet conditions are as follows: pressure 100 kPa, density 1 kg/m\(^3\), and velocity 100 m/s. At a particular downstream location, the gas velocity is 200 m/s. The static pressure at the downstream location is \_\_\_\_\_\_ kPa (answer in integer).

The mass flow rate in a supersonic wind tunnel is 2 kg/s when the stagnation pressure and stagnation temperature are 1 MPa and 800 K, respectively. If the stagnation pressure and stagnation temperature are changed to 3 MPa and 200 K, the mass flow rate in the tunnel changes to \_\_\_\_\_\_\_ kg/s (answer in integer).