List of top Questions asked in GATE Aerospace Engineering

Given vectors \[ \vec{A} = 9\hat{i} - 5\hat{j} + 2\hat{k}, \vec{B} = 11\hat{i} + 4\hat{j} + \hat{k}, \vec{C} = -7\hat{i} + 14\hat{j} - 3\hat{k} \] which of the following statements are TRUE?

Consider a one-dimensional inviscid supersonic flow in a diverging duct with heat addition ($Q_{in}$). Which of the following statement(s) is/are always TRUE? 

Consider the International Standard Atmosphere (ISA) with $h$ being the geopotential altitude (in km) and $\dfrac{dT}{dh}$ being the temperature gradient (in K/m). Which of the following combination(s) of $\Big(h, \dfrac{dT}{dh}\Big)$ is/are correct as per ISA?

A rigid bar $AB$ of length 3 m is subjected to a uniformly distributed load of $100 \,\text{N/m}$. The bar is supported at $A$ (pin) and by rod $CD$ connected at $D$. The rod $CD$ has axial stiffness $40 \,\text{N/mm}$, and $C$ is pinned. Find the vertical deflection at point $D$ (in mm). 

A cantilever beam of length $2a$ is loaded at the tip with force $F$. The beam is supported in the middle by a roller (pin). Find the reaction moment at the built-in end of the beam as $\alpha Fa$, where $\alpha =$ ....................... (round off to one decimal place). 

The shear flow distribution in a single cell, thin-walled beam under a shear load $S_y$ is shown in the figure. The cell has horizontal symmetry with booms marked $1$ to $4$. The shear modulus $G$ is same for all walls, and the area of the cell is $135000 \,\text{mm}^2$. With respect to point $O$, find the distance of shear centre $S$ (in mm). (round off to nearest integer) 

An airplane with wing planform area $S=20\,\text{m}^2$ and weight $W=8\,\text{kN}$ is flying straight and level with a speed of $V=100\,\text{m/s}$. The total drag coefficient is $C_D=0.026$ and the air density is $\rho=0.7\,\text{kg/m}^3$. The total thrust required to introduce a steady climb at angle $\gamma=0.1$ radians is ............. N. (round off to the nearest integer)
The maximum permissible load factor and the maximum lift coefficient for an airplane are $n_{\max}=7$ and $C_{L,\max}=2$, respectively. For a wing loading $W/S=6500\ \text{N/m}^2$ and air density $\rho=1.23\ \text{kg/m}^3$, the speed yielding the highest possible turn rate in the vertical plane is .............. m/s. (round off to the nearest integer)
A gas turbine combustor burns methane with air at equivalence ratio $\phi=0.5$, where $\displaystyle \phi=\frac{(F/A)}{(F/A)_{\text{st}}}$. If the air mass-flow rate is $\dot m_{\text{air}}=20\ \text{kg/s}$, find the methane mass-flow rate (kg/s). (round off to two decimal places)
Given $G=6.67\times10^{-11}\ \text{N\,m}^2\text{/kg}^2$, planet mass $M=6.4169\times10^{23}$ kg and radius $R=3390$ km, find the escape velocity (km/s). (round off to one decimal place)
A satellite is in a circular orbit around Earth with period $T=90$ minutes. Take Earth's radius $R_E=6370$ km, Earth's mass $M_E=5.98\times10^{24}$ kg, and $G=6.67\times10^{-11}\ \text{N\,m}^2\text{/kg}^2$. Find the altitude above mean sea level (km).
A centrifugal air compressor has inlet root diameter $D_1=0.25\,\text{m}$ and outlet impeller diameter $D_2=0.6\,\text{m}$. Pressure ratio $\pi_c=p_{02}/p_{01}=5.0$. Air at rotor inlet: $p_{01}=1\,\text{atm}$, $T_{01}=25^\circ\text{C}=298\,\text{K}$. Polytropic efficiency $\eta_p=0.8$, slip factor $\sigma=0.92$. Take $C_p=1.004\,\text{kJ/kg-K}$ and $\gamma=1.4$. Find the impeller speed (RPM). (round off to the nearest integer)
A cryogenic liquid rocket engine (expander cycle) burns liquid hydrogen and liquid oxygen at stoichiometry. The hydrogen mass-flow rate is $\dot m_{H_2}=32\,\text{kg/s}$, and the oxygen mass-flow rate satisfies $\dot m_{O_2}/\dot m_{H_2}=8$. Assuming the forward reaction dominates, find the rate of formation of $\mathrm{H_2O}$ (kmol/s). (round off to the nearest integer)
A single degree-of-freedom spring–mass–damper system has viscous damping ratio $\zeta = 0.1$. The mass has initial displacement of $10$ cm without velocity. After exactly two complete cycles of damped oscillation, find amplitude of displacement (in cm, round off to two decimals).
A thin-walled cylindrical pressure vessel of yield strength $300$ MPa has radius-to-thickness ratio $R/t = 100$. Using von Mises yield criterion, find internal pressure at failure. (round off to two decimals)
Solve differential equation: \[ x^2 \frac{d^2y}{dx^2} + 4x \frac{dy}{dx} + 2y = 0, x \geq 1 \] with initial conditions $y=0, \; y'(1)=1$ at $x=1$. Find $y$ at $x=2$. (round off to two decimals)
The operating characteristics of a pump are measured as $C_p = a \Phi^2$, where \[ C_p = \frac{P}{\rho \omega^3 D^5}, \Phi = \text{flow coefficient}, a=\text{constant}. \] If $\omega$ increases by 25% (i.e. $\omega \to 1.25\omega$) and the flow coefficient $\Phi$ is constant, determine $\alpha$ such that $P$ becomes $\alpha P$. (round off to two decimal places)
A thin cambered airfoil has lift coefficient $C_l=0$ at angle of attack $\alpha=-1^\circ$. Estimate $C_l$ at $\alpha=4^\circ$, assuming stall occurs at much higher $\alpha$. (round off to two decimal places)
In potential flow, a uniform stream of strength $U$ flows along x-axis. Line sources of strength $\pi/2, -\pi/3, \pi/4, -\pi/5$ are placed at $x=0,1,2,3$ respectively. Find strength of an additional line source at $x=4$ such that a closed streamline encircles all five sources. (round off to two decimal places)
Enstrophy is defined as square of magnitude of vorticity. For velocity field \[ \vec{V} = (4x - 1.5y + 2.5z)\hat{i} + (1.5x - 1.5y)\hat{j} + (0.7xy)\hat{k}, \] find enstrophy at $(1,1,1)$. (round off to two decimal places)
For an airfoil, which of the relations about the critical Mach number $M_{cr}$ and drag divergence Mach number $M_{dd}$ are correct?
Which of the following statement(s) about the elastic flexural buckling load of columns is/are correct?
The thickness of a uniform hollow circular shaft is equal to the difference between the outer radius and the inner radius. The ratio of the inner diameter to outer diameter of the shaft is $0.5$. For the shaft reacting to an applied torque, the ratio of the maximum shear stress $\tau$ to the maximum shear stress $\tau_{\text{thin-wall}}$ obtained using the thin-wall approximation is ............. (round off to one decimal place)
A general aviation airplane has $W=10 \,\text{kN}$, $S=15 \,\text{m}^2$, $\rho=0.60 \,\text{kg/m}^3$, $C_{D0}=0.025$, $K=0.05$, thrust $T=1 \,\text{kN}$. Find the maximum cruise speed.
Consider the equation $\dfrac{dy}{dx} + ay = \sin(\omega x)$, where $a$ and $\omega$ are constants. Given $y=1$ at $x=0$, select all correct statements as $x \to \infty$.