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GATE AE practice questions

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Question 1General Aptitude

A launch-vehicle stage has a structural mass equal to 12% of its lift-off mass, with the remainder being propellant. If the structural mass of the stage is 6,000 kg, what is its lift-off mass?

  1. 50,000 kg Correct answer.
  2. 44,000 kg
  3. 68,182 kg
  4. 52,800 kg

Explanation

Structural mass is 12% of lift-off mass, so lift-off mass equals 6,000 divided by 0.12. This gives 50,000 kg. A quick check confirms the propellant share, 88% of 50,000 kg, is 44,000 kg.

Question 2General Aptitude

In an aerospace control report, the statement that a control law is robust means that the controller:

  1. has been certified by the regulator for manned flight
  2. maintains stability and performance despite disturbances and modelling uncertainties Correct answer.
  3. requires a very large computational effort per time step
  4. is tuned to minimise fuel burn over a nominal mission profile

Explanation

In control engineering, robustness refers to insensitivity of stability and performance to plant uncertainty, unmodelled dynamics and external disturbances. A robust controller keeps the closed-loop system well behaved across a range of operating conditions rather than only at the nominal design point.

Question 3General Aptitude

A wind-tunnel campaign log lists 240 runs, of which 15% had to be repeated because of faulty pressure sensors. How many runs did not need repeating?

  1. 204 Correct answer.
  2. 180
  3. 216
  4. 36

Explanation

The repeated runs number 15% of 240, which is 36. The runs that did not need repeating are therefore 240 minus 36, equal to 204. Equivalently, 85% of 240 is 204.

Question 4General Aptitude

Two unmanned aerial vehicles fly towards each other along the same straight track, one at 60 m/s and the other at 40 m/s. If they are initially 5 km apart, how long does it take them to pass each other?

  1. 125 s
  2. 20 s
  3. 100 s
  4. 50 s Correct answer.

Explanation

Because the vehicles approach each other, their closing speed is the sum of the individual speeds, 60 + 40 = 100 m/s. Converting the separation to metres gives 5,000 m, so the time is 5,000 divided by 100, which is 50 s.

Question 5General Aptitude

A fleet register states that every aircraft in Fleet A is twin-engine, and that some twin-engine aircraft in the company are pressurised. Which conclusion follows necessarily?

  1. Every pressurised aircraft belongs to Fleet A.
  2. Some Fleet A aircraft are pressurised.
  3. No Fleet A aircraft is pressurised.
  4. Nothing about whether any Fleet A aircraft is pressurised follows necessarily. Correct answer.

Explanation

The second premise only asserts that some twin-engine aircraft are pressurised; those aircraft may all lie outside Fleet A. Since Fleet A is a subset of twin-engine aircraft but the pressurised ones need not overlap it, no definite conclusion about Fleet A pressurisation can be drawn.

Question 6General Aptitude

During a fatigue test, the measured crack lengths at successive load blocks are 2, 6, 12, 20 and 30 mm. Assuming the pattern continues, what is the crack length at the next block?

  1. 42 mm Correct answer.
  2. 40 mm
  3. 36 mm
  4. 44 mm

Explanation

The successive differences are 4, 6, 8 and 10 mm, increasing by 2 mm each time. The next difference must therefore be 12 mm, giving 30 + 12 = 42 mm. The sequence can also be written as n(n+1) for n = 1, 2, 3, ..., which gives 42 at n = 6.

Question 7General Aptitude

A flight-test team of 3 people must be formed from 5 pilots and 4 engineers, and the team must include at least one pilot and at least one engineer. How many distinct teams are possible?

  1. 60
  2. 84
  3. 70 Correct answer.
  4. 74

Explanation

Unrestricted selection of 3 people from 9 gives 84 teams. Subtracting the invalid all-pilot teams, 10, and all-engineer teams, 4, leaves 84 - 14 = 70 valid teams. Equivalently, add the mixed cases: 5×6 + 10×4 = 70.

Question 8General Aptitude

Choose the verb that correctly completes the sentence: "The flight-test report, along with the supporting telemetry logs, ___ submitted to the certification authority last week."

  1. are
  2. was Correct answer.
  3. have been
  4. were

Explanation

The grammatical subject is the singular noun "report"; the phrase "along with the supporting telemetry logs" is a parenthetical addition and does not change the subject's number. The verb must therefore be singular, and the past time marker "last week" selects "was".

Question 9General Aptitude

A fly-by-wire system uses two independent redundant computers, each with a probability of 0.02 of failing during a mission. The system fails only if both computers fail. What is the probability that the system does not fail?

  1. 0.9996 Correct answer.
  2. 0.98
  3. 0.9992
  4. 0.9604

Explanation

System failure requires both independent units to fail, with probability 0.02 × 0.02 = 0.0004. The probability that the system survives is therefore 1 - 0.0004 = 0.9996. Note that 0.98 would be the survival probability of a single computer.

Question 10General Aptitude

An aircraft with a still-air speed of 400 km/h flies 800 km outbound with a 100 km/h tailwind and returns 800 km along the same route against the same wind. What is its average ground speed for the round trip?

  1. 375 km/h Correct answer.
  2. 380 km/h
  3. 400 km/h
  4. 366.7 km/h

Explanation

Outbound ground speed is 500 km/h, so the leg takes 1.6 h; inbound ground speed is 300 km/h, so the return takes about 2.667 h. Total time is 4.267 h for 1,600 km, giving an average of 375 km/h. The answer is the harmonic mean of 500 and 300, not their arithmetic mean.

Question 11General Aptitude

In a flight-test debrief, an engineer notes that a sensor anomaly was transient. In this context, 'transient' means that the anomaly:

  1. lasted only for a short time Correct answer.
  2. was intentionally introduced
  3. could not be recorded by telemetry
  4. occurred at regular intervals

Explanation

Transient describes something that is brief or temporary. A transient sensor anomaly therefore persisted only for a short interval rather than repeating on a regular schedule.

Question 12General Aptitude

A wind-tunnel model has a wing span of 1.2 m and represents a full-scale wing span of 36 m. What is the scale of the model?

  1. 1:30 Correct answer.
  2. 1:25
  3. 1:40
  4. 1:35

Explanation

Scale is the ratio of model length to full-scale length: 1.2/36 = 1/30. The model is therefore at 1:30 scale.

Question 13General Aptitude

In a flight-test organisation, every engineer in Team X is certified in data acquisition. Some certified data-acquisition engineers are also qualified pilots. Which statement must be true?

  1. Every qualified pilot belongs to Team X.
  2. Some engineers in Team X are not certified in data acquisition.
  3. Every engineer in Team X holds data-acquisition certification. Correct answer.
  4. No certified data-acquisition engineer is a qualified pilot.

Explanation

The first premise states universally that all Team X engineers are data-acquisition certified, so the correct option follows directly. The existence of some certified pilots elsewhere does not establish any link to Team X.

Question 14General Aptitude

A test facility logs four wind-tunnel campaigns. Campaign A: 150 runs, 12 aborted. Campaign B: 200 runs, 10 aborted. Campaign C: 250 runs, 20 aborted. Campaign D: 120 runs, 18 aborted. Which campaign had the highest abort rate?

  1. Campaign D Correct answer.
  2. Campaign C
  3. Campaign B
  4. Campaign A

Explanation

Abort rates are A 12/150 = 8%, B 10/200 = 5%, C 20/250 = 8%, and D 18/120 = 15%. Campaign D therefore has the highest percentage of aborted runs.

Question 15General Aptitude

Two telemetry stations, working together, can process a batch of flight data in 6 hours. Station A alone takes 10 hours. How long would Station B take working alone?

  1. 12 hours
  2. 14 hours
  3. 16 hours
  4. 15 hours Correct answer.

Explanation

In one hour the pair completes 1/6 of the batch and Station A completes 1/10. Station B's rate is 1/6 − 1/10 = 1/15, so it needs 15 hours alone.

Question 16General Aptitude

The number of test points used in successive wind-tunnel campaigns is 3, 7, 15, 31, ... Assuming the pattern continues, how many test points are used in the next campaign?

  1. 55
  2. 63 Correct answer.
  3. 127
  4. 47

Explanation

Each term is one less than a power of two: 3 = 2^2 − 1, 7 = 2^3 − 1, 15 = 2^4 − 1, 31 = 2^5 − 1. The next term is 2^6 − 1 = 63.

Question 17General Aptitude

Five flight-test sorties P, Q, R, S and T are scheduled one after another. Sortie R must be third, and Q must immediately follow P. Which ordering satisfies both conditions?

  1. S P Q R T
  2. P Q R S T Correct answer.
  3. P R Q S T
  4. Q P R S T

Explanation

In the correct ordering, R occupies the third position and Q comes immediately after P. The other orderings either place R in the wrong position or put Q before P.

Question 18General Aptitude

Five distinct sensor faults are to be assigned to three identical redundant channels so that every channel receives at least one fault. In how many ways can this be done?

  1. 60
  2. 25 Correct answer.
  3. 90
  4. 150

Explanation

Because the channels are identical, the count is the Stirling number S(5,3). It equals (3^5 − 3·2^5 + 3)/6 = (243 − 96 + 3)/6 = 25.

Question 19General Aptitude

A rectangular hangar floor has a perimeter of 60 m and a diagonal of 25 m. What is its area?

  1. 150 m²
  2. 125 m²
  3. 175 m²
  4. 137.5 m² Correct answer.

Explanation

Let the sides be l and w. Then l + w = 30 and l² + w² = 25² = 625. Since (l + w)² = l² + w² + 2lw, 900 = 625 + 2lw, so lw = 137.5 m².

Question 20General Aptitude

Choose the grammatically correct completion: 'The engineer insisted ___ the calibration before signing the report.'

  1. on repeating Correct answer.
  2. repeating
  3. to repeat
  4. that repeating

Explanation

The verb insist takes the preposition on when followed by a gerund: insist on doing something. The infinitive and bare gerund forms are not standard after insist in this construction.

Question 21General Aptitude

The maintenance planner decided to ___ the inspection interval from 500 to 400 flight hours to increase the safety margin.

  1. postpone
  2. defer
  3. expand
  4. shorten Correct answer.

Explanation

The verb must mean to make the interval shorter. 'Shorten' is the only option that expresses reducing the interval from 500 to 400 flight hours, which is consistent with increasing the safety margin.

Question 22General Aptitude

A stores inventory lists 480 line items, of which 12.5% are avionics spares. How many avionics spares are listed?

  1. 60 Correct answer.
  2. 48
  3. 72
  4. 96

Explanation

12.5% is one eighth, so the number of avionics spares is 480 divided by 8, which equals 60. Equivalently, 0.125 multiplied by 480 gives 60.

Question 23General Aptitude

An altimeter measures altitude in the same way that a pitot-static system measures ___.

  1. airspeed Correct answer.
  2. heading
  3. temperature
  4. fuel quantity

Explanation

A pitot-static system derives airspeed from the difference between total pressure and static pressure. The analogy pairs each instrument with the quantity it measures: altimeter with altitude, pitot-static system with airspeed.

Question 24General Aptitude

One telemetry-processing unit can reduce a tape in 8 hours, and a second unit can reduce the same tape in 12 hours. Working together, what fraction of the tape do they process in 3 hours?

  1. 5/8 Correct answer.
  2. 2/3
  3. 3/8
  4. 1/2

Explanation

The combined rate is 1/8 + 1/12 = 5/24 of the tape per hour. In 3 hours the units process 3 multiplied by 5/24, which equals 15/24 or 5/8 of the tape.

Question 25General Aptitude

The daily number of telemetry channels checked follows the pattern 7, 10, 8, 11, 9, 12, ... What is the next value?

  1. 10 Correct answer.
  2. 13
  3. 14
  4. 11

Explanation

The sequence alternates adding 3 and subtracting 2: 7+3=10, 10-2=8, 8+3=11, 11-2=9, and 9+3=12. Applying the next subtraction gives 12-2=10.

Question 26General Aptitude

All inspected aircraft have serviceable batteries. Some aircraft with serviceable batteries have worn tyres. Which statement must be true?

  1. Some inspected aircraft have serviceable batteries. Correct answer.
  2. No uninspected aircraft has serviceable batteries.
  3. Some inspected aircraft have worn tyres.
  4. All aircraft with worn tyres are inspected.

Explanation

From 'All inspected aircraft have serviceable batteries', every inspected aircraft belongs to the serviceable-battery set, so at least some inspected aircraft have serviceable batteries. The other statements add links between tyres and inspection that the premises do not license.

Question 27General Aptitude

A crew of 3 must be formed from 4 pilots and 3 engineers, and the crew must contain exactly one pilot. In how many ways can the crew be formed?

  1. 6
  2. 18
  3. 9
  4. 12 Correct answer.

Explanation

Choose 1 of the 4 pilots and 2 of the 3 engineers: C(4,1) multiplied by C(3,2) equals 4 multiplied by 3, which is 12. The condition fixes the crew composition as one pilot plus two engineers.

Question 28General Aptitude

A campaign log records 300 wind-tunnel runs, of which 18% were aborted for instrumentation and 12% for model defects. How many runs were completed?

  1. 210 Correct answer.
  2. 204
  3. 180
  4. 195

Explanation

The aborted fraction is 18% plus 12%, which equals 30%, so 70% of the runs were completed. Multiplying 0.70 by 300 gives 210 completed runs.

Question 29General Aptitude

A telemetry link has three independent channels, each working with probability 0.9. The link is usable if at least two channels work. What is the probability that the link is usable?

  1. 0.972 Correct answer.
  2. 0.900
  3. 0.729
  4. 0.999

Explanation

For at least two working channels, either exactly two work or all three work: 3 times 0.9 squared times 0.1, plus 0.9 cubed, equals 0.243 plus 0.729, which is 0.972. Independence justifies multiplying the channel probabilities.

Question 30General Aptitude

Four ground tests W, X, Y and Z are scheduled one after another. X must precede Y, Z must be last, and W cannot be first. Which order satisfies all the constraints?

  1. Y, X, W, Z
  2. X, Y, Z, W
  3. X, W, Y, Z Correct answer.
  4. W, X, Y, Z

Explanation

X must come before Y, Z must occupy the last position, and W cannot be first. The order X, W, Y, Z satisfies all three constraints, while each other option violates at least one.

Question 31Engineering Mathematics

For the matrix A = [[2, 1], [0, 3]], which pair gives the eigenvalues of A?

  1. 2 and 3 Correct answer.
  2. 0 and 5
  3. 3 and 1
  4. 1 and 2

Explanation

A is upper triangular, so its characteristic determinant is det(A − λI) = (2 − λ)(3 − λ), which vanishes at λ = 2 and λ = 3. For any triangular matrix the eigenvalues are exactly the diagonal entries, independent of the off-diagonal term.

Question 32Engineering Mathematics

The directional derivative of f(x, y) = x²y at the point (1, 2) along the unit vector u = (3/5, 4/5) is

  1. 1.0
  2. 3.2 Correct answer.
  3. 4.0
  4. 2.4

Explanation

The gradient is ∇f = (2xy, x²), which equals (4, 1) at (1, 2). The directional derivative is the dot product ∇f · u = 4(3/5) + 1(4/5) = 12/5 + 4/5 = 3.2.

Question 33Engineering Mathematics

A random variable X follows a Poisson distribution with mean 2. The probability P(X = 0) equals

  1. 1 − e^(−2)
  2. e^(−2) Correct answer.
  3. 2e^(−2)
  4. e^(−1/2)

Explanation

The Poisson probability mass function is P(X = k) = e^(−λ) λ^k / k!. Setting λ = 2 and k = 0 gives P(X = 0) = e^(−2) ≈ 0.1353.

Question 34Engineering Mathematics

The residue of f(z) = e^z / (z − 1)² at the pole z = 1 is

  1. e Correct answer.
  2. 0
  3. e/2
  4. 1

Explanation

The pole at z = 1 is of order two, so the residue is the first derivative of the analytic numerator evaluated at the pole: d/dz(e^z) at z = 1 equals e. A double pole therefore contributes a nonzero residue unless the numerator vanishes to second order there.

Question 35Engineering Mathematics

The solution of the initial value problem y″ + 4y = 0 with y(0) = 1 and y′(0) = 0 is

  1. e^(−2x) cos 2x
  2. cosh 2x
  3. sin 2x
  4. cos 2x Correct answer.

Explanation

The characteristic equation r² + 4 = 0 gives r = ±2i, so y = A cos 2x + B sin 2x. The condition y(0) = 1 forces A = 1 and y′(0) = 2B = 0 forces B = 0, leaving y = cos 2x.

Question 36Engineering Mathematics

One step of the Newton–Raphson iteration applied to f(x) = x² − 2 with initial guess x₀ = 1 gives x₁ equal to

  1. 1.25
  2. 2.0
  3. 1.41421
  4. 1.5 Correct answer.

Explanation

The iteration is x₁ = x₀ − f(x₀)/f′(x₀). Here f(1) = −1 and f′(1) = 2, so x₁ = 1 − (−1)/2 = 1.5, which is a better approximation to √2 than the starting value.

Question 37Engineering Mathematics

For the vector field F = x²y i + yz j + z²x k, the divergence ∇ · F evaluated at the point (1, 1, 1) is

  1. 4
  2. 5 Correct answer.
  3. 3
  4. 6

Explanation

The divergence is the sum of partial derivatives: ∂(x²y)/∂x + ∂(yz)/∂y + ∂(z²x)/∂z = 2xy + z + 2zx. Substituting (1, 1, 1) gives 2 + 1 + 2 = 5.

Question 38Engineering Mathematics

The inverse Laplace transform of F(s) = 1/(s² + 4s + 5) is

  1. e^(−t) sin 2t
  2. e^(−2t) cos t
  3. e^(−2t) sin t Correct answer.
  4. e^(2t) sin t

Explanation

Completing the square gives s² + 4s + 5 = (s + 2)² + 1, which matches the standard pair 1/((s + a)² + ω²) ↔ e^(−at) sin ωt with a = 2 and ω = 1. Hence the inverse transform is e^(−2t) sin t.

Question 39Engineering Mathematics

The value of the real integral ∫₀^(2π) dθ/(5 + 4 cos θ) is

  1. π/3
  2. 2π/5
  3. 2π/3 Correct answer.
  4. 4π/3

Explanation

With z = e^(iθ) the integral becomes a contour integral over the unit circle whose only enclosed pole lies at z = −2 + √3. Evaluating the residue gives 2π/√(5² − 4²) = 2π/3, the standard result for ∫₀^(2π) dθ/(a + b cos θ).

Question 40Engineering Mathematics

The Fourier series of f(x) = x on the interval (−π, π) is evaluated at the endpoint x = π. By Dirichlet's theorem the series converges to

  1. π
  2. −π
  3. π/2
  4. 0 Correct answer.

Explanation

At a point where the periodic extension jumps, a Fourier series converges to the average of the one-sided limits. Here the right-hand limit is π and the left-hand limit is −π, so the series converges to (π − π)/2 = 0, not to the function value itself.

Question 41Engineering Mathematics

The rank of the matrix A = [[1, 2, 3], [2, 4, 6], [1, 1, 1]] is

  1. 1
  2. 0
  3. 2 Correct answer.
  4. 3

Explanation

The second row is exactly twice the first row, so it adds no new independent direction. The first and third rows are not scalar multiples of each other, so the row rank, and hence the rank, is two.

Question 42Engineering Mathematics

The limit lim_{x→0} sin(3x)/tan(5x) equals

  1. 0
  2. 5/3
  3. 1
  4. 3/5 Correct answer.

Explanation

Use the standard equivalents sin(3x) ≈ 3x and tan(5x) ≈ 5x as x tends to zero. Their ratio tends to 3/5, and the limit is finite and nonzero.

Question 43Engineering Mathematics

For the vector field F = y i − x j + 0 k, the curl ∇ × F is

  1. (0, 0, 2)
  2. (−2, 0, 0)
  3. (0, 0, 0)
  4. (0, 0, −2) Correct answer.

Explanation

Compute the curl componentwise: the z-component is ∂Q/∂x − ∂P/∂y = −1 − 1 = −2. The x- and y-components vanish because the field has no z-dependence, giving (0, 0, −2).

Question 44Engineering Mathematics

The general solution of the exact differential equation (2xy + y²) dx + (x² + 2xy) dy = 0 is

  1. xy + x²y² = C
  2. x²y + 2xy² = C
  3. x²y² + xy = C
  4. x²y + xy² = C Correct answer.

Explanation

Because M_y = 2x + 2y = N_x, the equation is exact. A potential function is F(x, y) = x²y + xy², so the level curves F = C give the general solution.

Question 45Engineering Mathematics

The contour integral ∮_{|z|=2} z²/(z − i) dz, taken counterclockwise, equals

  1. 0
  2. −2πi Correct answer.
  3. πi
  4. 2πi

Explanation

The integrand has a simple pole at z = i, which lies inside the circle |z| = 2. By Cauchy's integral formula, the integral is 2πi f(i) with f(z) = z², giving 2πi(−1) = −2πi.

Question 46Engineering Mathematics

If X is uniformly distributed on the interval [0, 2], then E[X²] equals

  1. 4/3 Correct answer.
  2. 8/3
  3. 2
  4. 1

Explanation

For a uniform density on [0, 2], f(x) = 1/2. Thus E[X²] = ∫₀² x²(1/2) dx = (1/2)(8/3) = 4/3.

Question 47Engineering Mathematics

Using the trapezoidal rule with two equal subintervals, the approximation of ∫₀² x² dx is

  1. 3 Correct answer.
  2. 8/3
  3. 4
  4. 2

Explanation

With n = 2, h = 1 and the nodes are 0, 1, 2, where x² takes values 0, 1, 4. The trapezoidal rule gives (h/2)[f(0) + 2f(1) + f(2)] = 0.5(0 + 2 + 4) = 3.

Question 48Engineering Mathematics

The solution of the heat problem u_t = 4u_xx on 0 < x < π, with u(0,t)=u(π,t)=0 and u(x,0)=sin(2x), is

  1. e^{−4t} sin(2x)
  2. e^{−16t} sin(2x) Correct answer.
  3. e^{−16t} sin(x)
  4. e^{−8t} sin(2x)

Explanation

Separation of variables gives modes e^{−4n²t} sin(nx) for integer n ≥ 1. The initial condition selects n = 2, so the exponent is −4(2²)t = −16t and the spatial factor is sin(2x).

Question 49Engineering Mathematics

For the 3×3 matrix A with entries a_{ij} = i^j for i, j = 1, 2, 3, det(A) equals

  1. 12 Correct answer.
  2. 24
  3. 0
  4. 6

Explanation

The matrix is [[1,1,1],[2,4,8],[3,9,27]]. Expanding along the first row gives 1(108−72) − 1(54−24) + 1(18−12) = 36 − 30 + 6 = 12.

Question 50Engineering Mathematics

If X and Y are independent standard normal random variables, then P(X² + Y² ≤ 1) equals

  1. e^{−1/2}
  2. 1 − e^{−1/2} Correct answer.
  3. 1/2
  4. 1 − e^{−1}

Explanation

The sum X² + Y² has a chi-square distribution with two degrees of freedom, which is exponential with rate 1/2. Hence P(X² + Y² ≤ 1) = 1 − e^{−(1/2)(1)} = 1 − e^{−1/2}.