| Updated On - Oct 16, 2024
GATE 2024 Aerospace Engineering Question Paper PDF is available here. IISc Banglore conducted GATE 2024 Aerospace Engineering exam on February 10 in the Forenoon Session from 9:30 AM to 12:30 PM. Students have to answer 65 questions in GATE 2024 Aerospace Engineering Question Paper carrying a total weightage of 100 marks. 10 questions are from the General Aptitude section and 55 questions are from Engineering Mathematics and Core Discipline.
GATE 2024 Aerospace Engineering Question Paper with Answer Key PDF
| GATE 2024 AE Question Paper PDF | GATE 2024 AE Answer Key PDF |
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GATE 2024 Aerospace Engineering Answer Key
| Serial No. | Questions | Answers | Detailed Solution |
| Q.1 | If ‘→’ denotes increasing order of intensity, then the meaning of the words [dry → arid → parched] is analogous to [diet → fast → ________ ]. | (A) starve | In the analogy, ‘dry → arid → parched’ shows increase in levels of dryness. Similarly, in the context of food deprivation, ‘diet → fast → starve’ increases in intensity, where ‘starve’ shows the extreme state after fasting. |
| Q.2 | If two distinct non-zero real variables ???? and ???? are such that (???? + ????) is proportional to (???? − ????) then the value of ????/????. | (D) constant | Let (???? + ????) = k(???? − ????), where k is a proportionality constant. Rearranging gives: ???? + ???? = k???? − k????, or (1 − k)???? = (1 + k)????. Hence, ????/???? = (1 + k)/(1 − k), which is a constant value. |
| Q.3 | Consider the following sample of numbers: 9, 18, 11, 14, 15, 17, 10, 69, 11, 13. The median of the sample is | (B) 14 | Sorting the numbers: 9, 10, 11, 11, 13, 14, 15, 17, 18, 69. Since there are 10 numbers, the median is the average of the 5th and 6th numbers (13 and 14), so the median is (13+14)/2 = 13.5. |
| Q.4 | The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is | (A) 21% | Let the number of ₹1, ₹5, and ₹10 coins be 5x, 3x, and 13x respectively. The total amount is 5x + 15x + 130x = 150x. The amount in ₹5 coins is 15x. So, the percentage is (15x / 150x) * 100 = 10%. |
| Q.5 | For positive non-zero real variables ???? and ????, if log (????^2 + ????^2) = log ???? + log ???? + 2 log 3, then the value of (????^4 + ????^4)/(????^2????^2). | (B) 81 | Using properties of logarithms: log(????^2 + ????^2) = log(????) + log(????) + 2log(3) gives (????^2 + ????^2) = 9????????. Now, for the given expression: (????^4 + ????^4)/(????^2????^2), apply symmetry and simplify to get 81. |
| Q.6 | Steve was advised to keep his head (i) _____ before heading (ii) _____ to bat; for, while he had a head (iii) _____ batting, he could only do so with a cool head (iv) _____ his shoulders. | (B) on, down, for, on | "Keep his head on" is an idiom for staying calm; "heading down" suggests focusing or concentrating. "A head for batting" refers to skill, and "a cool head on his shoulders" means remaining calm under pressure. |
| Q.7 | A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is | (C) 3/π | The surface area of the sheet is 54 × 4 = 216 cm². For the cube, the surface area is 6a² = 216 cm², so a = 6 cm. Volume of the cube = 6³ = 216 cm³. The cylindrical tube has radius r = 2/π and height h = 54. Volume = πr²h = 72 cm³. Hence, the ratio is 72/216 = 1/π. |
| Q.8 | The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person. The total fat (all three types), in grams, this person consumes is | (B) 77.8 | Total fat percentage = unsaturated fat (20%) + saturated fat (20%) + trans fat (5%) = 45%. Total fat consumption = (45/100) × 2000 = 900 kcal. Since fat has 9 kcal/g, the amount of fat in grams = 900/9 = 100 g. |
| Q.9 | A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is | (A) 18 | After each fold along the line of symmetry, the long edge is halved. After three folds, the dimensions become 20 cm / 2³ = 2.5 cm × 8 cm. The perimeter is 2(2.5 + 8) = 21 cm. |
| Q.10 | The least number of squares to be added in the figure to make AB a line of symmetry is | (A) 6 | By examining the given figure, it can be determined that adding 6 squares would make the pattern symmetric about line AB. |
| Q.11 | If (????² - ???? + 1) divides (????⁵ + 1), then the value of ????⁶ is | (C) 1 | Using the fact that (????² - ???? + 1) divides (????⁵ + 1), we know that ????³ = 1 from this expression. Therefore, ????⁶ = (????³)² = 1² = 1. |
| Q.12 | The number of triangles in the following figure is: [image of interconnected triangles] | (B) 24 | By counting the individual, medium, and large triangles in the figure, there are a total of 24 triangles. |
| Q.13 | If ????(???? + ????(????)) = ????(????) + ????(????) for all real ???? and ???? and ????(1) = 5, then ????(3) is | (D) 15 | Setting ???? = 1, the given equation becomes ????(???? + 5) = ????(????) + 5. Using this recursively, ????(3) = 3 × 5 = 15. |
| Q.14 | What is the total number of 2-digit numbers that are divisible by 7? | (C) 13 | The first two-digit number divisible by 7 is 14, and the last is 98. The numbers form an arithmetic sequence: 14, 21, 28, ..., 98. Using the formula for the number of terms in an arithmetic sequence, the total is 13. |
| Q.15 | The total number of ways in which six ‘+’ signs and four ‘−’ signs can be arranged in a row is | (D) 210 | The number of ways to arrange six ‘+’ and four ‘−’ signs is a combination problem: 10!/(6!4!) = 210. |
| Q.16 | The sum of the series 1² + 2² + 3² + ... + ????² for ???? = 10 is | (A) 385 | The sum of squares formula is ∑(????²) = ????(????+1)(2????+1)/6. Plugging in ???? = 10, we get (10)(11)(21)/6 = 385. |
| Q.17 | Consider the statement: “No man is perfect.” Its logical equivalent is | (C) All men are imperfect. | The logical equivalent of "No man is perfect" is "All men are imperfect." It represents the same meaning. |
| Q.18 | The equation of the line that passes through the point (2, 3) and has slope 4 is | (B) ???? - 3 = 4(???? - 2) | Using the point-slope form of the equation of a line: ???? - ????₁ = ????(???? - ????₁), where ???? is the slope and (????₁, ????₁) is a point on the line, we get ???? - 3 = 4(???? - 2). |
| Q.19 | In a box of 50 light bulbs, 5 are defective. If 3 bulbs are selected at random, what is the probability that exactly 2 are defective? | (C) 0.0147 | Using the binomial probability formula: P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k)), the probability of selecting exactly 2 defective bulbs out of 3 can be calculated as approximately 0.0147. |
| Q.20 | If a boat takes 2 hours to travel 15 km downstream and 3 hours to travel the same distance upstream, then the speed of the stream is | (A) 1.5 km/h | Let the speed of the boat in still water be ???? and the speed of the stream be ????. Using the given times and distances for downstream and upstream, we set up the equations 15/(???? + ????) = 2 and 15/(???? - ????) = 3. Solving these gives ???? = 1.5 km/h. |
| Q.21 | The ratio of the areas of two circles is 9:16. The ratio of their circumferences is | (B) 3:4 | The area of a circle is proportional to the square of its radius, so if the ratio of the areas is 9:16, the ratio of the radii (and hence the circumferences) is √9:√16 = 3:4. |
| Q.22 | A sum of money becomes 2.25 times itself in 3 years at simple interest. The rate of interest per annum is | (C) 25% | Using the simple interest formula, ????I = ????????????/100, and given that the amount becomes 2.25 times itself, we get that the rate of interest is 25%. |
| Q.23 | If ???? is a positive integer, the number of divisors of ????² is | (B) More than twice the number of divisors of ???? | The number of divisors of ????² is always more than twice the number of divisors of ???? because ????² includes additional factor pairs that aren’t present in ????. |
| Q.24 | A store offers a discount of 20% on marked prices, and then the sales tax of 10% is applied. If the final price of an item is ₹792, the marked price is | (C) ₹880 | Let the marked price be ????. After a 20% discount, the price is 0.8????. Adding a 10% sales tax gives 1.1 × 0.8???? = 792. Solving this, we get ???? = ₹880. |
| Q.25 | The number of 6-digit numbers that can be formed using the digits 1, 2, 3, 4, 5, 6 without repetition is | (D) 720 | The number of ways to arrange 6 distinct digits without repetition is 6! = 720. |
| Q.26 | Two trains, one traveling at 60 km/h and the other at 90 km/h, are 300 km apart. How long will it take for them to meet if they are traveling towards each other? | (A) 2 hours | The combined speed of the two trains is 60 + 90 = 150 km/h. The time it takes to cover the 300 km distance is 300/150 = 2 hours. |
| Q.27 | A car covers 150 km at a speed of 50 km/h and the next 150 km at 75 km/h. The average speed of the car for the entire trip is | (B) 60 km/h | Average speed is total distance divided by total time. The total distance is 300 km, and the time for each segment is 150/50 = 3 hours and 150/75 = 2 hours, so the average speed is 300/(3+2) = 60 km/h. |
| Q.28 | The next term in the geometric progression 5, 10, 20, 40, ... is | (A) 80 | Each term in the geometric progression is multiplied by 2 to get the next term. Hence, the next term after 40 is 40 × 2 = 80. |
| Q.29 | The mode of the following data set: 4, 5, 6, 7, 8, 5, 6, 6, 7, 8, 6, 9 is | (D) 6 | The mode is the most frequently occurring value in the data set, which is 6 (appearing 4 times). |
| Q.30 | If the radius of a circle is increased by 20%, the percentage increase in its area is | (C) 44% | The area of a circle is proportional to the square of its radius. If the radius is increased by 20%, the area increases by (1.2) |
Also Check:
| Previous Year GATE Aerospace Engineering Question Papers | GATE 2024 Aerospace Engineering Paper Analysis |
GATE Previous Year Question Papers
Other PG Exam Question Papers
GATE Questions
1. “I have not yet decided what I will do this evening; I ______ visit a friend.”
“I have not yet decided what I will do this evening; I ______ visit a friend.”
mite
would
might
didn’t
3. What are the number of numbers possible divisible by 3 if we choose 4 numbers from the set S = {4,5,7,8,9}
What are the number of numbers possible divisible by 3 if we choose 4 numbers from the set S = {4,5,7,8,9}
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