Aptitude GATE previous year questions with answer
Ques 1 Gate 2024 Set-1
If ‘→’ denotes increasing order of intensity, then the meaning of the words
[dry → arid → parched] is analogous to [diet → fast → ________ ].
Which one of the given options is appropriate to fill the blank?
dry → arid → parched shows increasing intensity of dryness.
Similarly, we need increasing intensity in:
diet → fast → ________
diet = controlled eating
fast = no eating for a period
starve = extreme lack of food (highest intensity)
So the correct order is:
diet → fast → starve
And the correct option is (a) starve.
Ques 2 Gate 2024 Set-1
If two distinct non-zero real variables 𝑥 and 𝑦 are such that (𝑥 + 𝑦) is proportional to (𝑥 − 𝑦) then the value of (𝑥/𝑦)
If (x + y) is proportional to (x − y), then:
x + y = k(x − y)
Solving:
x + y = kx − ky
x − kx = −ky − y
x(1 − k) = −y(k + 1)
So,
x/y = (k + 1) / (k − 1)
This value depends only on the constant k, not on x or y.
Therefore, x/y is a constant.
Ques 3 Gate 2024 Set-1
Consider the following sample of numbers:
9, 18, 11, 14, 15, 17, 10, 69, 11, 13
The median of the sample is
Sorted Order:
9, 10, 11, 11, 13, 14, 15, 17, 18, 69
Total Numbers: 10 (Even count)
Median Calculation:
Average of 5th and 6th terms → (13 + 14) / 2 = 13.5
Correct Answer: A) 13.5
Ques 4 Gate 2024 Set-1
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
Ratio of number of coins = 5 : 3 : 13
Let the number of coins be:
₹1 coins = 5k
₹5 coins = 3k
₹10 coins = 13k
Total value from each denomination:
Value from ₹1 coins = 5k × 1 = ₹5k
Value from ₹5 coins = 3k × 5 = ₹15k
Value from ₹10 coins = 13k × 10 = ₹130k
Total amount:
Total = 5k + 15k + 130k = ₹150k
Percentage from ₹5 coins:
Percentage = (15k / 150k) × 100
Percentage = (15 / 150) × 100
Percentage = (1 / 10) × 100
Percentage = 10%
Answer: C) 10%
Ques 5 Gate 2024 Set-1
For positive non-zero real variables 𝑝 and 𝑞, if
log (𝑝2 + 𝑞2) = log 𝑝 + log 𝑞 + 2 log 3 ,
then, the value of (𝑝4+𝑞4)/(𝑝2𝑞2) is
Simplifing the given equation using logarithm properties:
log(p² + q²) = log p + log q + 2 log 3
log(p² + q²) = log p + log q + log 3²
log(p² + q²) = log(pq) + log 9
log(p² + q²) = log(9pq)
Since log(p² + q²) = log(9pq), we have:
p² + q² = 9pq
We need to find (p⁴ + q⁴)/(p²q²)
Let's use the identity: p⁴ + q⁴ = (p² + q²)² - 2p²q²
(p² + q²)²:
From Step 2: p² + q² = 9pq
(p² + q²)² = (9pq)²
(p² + q²)² = 81p²q²
Calculating p⁴ + q⁴:
p⁴ + q⁴ = (p² + q²)² - 2p²q²
p⁴ + q⁴ = 81p²q² - 2p²q²
p⁴ + q⁴ = 79p²q²
The final value:
(p⁴ + q⁴)/(p²q²) = 79p²q² / p²q²
(p⁴ + q⁴)/(p²q²) = 79
Answer: A) 79
Ques 6 Gate 2024 Set-1
In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks.
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.
For each blank with common English idioms:
Blank (i): "keep his head ___"
• "keep his head down" = stay calm, stay focused, avoid attention
✓ Answer: down
Blank (ii): "heading ___ to bat"
• "heading out" = going out, moving forward to do something
• This is the natural phrase for going to bat
✓ Answer: out
Blank (iii): "had a head ___ batting"
• "have a head for" = have a natural talent or aptitude for something
✓ Answer: for
Blank (iv): "cool head ___ his shoulders"
• "head on his shoulders" = sensible, level-headed thinking
✓ Answer: on
Answer: C) (i) down (ii) out (iii) for (iv) on
Ques 7 Gate 2024 Set-1
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
Given: Rectangle dimensions = 54 cm × 4 cm
Area of rectangular sheet = 54 × 4 = 216 cm²
Form the cylinder
When the two longer edges (54 cm) are joined:
• The 4 cm side wraps around to form the circumference
• Height of cylinder = 54 cm
• Circumference = 4 cm
Radius of cylinder
2πr = 4
r = 2/π cm
Volume of cylinder
Volume = πr²h
Volume = π × (2/π)² × 54
Volume = π × (4/π²) × 54
Volume = 216/π cm³
Side of cube
Surface area of cube = 6a² = 216
a² = 36
a = 6 cm
Volume of cube = a³ = 6³ = 216 cm³
Ratio = (216/π) ÷ 216
Ratio = 216/(216π)
Ratio = 1/π
Answer: A) 1/π
Ques 8 Gate 2024 Set-1
The pie chart presents the percentage contribution of different macronutrients to a
typical 2,000 kcal diet of a person.
Ques 9 Gate 2024 Set-1
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
Ques 10 Gate 2024 Set-1
The least number of squares to be added in the figure to make AB a line of symmetry is
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