CS and IT Gate 2024 Set-1 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?

starve

reject

feast

deny

(a) is the correct answer.

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)

depends on 𝑥𝑦

depends only on 𝑥 and not on 𝑦

depends only on 𝑦 and not on 𝑥

is a constant

(d) is the correct answer.

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

13.5

18.7

(a) is the correct answer.

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

21%

14(2/7) %

10%

30%

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

(a) is the correct answer.

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.

(i) down (ii) down (iii) on (iv) for

(i) on (ii) down (iii) for (iv) on

(i) down (ii) out (iii) for (iv) on

(i) on (ii) out (iii) on (iv) for

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

1/π

2/π

3/π

4/π

(a) is the correct answer.

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.

The typical energy density (kcal/g) of these macronutrients is given in the table.

The total fat (all three types), in grams, this person consumes is

44.4

77.8

100

3,600

(a) is the correct answer.

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

(a) is the correct answer.

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

(a) is the correct answer.

Ques 11 Gate 2024 Set-1

Consider the following C program:

Which one of the following statements is CORRECT?

The program prints 9 as output

The program prints 10 as output

The program gets stuck in an infinite loop

The program prints 6 as output

(a) is the correct answer.

Ques 12 Gate 2024 Set-1

Consider the following C program:

Assume that the input to the program from the command line is 1234 followed by a newline character. Which one of the following statements is CORRECT?

The program will not terminate

The program will terminate with no output

The program will terminate with 4321 as output

The program will terminate with 1234 as output

(a) is the correct answer.

Ques 13 Gate 2024 Set-1

A user starts browsing a webpage hosted at a remote server. The browser opens a single TCP connection to fetch the entire webpage from the server. The webpage consists of a top-level index page with multiple embedded image objects. Assume that all caches (e.g., DNS cache, browser cache) are all initially empty. The following packets leave the user’s computer in some order.
(i) HTTP GET request for the index page
(ii) DNS request to resolve the web server’s name to its IP address
(iii) HTTP GET request for an image object
(iv) TCP SYN to open a connection to the web server
Which one of the following is the CORRECT chronological order (earliest in time to latest) of the packets leaving the computer ?

(iv), (ii), (iii), (i)

(ii), (iv), (iii), (i)

(ii), (iv), (i), (iii)

(iv), (ii), (i), (iii)

(a) is the correct answer.

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