GATE DA 2025 Question Paper with Solutions: 65 Questions, Answer Key & Section-wise Analysis

GATE DA 2025 previous year paper: 65 questions with answer key and detailed solutions, section-wise breakdown and free sample questions.

Paper breakdown

65 questions · 100 marks · 3 minutes. Probability and Statistics: 13 · Programming, Data Structures and Algorithms: 9 · Linear Algebra: 9 · Machine Learning: 7 · Database Management and Warehousing: 7 · Calculus and Optimization: 6 · Quantitative Aptitude: 4 · Verbal Aptitude: 3 · Artificial Intelligence: 3 · Spatial Aptitude: 2 · Analytical Aptitude: 2

Free sample questions from GATE DA 2025 Question Paper

Question 1 · Verbal Aptitude MCQ

Courage : Bravery :: Yearning : __________

Select the most appropriate option to complete the analogy.

A.
Longing
B.
Yelling
C.
Yawning
D.
Glaring

Question 2 · Verbal Aptitude MCQ

We __________ tennis in the lawn when it suddenly started to rain.

Select the most appropriate option to complete the above sentence.

A.
have been playing
B.
had been playing
C.
would have been playing
D.
could be playing

Question 3 · Quantitative Aptitude MCQ

4 \times 4

digital image has pixel intensities

(U)

as shown in the figure. The number of pixels with

U \leq 4

is:

A.
3
B.
8
C.
11
D.
9

Correct Answer:

Step-by-Step Solution

Key idea: This is a systematic counting question on a matrix, recognisable because it provides a grid of numerical values and asks for the count of cells satisfying a specific inequality condition.

Step 1: Identify the condition. We need to count cells where the pixel intensity U \leq 4.

Step 2: Examine each row systematically.

Row 1: 0, 1, 0, 2 (All 4 values are \leq 4) -> Count = 4
Row 2: 4, 7, 3, 3 (4, 3, 3 are \leq 4) -> Count = 3
Row 3: 5, 5, 4, 4 (4, 4 are \leq 4) -> Count = 2
Row 4: 6, 7, 3, 2 (3, 2 are \leq 4) -> Count = 2

Step 3: Sum the counts. Total = 4 + 3 + 2 + 2 = 11.

Answer: C

Question 4 · Spatial Aptitude MCQ

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are

1, 2,

and

3

, respectively. Which one among the given options is the most appropriate combination of

P, Q,

and

R

A.
$P = 6; Q = 5; R = 3$
B.
$P = 5; Q = 6; R = 3$
C.
$P = 3; Q = 6; R = 6$
D.
$P = 5; Q = 3; R = 6$

Question 5 · Quantitative Aptitude MCQ

A rectangle has a length $L$ and a width $W$ , where $L > W$ . If the width, $W$ , is increased by $10%$ , which one of the following statements is correct for all values of $L$ and $W$ ?

A.
Perimeter increases by $10%$ .
B.
Length of the diagonals increases by $10%$ .
C.
Area increases by $10%$ .
D.
The rectangle becomes a square.

Question 6 · Verbal Aptitude MCQ

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.

Column-I	Column-II
P. This house is in a mess.	1. Alright, I won’t bring it up during our conversations.
Q. I am not happy with the marks given to me.	2. Well, you can easily look it up.
R. Politics is a subject I avoid talking about.	3. No problem, let me clear it up for you.
S. I don’t know what this word means.	4. Don’t worry, I will take it up with your teacher.

Identify the option that has the correct match between Column-I and Column-II.

A.
P – 2; Q – 3; R – 1; S – 4
B.
P – 3; Q – 4; R – 1; S – 2
C.
P – 4; Q – 1; R – 2; S – 3
D.
P – 1; Q – 2; R – 4; S – 3

Question 7 · Analytical Aptitude MCQ

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of

50

years and then it monotonically decreases. Let

a_{1}

and

a_{2}

(in years) denote the ages of the brothers and

a_{1} < a_{2}

.
Which one of the following statements is correct about their age on the day when they attain the same weight?

A.
$a_{1} < a_{2} < 50$
B.
$a_{1} < 50 < a_{2}$
C.
$50 < a_{1} < a_{2}$
D.
Either $a_{1} = 50$ or $a_{2} = 50$

Correct Answer:

Step-by-Step Solution

Key idea: This is a monotonicity-based logical deduction question, recognizable by the function's trend (increasing then decreasing) and the equality of outputs for two different inputs.

Step 1: Understand the function's behavior. The weight function $W (a)$ monotonically increases for $a \leq 50$ and monotonically decreases for $a > 50$ . This creates a single peak at $a = 50$ .

Step 2: Analyze the condition $W (a_{1}) = W (a_{2})$ with $a_{1} < a_{2}$ .

Step 3: Evaluate the positions of $a_{1}$ and $a_{2}$ relative to the peak.

If both $a_{1} < a_{2} \leq 50$ , they lie on the monotonically increasing segment. For a strictly monotonic function, $W (a_{1}) < W (a_{2})$ , so they cannot be equal.

If both $50 \leq a_{1} < a_{2}$ , they lie on the monotonically decreasing segment. Similarly, $W (a_{1}) > W (a_{2})$ , so they cannot be equal.

Step 4: The only way for $W (a_{1}) = W (a_{2})$ with $a_{1} \neq = a_{2}$ is if one age is on the increasing slope and the other is on the decreasing slope.

Step 5: Since $a_{1} < a_{2}$ , it must be that $a_{1} < 50$ and $a_{2} > 50$ .

Step 6: This matches the condition $a_{1} < 50 < a_{2}$ .

Answer: B

Question 8 · Spatial Aptitude MCQ

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius

r

cm as shown in the figure. The side of the dodecagon is

d

cm. All the triangles (numbered 1 to 12) in the figure are used to form squares of side

r

cm and each numbered triangle is used only once to form a square.
The number of squares that can be formed and the number of triangles required to form each square, respectively, are:

Note: The figure shown is representative.

A.
3; 4
B.
4; 3
C.
3; 3
D.
3; 2

Question 9 · Quantitative Aptitude MCQ

If a real variable $x$ satisfies $3^{x^{2}} = 27 \times 9^{x}$ , then the value of $\frac{2 ^{x^{2}}}{( 2 ^{x} ) ^{2}}$ is:

A.
$2^{- 1}$
B.
$2^{0}$
C.
$2^{3}$
D.
$2^{15}$

Question 10 · Quantitative Aptitude MCQ

The number of patients per shift

(X)

consulting Dr. Gita in her past

100

shifts is shown in the figure. If the amount she earns is ₹

1000 (X - 0.2)

, what is the average amount (in ₹) she has earned per shift in the past

100

shifts?

Note: The figure shown is representative.

A.
6,100
B.
6,300
C.
6,000
D.
6,500

Correct Answer:

Step-by-Step Solution

Key idea: This is a weighted average and linear transformation question, recognisable because it gives a frequency distribution (bar chart) and asks for the average of a linear function of the variable.

Step 1: Calculate the total number of patients across all shifts. From the chart: (5 20) + (6 40) + (7 30) + (8 10) = 100 + 240 + 210 + 80 = 630.

Step 2: Calculate the average number of patients per shift, \bar{X}. \bar{X} = 630 / 100 = 6.3.

Step 3: Apply the linear transformation for earnings. The average earnings per shift is 1000(\bar{X} - 0.2).

Step 4: Substitute \bar{X}: 1000(6.3 - 0.2) = 1000(6.1) = 6100.

Answer: A

Other GATE DA papers

GATE DA

Previous Year Papers

Verified Solutions Included

GATE DA 2025 Question Paper with Solutions: 65 Questions, Answer Key & Section-wise Analysis

GATE DA 2025 previous year paper: 65 questions with answer key and detailed solutions, section-wise breakdown and free sample questions.

65 Qs

Total Questions

100 Marks

Total Marks

3 Mins

Duration

+3 / -1 / 0

Marking Scheme

Section-wise Paper Structure

Probability and Statistics

13 Qs

20% of total marks

Programming, Data Structures and Algorithms

9 Qs

14% of total marks

Linear Algebra

9 Qs

14% of total marks

Machine Learning

7 Qs

11% of total marks

Database Management and Warehousing

7 Qs

11% of total marks

Calculus and Optimization

6 Qs

9% of total marks

Quantitative Aptitude

4 Qs

6% of total marks

Verbal Aptitude

3 Qs

5% of total marks

Artificial Intelligence

3 Qs

5% of total marks

Spatial Aptitude

2 Qs

3% of total marks

Analytical Aptitude

2 Qs

3% of total marks

Free Solved Questions with Step-by-Step Solutions

Authentic examination problems with detailed derivations and answer keys.

Question 1

Courage : Bravery :: Yearning : __________Select the most appropriate option to complete the analogy.

Question 2

We __________ tennis in the lawn when it suddenly started to rain. Select the most appropriate option to complete the above sentence.

Question 3

A 4 \times 4 digital image has pixel intensities (U) as shown in the figure. The number of pixels with U \leq 4 is: 0102473355446732

Question 4

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ? 1243 P Q R

Question 5

A rectangle has a length L and a width W, where L > W . If the width, W, is increased by 10%, which one of the following statements is correct for all values of L and W ?

Question 6

Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk. Column-I Column-II P. This house is in a mess. 1. Alright, I won’t bring it up during our conversations. Q. I am not happy with the marks given to me. 2. Well, you can easily look it up. R. Politics is a subject I avoid talking about. 3. No problem, let me clear it up for you. S. I don’t know what this word means. 4. Don’t worry, I will take it up with your teacher. Identify the option that has the correct match between Column-I and Column-II.

Question 7

Weight of a person can be expressed as a function of their age. The function usually varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let a_{1} and a_{2} (in years) denote the ages of the brothers and a_{1} < a_{2} . Which one of the following statements is correct about their age on the day when they attain the same weight?

Question 8

A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as shown in the figure. The side of the dodecagon is d cm. All the triangles (numbered 1 to 12) in the figure are used to form squares of side r cm and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are: Note: The figure shown is representative. 12345678910

Question 9

If a real variable x satisfies 3^{x^{2}} = 27 \times 9^{x}, then the value of \frac{2 ^{x^{2}}}{( 2 ^{x} ) ^{2}} is:

Question 10

The number of patients per shift (X) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ 1000 (X - 0.2), what is the average amount (in ₹) she has earned per shift in the past 100 shifts? Note: The figure shown is representative. 20403010010203040505678 Number of patients per shift (X) Number of shifts

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