GATE DA 2026 Question Paper with Solutions: 65 Questions, Answer Key & Section-wise Analysis

GATE DA 2026 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: 12 · Database Management and Warehousing: 11 · Programming, Data Structures and Algorithms: 9 · Machine Learning: 9 · Quantitative Aptitude: 6 · Linear Algebra: 5 · Artificial Intelligence: 5 · Verbal Aptitude: 3 · Calculus and Optimization: 2 · Analytical Aptitude: 2 · Spatial Aptitude: 1

Free sample questions from GATE DA 2026 Question Paper

Question 1 · Verbal Aptitude MCQ

Verbosity : Brevity :: Insolence :___________
Choose the word that best fills the blank.

A.
Innocence
B.
Respect
C.
Solace
D.
Wealth

Question 2 · Quantitative Aptitude MCQ

The product of the digits of a three-digit number is 70. The sum of the digits of this three-digit number is _____

A.
12
B.
14
C.
16
D.
18

Question 3 · Spatial Aptitude MCQ

The four pieces of a puzzle are shown in the figure below.

Which one of the figures labelled as P, Q, R, and S can be constructed by using each of the four pieces only once without overlaps?

A.
P
B.
Q
C.
R
D.
S

Question 4 · Quantitative Aptitude MCQ

Consider two distinct positive real numbers

m, n

, with

m > n

.
Let

x = n^{l o g_{10} (m)}

and

y = m^{l o g_{10} (n)}

. The relation between

x

and

y

is _______.

A.
$x > y$
B.
$x < y$
C.
$x = y$
D.
$x = lo g_{10} (y)$

Question 5 · Verbal Aptitude MCQ

‘If his latest movie had been a commercial success, the actor would have made enough money to sponsor his next movie.’
Based only on the above sentence, which one of the following statements is true?

A.
The actor will certainly sponsor his next movie.
B.
His latest movie was a commercial success.
C.
The actor made enough money from his latest movie.
D.
His latest movie was not commercially successful.

Question 6 · Verbal Aptitude MCQ

‘My friend and I parted __ the door __ the cabin that I had rented __ the night.’
Choose the option with the correct sequence of words to fill the blanks.

A.
at; of; for
B.
for; at; of
C.
of; for; in
D.
in; of; for

Question 7 · Quantitative Aptitude MCQ

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.
Ignoring permutations, the number of ways to pick these five integers is _____

A.
0
B.
1
C.
2
D.
3

Correct Answer:

Step-by-Step Solution

Key idea: This is a statistical constraint satisfaction question, recognisable because it asks to reconstruct a specific data set given its mean, median, and mode.

Step 1: Use the mean to find the sum. For 5 integers with a mean of 12, the sum is $5 \times 12 = 60$ .

Step 2: Use the median to fix the middle value. Sorting the 5 integers as $x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5}$ , the median is $x_{3}$ . Thus, $x_{3} = 18$ .

Step 3: Use the mode to fix the highest values. The mode is 20, meaning 20 must appear more frequently than any other number. Since $x_{3} = 18$ , the only way to include 20 is if $x_{4} = 20$ and $x_{5} = 20$ .

Step 4: Find the remaining sum. We have $x_{1} + x_{2} + 18 + 20 + 20 = 60$ , which simplifies to $x_{1} + x_{2} = 2$ .

Step 5: Find integer pairs for $x_{1}$ and $x_{2}$ . Since the integers are from 0 to 20 and $x_{1} \leq x_{2} \leq 18$ , the possible pairs summing to 2 are $(0, 2)$ and $(1, 1)$ .

Step 6: Apply the "single mode" constraint. If the pair is $(1, 1)$ , the set is ${1, 1, 18, 20, 20}$ , which has two modes (1 and 20). This violates the single mode condition. If the pair is $(0, 2)$ , the set is ${0, 2, 18, 20, 20}$ , which has a single mode of 20.

Answer: There is exactly 1 valid way to pick these integers.

Question 8 · Analytical Aptitude MCQ

Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:
(i) the first game was the only game where two students of the same class played against each other,
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.
The student who did not lose any game is __________.

A.
Pavan
B.
Rishi
C.
Swathi
D.
Tanvi

Correct Answer:

Step-by-Step Solution

Key idea: This is a constraint-based sequencing and elimination question, recognizable by the sequential games, elimination rules, and conditions on wins/classes.

Step 1: Understand the game format. There are 4 students and 3 games. A loser is eliminated. For all 4 students to play, the format must be: Game 1 (A vs B), Game 2 (Winner of G1 vs C), Game 3 (Winner of G2 vs D).

Step 2: Use condition (i). Game 1 is the ONLY game where two students of the same class played. The same-class pairs are (Rishi, Swathi) in Class 5 and (Pavan, Tanvi) in Class 4. Thus, Game 1 must be either (R, S) or (P, T).

Step 3: Test if Game 1 is (P, T). If Class 4 plays each other in G1, Class 4 wins G1. Condition (ii) states Class 5 won more games than Class 4. Since there are 3 games total, Class 5 must win 2 and Class 4 must win exactly 1. This means Class 5 must win G2 and G3. If Class 5 wins G2, the winner is R or S. Then Game 3 would be (R or S) vs the remaining (S or R), which is a same-class game. This violates condition (i). Thus, Game 1 cannot be (P, T).

Step 4: Test if Game 1 is (R, S). Game 1 is R vs S. Class 5 wins G1. To satisfy the quotas (Class 5 wins 2, Class 4 wins 1; Boys win 2, Girls win 1), Rishi (Boy) must win G1. If Swathi won, we would need 2 Boy wins from the remaining games, forcing Class 4 to win 2 games, violating (ii). So Rishi wins G1.

Step 5: Determine Game 2 and 3. Rishi plays Game 2 against Pavan or Tanvi. If Rishi loses G2, the Class 4 student wins, and Class 4 would end up winning 2 games total (violating ii). Thus, Rishi must win G2.

Step 6: Now Rishi has won G1 and G2 (2 Boy wins, 2 Class 5 wins). The quotas for Boys and Class 5 are fully met. Therefore, Game 3 must be won by a Girl from Class 4 to satisfy the remaining quotas (1 Girl win, 1 Class 4 win).

Step 7: Game 3 is Rishi vs Tanvi. Tanvi must win. Since Tanvi won her only game and didn't play before, she never lost any game.

Answer: D

Question 9 · Quantitative Aptitude MCQ

P, Q, R, S, X,

and

Y

are distinct single-digit whole numbers taking values from 0 to 9.

P Q

is a two-digit number with

Q

being in the units place and

P

in the tens place. Similarly,

R S

is a two-digit number.
It is known that

P Q

and

R S

are consecutive numbers and

(P Q)^{2} + (R S)^{2} = X Y P,

with

X Y P

being a three-digit number.
The value of

Y

is __________

A.
4
B.
5
C.
6
D.
7

Question 10 · Quantitative Aptitude MCQ

In the given figure,

P, Q,

and

R

are three points on a circle of radius 10 cm with

O

as its center,

\overline{P Q} = \overline{R Q}

, and

∠ P QR = 4 5^{\circ}

. The figure is representative.

The area of the shaded region

P QR O

is ______________

c m^{2}

A.
50
B.
$252$
C.
$502$
D.
100

Other GATE DA papers

GATE DA

Previous Year Papers

Verified Solutions Included

GATE DA 2026 Question Paper with Solutions: 65 Questions, Answer Key & Section-wise Analysis

GATE DA 2026 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

12 Qs

18% of total marks

Database Management and Warehousing

11 Qs

17% of total marks

Programming, Data Structures and Algorithms

9 Qs

14% of total marks

Machine Learning

9 Qs

14% of total marks

Quantitative Aptitude

6 Qs

9% of total marks

Linear Algebra

5 Qs

8% of total marks

Artificial Intelligence

5 Qs

8% of total marks

Verbal Aptitude

3 Qs

5% of total marks

Calculus and Optimization

2 Qs

3% of total marks

Analytical Aptitude

2 Qs

3% of total marks

Spatial Aptitude

1 Qs

2% of total marks

Free Solved Questions with Step-by-Step Solutions

Authentic examination problems with detailed derivations and answer keys.

Question 1

Verbosity : Brevity :: Insolence :___________Choose the word that best fills the blank.

Question 2

The product of the digits of a three-digit number is 70. The sum of the digits of this three-digit number is _____

Question 3

The four pieces of a puzzle are shown in the figure below. P Q R S Which one of the figures labelled as P, Q, R, and S can be constructed by using each of the four pieces only once without overlaps?

Question 4

Consider two distinct positive real numbers m, n, with m > n . Let x = n^{l o g_{10} (m)} and y = m^{l o g_{10} (n)} . The relation between x and y is _______.

Question 5

‘If his latest movie had been a commercial success, the actor would have made enough money to sponsor his next movie.’ Based only on the above sentence, which one of the following statements is true?

Question 6

‘My friend and I parted __ the door __ the cabin that I had rented __ the night.’ Choose the option with the correct sequence of words to fill the blanks.

Question 7

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20. Ignoring permutations, the number of ways to pick these five integers is _____

Question 8

Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that: (i) the first game was the only game where two students of the same class played against each other, (ii) the students of Class 5 won more games than the students of Class 4, and (iii) the boys won two games and the girls won one game. The student who did not lose any game is __________.

Question 9

P, Q, R, S, X, and Y are distinct single-digit whole numbers taking values from 0 to 9. P Q is a two-digit number with Q being in the units place and P in the tens place. Similarly, R S is a two-digit number. It is known that P Q and R S are consecutive numbers and (P Q)^{2} + (R S)^{2} = X Y P, with X Y P being a three-digit number. The value of Y is __________

Question 10

In the given figure, P, Q, and R are three points on a circle of radius 10 cm with O as its center, \overline{P Q} = \overline{R Q}, and ∠ P QR = 4 5^{\circ} . The figure is representative. 45° Q P R O The area of the shaded region P QR O is ______________c m^{2} .

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