GATE AE Analytical & Spatial Reasoning: Previous Year Questions

GATE AE 2026, Question 2 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

In the sequence of tiles shown below, the missing tile indicated by the question mark should be

Official answer: B

GATE AE 2026, Question 7 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

1. Only (i) can correspond to the unfolded cube in Panel I.
2. Only (ii) can correspond to the unfolded cube in Panel I.
3. Both (i) and (ii) can correspond to the unfolded cube in Panel I.
4. Neither (i) nor (ii) can correspond to the unfolded cube in Panel I.

Official answer: A

GATE AE 2026, Question 8 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Consider the cube shown below with its 8 corners labelled a, b, c, d, e, f, g, and h. The figure is representative. All corners are to be colored such that any two corners that are connected by an edge must be of different colors. The minimum number of colors required to achieve this is ________

1. 8
2. 4
3. 3
4. 2

Official answer: D

GATE AE 2026, Question 9 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Four hills H1, H2, H3, and H4 are present in an area. The following observations are made about them: i. Neither H2 nor H3 is the easternmost hill. ii. Neither H2 nor H3 is the westernmost hill. iii. Neither the easternmost hill nor the westernmost hill is the southernmost hill. iv. Two hills are located to the west of H2. v. The southernmost hill has at least two hills to its east. The southernmost hill is ________.

1. H1
2. H2
3. H3
4. H4

Official answer: C

GATE AE 2026, Question 10 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

As shown in the figure, circle $C_1$ with center $O_1$ and radius $r_1$ touches the square $VWXY$ at points $P$ and $Q$ while circle $C_2$ with center $O_2$ and radius $r_2$ touches the square $VWXY$ at points $R$ and $S$. The two circles touch each other at $T$. Given $r_1 = 1$ cm and $\overline{VY} = \overline{VW} = 4$ cm, $r_2 =$ ______ cm.

1. $4 - 3\sqrt{2}$
2. $1 + 2\sqrt{2}$
3. $7 - 4\sqrt{2}$
4. $5 + 3\sqrt{2}$

Official answer: C

GATE AE 2025, Question 3 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

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

1. 3
2. 8
3. 11
4. 9

Official answer: C

GATE AE 2025, Question 8 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

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.

1. 3; 4
2. 4; 3
3. 3; 3
4. 3; 2

Official answer: A

GATE AE 2024, Question 8 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

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: $$\begin{array}{|l|c|}\hline \text{Macronutrient} & \text{Energy density (kcal/g)} \\ \hline \text{Carbohydrates} & 4 \\ \text{Proteins} & 4 \\ \text{Unsaturated fat} & 9 \\ \text{Saturated fat} & 9 \\ \text{Trans fat} & 9 \\ \hline\end{array}$$ The total fat (all three types), in grams, this person consumes is

1. 44.4
2. 77.8
3. 100
4. 3,600

Official answer: C

GATE AE 2024, Question 10 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

The least number of squares to be added in the figure to make AB a line of symmetry is

1. 6
2. 4
3. 5
4. 7

Official answer: A

GATE AE 2023, Question 3 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)

1. $\dfrac{20}{7}$
2. $\dfrac{28}{5}$
3. $\dfrac{9}{2}$
4. $\dfrac{35}{4}$

Official answer: B

GATE AE 2023, Question 4 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics. When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college. Based only on the above information, which one of the following statements can be logically inferred with certainty?

1. Every Fields medalist has won a medal in an International Mathematics Olympiad.
2. Everyone who has dropped out of college has won the Fields medal.
3. All Fields medalists are part-time poets.
4. Some Fields medalists have dropped out of college.

Official answer: D

GATE AE 2023, Question 5 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image of the other part about that line. The given figure consists of 16 unit squares arranged as shown. In addition to the three black squares, what is the minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (The figure is representative)

1. 3
2. 4
3. 5
4. 6

Official answer: C

GATE AE 2023, Question 6 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Human beings are one among many creatures that inhabit an imagined world. In this imagined world, some creatures are cruel. If in this imagined world, it is given that the statement “Some human beings are not cruel creatures” is FALSE, then which of the following set of statement(s) can be logically inferred with certainty? (i) All human beings are cruel creatures. (ii) Some human beings are cruel creatures. (iii) Some creatures that are cruel are human beings. (iv) No human beings are cruel creatures.

1. only (i)
2. only (iii) and (iv)
3. only (i) and (ii)
4. (i), (ii) and (iii)

Official answer: D

GATE AE 2022, Question 2 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Which one of the following is a representation (not to scale and in bold) of all values of $x$ satisfying the inequality $2 - 5x \le -\dfrac{6x-5}{3}$ on the real number line?

Official answer: C

GATE AE 2022, Question 5 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other? (rotation and translation operations may be used).

GATE AE 2022, Question 9 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Four cities P, Q, R and S are connected through one-way routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train. If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?

1. 6 hours 30 minutes
2. 3 hours 45 minutes
3. 4 hours 30 minutes
4. 5 hours 15 minutes

Official answer: A

GATE AE 2022, Question 10 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet. What is the ratio of the areas of unshaded regions of case M to that of case N?

1. 2 : 3
2. 1 : 1
3. 3 : 2
4. 2 : 1

Official answer: B

GATE AE 2018, Question 10 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head and T stands for tail, the following are the observations from the four trials: (1) HTHTHT (2) TTHHHT (3) HTTHHT (4) HHHT__ __. Which statement describing the last two coin tosses of the fourth trial has the highest probability of being correct?

1. Two T will occur.
2. One H and one T will occur.
3. Two H will occur.
4. One H will be followed by one T.

Official answer: B

GATE AE 2016, Question 4 (1 mark, MCQ)

General Aptitude - Analytical & Spatial Reasoning

R2D2 is a robot. R2D2 can repair aeroplanes. No other robot can repair aeroplanes. Which of the following can be logically inferred from the above statements?

1. R2D2 is a robot which can only repair aeroplanes.
2. R2D2 is the only robot which can repair aeroplanes.
3. R2D2 is a robot which can repair only aeroplanes.
4. Only R2D2 is a robot.

Official answer: B

GATE AE 2016, Question 6 (2 marks, NAT)

General Aptitude - Analytical & Spatial Reasoning

The following graph represents the installed capacity for cement production (in tonnes) and the actual production (in tonnes) of nine cement plants of a cement company. Capacity utilization of a plant is defined as ratio of actual production of cement to installed capacity. A plant with installed capacity of at least 200 tonnes is called a large plant and a plant with lesser capacity is called a small plant. The difference between total production of large plants and small plants, in tonnes is ____.

Official answer: 120

GATE AE 2016, Question 7 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

A poll of students appearing for masters in engineering indicated that 60 % of the students believed that mechanical engineering is a profession unsuitable for women. A research study on women with masters or higher degrees in mechanical engineering found that 99 % of such women were successful in their professions. Which of the following can be logically inferred from the above paragraph?

1. Many students have misconceptions regarding various engineering disciplines.
2. Men with advanced degrees in mechanical engineering believe women are well suited to be mechanical engineers.
3. Mechanical engineering is a profession well suited for women with masters or higher degrees in mechanical engineering.
4. The number of women pursuing higher degrees in mechanical engineering is small.

Official answer: C

GATE AE 2014, Question 7 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

Anuj, Bhola, Chandan, Dilip, Eswar and Faisal live on different floors in a six-storeyed building (the ground floor is numbered 1, the floor above it 2, and so on). Anuj lives on an even-numbered floor. Bhola does not live on an odd numbered floor. Chandan does not live on any of the floors below Faisal's floor. Dilip does not live on floor number 2. Eswar does not live on a floor immediately above or immediately below Bhola. Faisal lives three floors above Dilip. Which of the following floor-person combinations is correct?

Official answer: B

GATE AE 2014, Question 10 (2 marks, MCQ)

General Aptitude - Analytical & Spatial Reasoning

The monthly rainfall chart based on 50 years of rainfall in Agra is shown in the following figure. Which of the following are true? ($k$ percentile is the value such that $k$ percent of the data fall below that value) (i) On average, it rains more in July than in December. (ii) Every year, the amount of rainfall in August is more than that in January. (iii) July rainfall can be estimated with better confidence than February rainfall. (iv) In August, there is at least 500 mm of rainfall.

1. (i) and (ii)
2. (i) and (iii)
3. (ii) and (iii)
4. (iii) and (iv)

Official answer: B