General Aptitude- 1 | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

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Q1: Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is [GATE CE 2024 SET-2]
(a) 60º
(b) 180º
(c) 120º
(d) 90º
Ans: (c)
When the cube is rotated that is held with one of the four body diagonals aligned to the vertical axis

Q2: Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction X, the planar image of the assembly appears as Figure B.

If viewed from direction Y, the planar image of the assembly (Figure A) will appear as  [GATE CE 2024 SET-2]

(a)
(b)
(c)
(d)
Ans: (a)

Q3: The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true?  [GATE CE 2024 SET-2]
(a) The risk reduction on increasing the steps/ day from 0 to 10000 is less than the risk reduction on increasing the steps/day from 10000 to 20000.
(b) The risk reduction on increasing the steps/ day from 0 to 5000 is less than the risk reduction on increasing the steps/day from 15000 to 20000.
(c) For any 5000 increment in steps/day the largest risk reduction occurs on going from 0 to 5000.
(d) For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000.
Ans: (c)
Risk reduction value $(0-5000)$
= 1 − 0.45$=0.55$
which is maximum.

Q4: Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.

The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is  [GATE CE 2024 SET-2]
(a) 5/2
(b) 7/2
(c) 9/2
(d) 3
Ans: (b)

Let the radius of cylinder = R and the radius of chalk = r
2r + 2r + 2r = 2R
r = (R/3)
Volume of cylinder = πR²h
Volume of chalk =

= (7/9)/(2/9) = 7/2.

Q5: In the given text, the blanks are numbered (i)−(iv). Select the best match for all the blanks.  [GATE CE 2024 SET-2]
Yoko Roi stands ___(i)____ as an author for standing ___(ii)___ as an honorary fellow, after she stood ___(iii)___ her writings that stand ___(iv)___ the freedom of speech.
(a) (i) out (ii) down (iii) in (iv) for
(b) (i) down (ii) out (iii) by (iv) in
(c) (i) down (ii) out (iii) for (iv) in
(d) (i) out (ii) down (iii) by (iv) for
Ans: (d)

Q6: The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360, respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is  [GATE CE 2024 SET-2]
(a) 150
(b) 200
(c) 250
(d) 175
Ans: (b)
Let no. of girls in 8^th = no. of girls in 9^th = x

x² = (450 − x)(360 − x)
x² = 16200 − 450x − 360x + x²
x = 16200/810
= 200

Q7: If the sum of the first 20 consecutive positive odd numbers is divided by 20², the result is [GATE CE 2024 SET-2]
(a) 1
(b) 20
(c) 2
(d) 01-Feb
Ans: (a) 
1 + 3 = 4 = 2²
1 + 3 + 5 = 9 = 3²
1 + 3 + 5 + 7 = 4²
(1 + 3 + 5 + 4 .. 2 times) = 20²
20²/20² = 1

Q8: A student was supposed to multiply a positive real number p with another positive real number q. Instead, the student divided p by q. If the percentage error in the student’s answer is 80%, the value of q is  [GATE CE 2024 SET-2]
(a) 5
(b) √2
(c) 2
(d) √5
Ans: (d)
Actual result = pq
wrong result = pq
Wrong result/Actual result = 0.2 (result reduced by 80%)


Q9: Statements:
1. All heroes are winners.
2. All winners are lucky people.
Inferences:
I. All lucky people are heroes.
II. Some lucky people are heroes.
III. Some winners are heroes.
Which of the above inferences can be logically deduced from statements 1 and 2?  [GATE CE 2024 SET-2]
(a) Only I and II
(b) Only II and III
(c) Only I and III
(d) Only III
Ans: (b)
From above Venn diagram its clear that (ii) and (iii) are valid deductions.

Q10: If → denotes increasing order of intensity, then the meaning of the words [drizzle → rain → downpour] is analogous to [ ______ → quarrel → feud].
Which one of the given options is appropriate to fill the blank?  [GATE CE 2024 SET-2]
(a) bicker
(b) bog
(c) dither
(d) dodge
Ans: (a) 
Drizzle means intermittant rain
Downpour means heavy rain
Quarrel means an angry argument
Feud means an angry and bitter argument
Bicker means to argue about things that are not important.
Now its very clear that
drizzle $\to$→ rain $\to$→ downpour is analogous to bicker $\to$→ quarrel $\to$→ feud

Q11: During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-EarthSun angle at this half-moon phase is measured to be 89.85º, the ratio of the Earth-Sun and Earth-Moon distances is closest to  [GATE CE 2024 SET-1]
(a) 328
(b) 382
(c) 238
(d) 283
Ans: (b)
The distance from the earth to the moon = 240000 mile (estimated)
cos 89.85 = 240000/SE
SE = 91673351.94 mile 
= 381.97 = 382

Q12: In the 4 × 4 array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.

Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top. bottom, diagonals).
As per this rule, the maximum number of crosses possible in the empty column is  [GATE CE 2024 SET-1]
(a) 0
(b) 1
(c) 2
(d) 3
Ans: (c)

Q13: The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3 and T4 and their Electricity Generation (MWh) in a time of 1000 hours (h).

The capacity factor of a power generation technology is:
Capacity Factor = Electrivity Generation (MM)/Installed Capacity (MW)×1000( h)
Which one of the given technologies has the highest Capacity Factor?  [GATE CE 2024 SET-1]
(a) T1
(b) T2
(c) T3
(d) T4
Ans: (a)
Capacity factor of T1 =

Capacity factor of T2 =

Capacity factor of T3 =

Capacity factor of T4 =

So, the capacity of power generation technology T1 (0.5) is highest.

Q14: Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs.. Unique seating arrangements are defined by the relative positions of the people.
How many unique seating arrangements are possible such that each person is sitting next to their twin?  [GATE CE 2024 SET-1]
(a) 12
(b) 14
(c) 10
(d) 28
Ans: (a)

Q15: In the given text, the blanks are numbered (1)-(iv). Select the best match for all the blanks.
From the ancient Athenian arena to the modern Olympic stadiums, athletics (i) the potential for a spectacle. The crowd (ii) with bated breath as the Olympian artist twists his body, stretching the javelin behind him. Twelve strides in, he begins to crossstep. Six cross-steps  (iii) in an abrupt stop on his left foot. As his body (iv) like a door turning on a hinge, the javelin is launched skyward at a precise angle.  [GATE CE 2024 SET-1]
(a) (i) hold (ii) Waits (iii) culminates (iv) pivot
(b) (i) holds (ii) wait (iii) culminates (iv) pivot
(c) (i) hold (ii) wait (iii) culminate (iv) pivots
(d) (i) holds (ii) waits (iii) culminate (iv) pivots
Ans: (d)
According to subject verb agreement,
singular noun takes singular verb and plural noun takes plural verb.
"athletics" is placed as a game (singular common noun) so singular verb form is used.
'crowd' is a singular noun, so singular verb form is used.
"cross-steps" is a plural form of noun, so it will be followed with a plural form of verb.
"his body" is a singular noun so singular form of verb is used.

Q16: On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 hours?  [GATE CE 2024 SET-1]
(a) 51
(b) 49
(c) 50
(d) 55
Ans: (c)
Between 12:05:00 to 12:55:00
There are 50 interval of 1 minute in which a second hand and minute hand crosses one another time. So during 12:05:00 to 12:55:00 minute and second hand crosses 50 times.

Q17: Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255  [GATE CE 2024 SET-1]
(a) 35
(b) 40
(c) 45
(d) 31
Ans: (d)
3 × 2 + 1 = 7
7 × 2 + 1 = 15
15 × 2 + 1 = 31
31 x 2 + 1 = 63
63 x 2 + 1 = 127
127 x 2 + 1 = 255

Q18: For positive integers p and q, with  Then,
(a) q^p = p^q
(b) q^p = p^2q
(c)
(d)
Ans: Given, p > 0, q > 0 and

∴

q^p = p^q

Q19: In a locality, the houses are numbered in the following way:
The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302 . The total number of houses is the same on both sides of the road.
If the difference of the surn of the house-numbers between the two sides of the road is 27 , then the number of houses on each side of the rood is  [GATE CE 2024 SET-1]
(a) 27
(b) 52
(c) 54
(d) 26
Ans: (a)

Let sum of 301 + 303 + 305 + ….. = A
and 302 + 304 + 306 +…… = B
Given, A − B = 27
and 302 − 301 = 1
304 − 303 = 1
As difference of one pair is 1 and total difference is 27.
∴ Number of house in one side is 27.

Q20: If '→' denotes increasing order of intensity, then the meaning of the words [simmer → seethe → smolder] is analogous to [break → raze → 1. Which one of the given options is appropriate to fill the blank?  [GATE CE 2024 SET-1]
(a) obfuscate
(b) obliterate
(c) fracture
(d) fissure
Ans: (b)
Meaning of the words
simmer → seethe → smolder
is analogous to
brake → raze → obliterate

Q1: Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds v_P, v_Q, and v_R, respectively.
Which one of the following options is CORRECT?  [GATE CE 2023 SET-2]
(a) v_P < v_R < v_Q
(b) v_P < v_Q < v_R
(c) v_P > v_R > v_Q
(d)
Ans: (c)

Velocity, V = ωr.Here, ω = constant.
Hence, more is the distance from the axis of rotation more will be the velocity.
∴V_P > V_R > V_Q

Q2: If x satisfies the equation then x is equal to [GATE CE 2023 SET-2]
(a) 1/2
(b) log₁₆8
(c) 2/3
(d) log₄8
Ans: (c)

→ Taking log to the base 4 . on both side.
8^x = log₄256 = 4
Taking lot to the base 8 on both sides, we get
x = log₈ 4

x = 2/3

Q3: Based only on the following passage, which one of the options can be inferred with certainty?
When the congregation sang together, Apenyo would also join, though her little screams were not quite audible because of the group singing. But whenever there was a special number, trouble would begin; Apenyo would try singing along, much to the embarrassment of her mother. After two or three such mortifying Sunday evenings, the mother stopped going to church altogether until Apenyo became older and learnt to behave.
At home too, Apenyo never kept quiet; she hummed or made up silly songs to sing by herself, which annoyed her mother at times but most often made her become pensive. She was by now convinced that her daughter had inherited her love of singing from her father who had died unexpectedly away from home.
[Excerpt from These Hills Called Home by Temsula Ao]  [GATE CE 2023 SET-2]
(a) The mother was embarrassed about her daughter's singing at home.
(b) The mother's feelings about her daughter's singing at home were only of annoyance
(c) The mother was not sure if Apenyo had inherited her love of singing from her father.
(d) When Apenyo hummed at home, her mother tended to become thoughtful.
Ans: (c)

Q4: Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative position of the people. How many seating arrangements are possible such that every husband sits next to his wife?  [GATE CE 2023 SET-2]
(a) 16
(b) 4
(c) 120
(d) 720
Ans: (a)
Let us form the pairs of Husband-wife. Now these pairs can be arranged around circular table in
=(3−1)! ways 
= 2 ways 
Their possible internal arrangement ss
= 2! × 2! × 2! = 8 
Hence, total seating arrangement.
= 2 × 8 = 16 

Q5: Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one's love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?  [GATE CE 2023 SET-2 ]
(i) In Elvesland, one always declares one's love by gifting a white flower.
(ii) In Elvesland, all emotions are declared by gifting flowers.
(iii) In Elvesland, sometimes one expresses one's anger by gifting a flower that is not yellow.
(iv) In Elvesland, sometimes one expresses one's love by gifting a white flower.
(a) only (ii)
(b) (i), (ii) and (iii)
(c) (i), (iii) and (iv)
(d) only (iv)
Ans: (d)

Q6: Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle.
Operation 1: Scale independently along the x and y axes.
Operation 2: Rotation in any direction about the origin.
Which figure among the options can be achieved through a combination of these two operations on the given circle?  [GATE CE 2023 SET-2]
(a)
(b)
(c)
(d)
Ans: (a)

Q7: There are 4 red, 5 green, and 6 blue balls inside a box. If ?? number of balls are picked simultaneously, what is the smallest value of ?? that guarantees there will be at least two balls of the same colour?
One cannot see the colour of the balls until they are picked.  [GATE CE 2023 SET-2]
(a) 4
(b) 15
(c) 5
(d) 2
Ans: (a)

Q8: In how many ways can cells in a 3 ? 3 grid be shaded,such that each row and each column have exactly one shaded cell? An example of one valid shading is shown.  [GATE CE 2023 SET-2]
(a) 2
(b) 9
(c) 3
(d) 6
Ans: (d)
No. of such cases = ³C₁ × ²C₁ × ¹C₁= 6

Q9: Kind : _______ : : Often : Seldom  [GATE CE 2023 SET-2]
(a) Cruel
(b) Variety
(c) Type
(d) Kindred
Ans: (a)
Often and seldom are antonyms. Hence, correct option will be the antonym of kind i.e. Cruel.

Q10: The line ran ______ the page, right through the centre, and divided the page into two.  [GATE CE 2023 SET-2]
(a) across
(b) of
(c) between
(d) about
Ans: (a)

Q11: A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius 2 cm², as shown.
The area of the shaded region is cm². [GATE CE 2023 SET-1]
(a) 8
(b) 4
(c) 12
(d) 10
Ans: (a)
Top shaded area = 4 × 2−π2²/2 = 8 − 2π
Bottom shaded area
Total shaded area = 8 − 2π + 2π = 8

Q12: Let a = 30!, b = 50!, and c = 100;. Consider the following numbers:
log_ac, log_ca, log_ba, log_ab
Which one of the following inequalities is CORRECT?  [GATE CE 2023 SET-1]
(a) log_c a < log_b a < log_a b < log_a c
(b) log_c a < log_b b < log_b a < log_b c
(c) log_c a < log_b a < log_a c < log_a b
(d) log_b a < log_c a < log_a b < log_a c
Ans: (a)

So log⁡_a C is greatest one.

So, log⁡_c a is smallest one.

log_b a < 1 and log⁡_a b > 1
So log⁡_a b > log⁡_b a
Hence, option (A)
log⁡_c a < log⁡_b a < log_⁡a b < lo⁡g_a c is correct.

Q13: The James Webb telescope, recently launched in space, is given humankind unprecedented access to the depths of time by imaging very old stars formed almost 13 billion years ago. Astrophysicists and cosmologists believe that this odyssey in space may even shed light on the existence of dark matter. Dark matter is supposed to interact only via the gravitational interaction and not through the electromagnetic-, the weak - or the stronginteraction. This may justify the epithet "dark" in dark matter.
Based on the above paragraph, which one of the following statements is FALSE?  [GATE CE 2023 SET-1]
(a) No other telescope has captured images of starts older than those captured by the James Webb telescope.
(b) People other than astrophysicists and cosmologists may also believe in the existence of dark matter.
(c) The James Webb telescope could be of use in the research on dark matter.
(d) If dark matter was known to interact via the strong-interaction, then the epithet "dark" would be justified.
Ans: (d) 

Q14: Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), P(x), of a variable x?  [GATE CE 2023 SET-1]

(a) mean = median  mode
(b) mean = median = mode
(c) mean  median = mode
(d) mean  mode = median
Ans: (a)
Median = (-1+1)/2=0
Mode = -13,13 (Date with high probability)
Its Bi-Modal data :
So, Median  Mode

Q15: Based only on the truth of the statement 'Some humans are intelligent', which one of the following options can be logically inferred with certainty?  [GATE CE 2023 SET-1]
(a) No human is intelligent.
(b) All humans are intelligent.
(c) Some non-humans are intelligent.
(d) Some intelligent beings are humans.
Ans: (d)
1. "Some humans are intelligent" can be represented by Venn diagram.
2. "Same human's are intelligent" can be also represented by Venn-Diagram
Being are human is correct so some intelligent beings are human is also correct.
Hence, option (d) can be logically correct. Option (c) same non humans are intelligent is a possibility only which true in (1) diagram but false in (2).

Q16: 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 figure below consists of 20 unit squares arranged as shown. In addition to the given black squares, upto 5 more may be coloured black. Which one among the following options depicts the minimum number of boxes that must be coloured black to achieve two lines of symmetry? (The figure is representative)  [GATE CE 2023 SET-1]
(a) d
(b) c, d, i
(c) c, i
(d) c, d, I, f, g
Ans: (d)

Q17: A duck named Donald Duck says "All ducks always lie." Based only on the information above, which one of the following statements can be logically inferred with certainty?  [GATE CE 2023 SET-1]
(a) Donald Duck always lies.
(b) Donald Duck always tells the truth
(c) Donald Duck's statement is true.
(d) Donald Duck's statement is false.
Ans: (d) 

Q18: In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. What is the area (in cm²) of the shaded region? (The diagram is representative) [GATE CE 2023 SET-1]
(a) 25π/3
(b) 20π/3
(c) 6π
(d) 7π
Ans: (a)

Q19: Eject : Insert : : Advance : ______
(By word meaning)  [GATE CE 2023 SET-1]
(a) Advent
(b) Progress
(c) Retreat
(d) Loan
Ans: (c)

Q20: "I have not yet decided what I will do this evening; I _____ visit a friend."  [GATE CE 2023 SET-1]
(a) mite
(b) would
(c) might
(d) didn't
Ans: (c)

Q1: An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72º anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.
1. moves forward for 10 cm.
2. turns 144º clockwise.
The pattern made by the trace left behind by the ant is  [GATE CE 2022 SET-2]

(a)
(b)
(c)
(d)
Ans: (c)
MTA - Marks to All

Q2: Given below are two statements and four conclusions drawn based on the statements.
Statement 1: Some soaps are clean.
Statement 2: All clean objects are wet.
Conclusion I: Some clean objects are soaps.
Conclusion II: No clean object is a soap.
Conclusion III: Some wet objects are soaps.
Conclusion IV: All wet objects are soaps.
Which one of the following options can be logically inferred?  [GATE CE 2022 SET-2]
(a) Only conclusion I is correct
(b) Either conclusion I or conclusion II is correct
(c) Either conclusion III or conclusion IV is correct
(d) Only conclusion I and conclusion III are correct
Ans: (d)

Q3: Consider the following equations of straight lines:
Line L1: 2x - 3y = 5
Line L2: 3x + 2y = 8
Line L3: 4x - 6y = 5
Line L4: 6x - 9y = 6
Which one among the following is the correct statement?  [GATE CE 2022 SET-2]
(a) L1 is parallel to L2 and L1 is perpendicular to L3
(b) L2 is parallel to L4 and L2 is perpendicular to L1
(c) L3 is perpendicular to L4 and L3 is parallel to L2
(d) L4 is perpendicular to L2 and L4 is parallel to L3
Ans: (d)

Q4: In a partnership business the monthly investment by three friends for the first six months is in the ratio 3: 4: 5. After six months, they had to increase their monthly investments by 10%, 15% and 20%, respectively, of their initial monthly investment. The new investment ratio was kept constant for the next six months.
What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?  [GATE CE 2022 SET-2]
(a) 22:23:24
(b) 22:33:50
(c) 33 : 46 : 60
(d) 63 : 86 : 110
Ans: (d)

Q5: In the last few years, several new shopping malls were opened in the city. The total number of visitors in the malls is impressive. However, the total revenue generated through sales in the shops in these malls is generally low.
Which one of the following is the CORRECT logical inference based on the information in the above passage?  [GATE CE 2022 SET-2]
(a) Fewer people are visiting the malls but spending more
(b) More people are visiting the malls but not spending enough
(c) More people are visiting the malls and spending more
(d) Fewer people are visiting the malls and not spending enough
Ans: (b)

Q6: 

For the picture shown above, which one of the following is the correct picture representing reflection with respect to the mirror shown as the dotted line?  [GATE CE 2022 SET-2]
(a)
(b)
(c)
(d)
Ans: (a)

Q7: A survey of 450 students about their subjects of interest resulted in the following outcome.

• 150 students are interested in Mathematics.
• 200 students are interested in Physics.
• 175 students are interested in Chemistry.
• 50 students are interested in Mathematics and Physics.
• 60 students are interested in Physics and Chemistry.
• 40 students are interested in Mathematics and Chemistry.
• 30 students are interested in Mathematics, Physics and Chemistry.
• Remaining students are interested in Humanities.

Based on the above information, the number of students interested in Humanities is  [GATE CE 2022 SET-2]
(a) 10
(b) 30
(c) 40
(d) 45
Ans: (d)

Q8: Both the numerator and the denominator of frac34 are increased by a positive integer, x, and those of frac1517 are decreased by the same integer. This operation results in the same value for both the fractions.
What is the value of x?  [GATE CE 2022 SET-2]
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (c)

Q9:
What is the value of fracx + z − yy  [GATE CE 2022 SET-2]
(a) 0.75
(b) 1.25
(c) 2.25
(d) 3.25
Ans: (b)

Q10: The movie was funny and I _________.   [GATE CE 2022 SET-2]
(a) could help laughing
(b) couldn't help laughed
(c) couldn't help laughing
(d) could helped laughed
Ans: (c)

Q11: 

Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank.
Which one of the following represents a possible unfolding of the cube?  [GATE CE 2022 SET-1]
(a)
(b)
(c)
(d)
Ans: (a)
MTA - Marks to All

Q12: In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, "two moves along one direction followed by one move in a perpendicular direction". The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is  [GATE CE 2022 SET-1]
(a) 4
(b) 5
(c) 6
(d) 7
Ans: (b)
Minimum number of steps required are:
P2 → Q4 → S3 → T5 → R4 → P5

Q13: The above frequency chart shows the frequency distribution of marks obtained by a set of students in an exam.
From the data presented above, which one of the following is CORRECT?  [GATE CE 2022 SET-1]
(a) mean > mode > median
(b) mode > median > mean
(c) mode > mean > median
(d) median > mode > mean
Ans: (b)


= (6 + 6)/2 = 6
Mode = frequently occured observation (data with high frequency) = 7

Q14: P invested Rs. 5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is shared in proportion to the total investment made in that year.
If at the end of that investment year, Q receives 4/9 of the total profit, what is the value of x (in Rs)?  [GATE CE 2022 SET-1]
(a) 2500
(b) 3000
(c) 4687
(d) 8437
Ans: (b)
Let total profit = K
So, profit by Q = 4/9 K
profit by P = K - (4/9)K = (5/9) K

x = 3000

Q15: Healthy eating is a critical component of healthy aging. When should one start eating healthy? It turns out that it is never too early. For example, babies who start eating healthy in the first year are more likely to have better overall health as they get older.
Which one of the following is the CORRECT logical inference based on the information in the above passage?  [GATE CE 2022 SET-1]
(a) Healthy eating is important for those with good health conditions, but not for others
(b) Eating healthy can be started at any age, earlier the better
(c) Eating healthy and better overall health are more correlated at a young age, but not older age
(d) Healthy eating is more important for adults than kids
Ans: (b)

Q16: In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of the squares, PXWR, RUVZ and SPQT is  [GATE CE 2022 SET-1]
(a) Area of SPQT = Area of RUVZ = Area of PXWR
(b) Area of SPQT = Area of PXWR - Area of RUVZ
(c) Area of PXWR = Area of SPQT - Area of RUVZ
(d) Area of PXWR = Area of RUVZ - Area of SPQT
Ans: (b)
From ΔPQR by Pythagoras theorem,
PR² = PQ² + QR²
Also, QR = RZ,
⇒ PR² = PQ² + RZ²
⇒ Area of PXWR = Area of SPQT + Area of RUVZ
⇒ Area of SPQT = Area of PXWR - Area of RUVZ

Q17: Given the statements:
P is the sister of Q.
Q is the husband of R.
R is the mother of S.
T is the husband of P.
Based on the above information, T is ______ of S.  [GATE CE 2022 SET-1]
(a) the grandfather
(b) an uncle
(c) the father
(d) a brother
Ans: (b)


Q18: If
p:q = 1:2
q:r = 4:3
r:s = 4:5
and u is 50% more than s, what is the ratio p?u?  [GATE CE 2022 SET-1]
(a) 02:15
(b) 16:15
(c) 01:05
(d) 16:45
Ans: (d)
Given,



Q19: Two straight lines pass through the origin (x₀, y₀) = (0, 0). One of them passes through the point (x₁, y₁) = (1, 3) and the other passes through the point (x₂, y₂) = (1, 2).
What is the area enclosed between the straight lines in the interval [0, 1] on the x-axis?  [GATE CE 2022 SET-1]
(a) 0.5
(b) 1
(c) 1.5
(d) 2
Ans: (a)
Equation of first straight line passing through (0, 0) and (1, 3)

y = 3x
Equation of second stragith line passing through (0, 0) and (1, 2)

y = 2x

Q20: You should _________ when to say _________.  [GATE CE 2022 SET-1]
(a) no / no
(b) no / know
(c) know / know
(d) know / no
Ans: (d)

Q1: In an equilateral triangle PQR, side PQ is divided into four equal parts, side QR is divided into six equal parts and side PR is divided into eight equals parts. The length of each subdivided part in cm is an integer. The minimum area of the triangle PQR possible, in cm², is [GATE CE 2021 SET-2]
(a) 18
(b) 24
(c) 48√3
(d) 144√3
Ans: (d)
For  to be integer, a must be LCM of 4, 6 and 8. So a = 24
Area = 

Q2: In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centers at S and Q.
The probability that any point picked randomly within the square falls in the shaded area is _________  [GATE CE 2021 SET-2]
(a) 4 - (π/2)
(b) 1/2
(c) (π/2) - 1
(d) π/4
Ans: (c)
Probability = fA/TA


Q3: 1. Some football players play cricket.
2. All cricket players play hockey.
Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is :  [GATE CE 2021 SET-2]
(a) No football player plays hockey
(b) Some football players play hockey
(c) All football players play hockey
(d) All hockey players play football
Ans: (b)

Q4: The author said, "Musicians rehearse before their concerts. Actors rehearse their roles before the opening of a new play. On the other hand, I find it strange that many public speakers think they can just walk onto the stage and start speaking. In my opinion, it is no less important for public speaker to rehearse their talks."
Based on the above passage., which one of the following is TRUE?  [GATE CE 2021 SET-2]
(a) The author is of the opinion that rehearsing is important for musicians, actors and public speakers
(b) The author is of the opinion that rehearsing is less important for public speakers than for musicians and actors
(c) The author is of the opinion that rehearsing is more important only for musicians than public speakers
(d) The author is of the opinion that rehearsal is more important for actors than musicians
Ans: (a)
The last sentence of the passage decides the answer with the key words "No Less Important".

Q5: On a planar field, you travelled 3 units East from a point O. Next you travelled 4 units South to arrive at point P. Then you travelled from P in the North-East direction such that you arrive at a point that is 6 units East of point O. Next, you travelled in the North-West direction, so that you arrive at point Q that is 8 units North of point P.
The distance of point Q to point O, in the same units, should be ______  [GATE CE 2021 SET-2]
(a) 3
(b) 4
(c) 5
(d) 6
Ans: (c)


Q6: Four persons P, Q, R and S are to be seated in a row. R should not be seated at the second position from the left end of the row. The number of distinct seating arrangements possible is:  [GATE CE 2021 SET-2]
(a) 6
(b) 9
(c) 18
(d) 24
Ans: (c)
Number of arrangements = 3 × 3! = 18

Q7: ⊕ and ⊙ are two operators on numbers p and q such that p ⊙ q = p − q, and p ⊕ q = p × q 
Then, (9 ⊙ (6 ⊕ 7))⊙(7 ⊕ (6 ⊙ 5))=  [GATE CE 2021 SET-2]
(a) 40
(b) -26
(c) -33
(d) -40
Ans: (d)
[9 − (6 × 7)] − [7 × 1] = −33 − 7 = -40

Q8: Two identical cube shaped dice each with faces numbered 1 to 6 are rolled simultaneously. The probability that an even number is rolled out on each dice is:  [GATE CE 2021 SET-2]
(a) 1/36
(b) 1/12
(c) 1/8
(d) 1/4
Ans: (d)
Probability of getting even number on a dice = 3/6 = 1/2
∴ Two dice are rolled simultaneously,
Hence required probability = 1/2 x 1/2 = 1/4

Q9: The mirror image of the above text about X-axis is [GATE CE 2021 SET-2]
(a)
(b)
(c)
(d)
Ans: (b)

Q10: i. Arun and Aparna are here.
ii. Arun and Aparna is here.
iii. Arun's families is here.
iv. Arun's family is here.
Which of the above sentences are grammatically CORRECT?  [GATE CE 2021 SET-2]
(a) (i) and (ii)
(b) (i) and (iv)
(c) (ii) and (iv)
(d) (iii) and (iv)
Ans: (b)
Two subject joined with 'and' become plural and hence plural verb is there in first statement, in fourth sentence the subject is family which is singular and takes singular verb.

Q11: Humans have the ability to construct worlds entirely in their minds, which don't exist in the physical world. So far as we know, no other species possesses this ability. This skill is so important that we have different words to refer to its different flavors, such as imagination, invention and innovation.
Based on the above passage, which one of the following is TRUE?  [GATE CE 2021 SET-1]
(a) No species possess the ability to construct worlds in their minds
(b) The terms imagination, invention and innovation refer to unrelated skills
(c) We do not know of any species other than humans who possess the ability to construct mental worlds
(d) Imagination, invention and innovation are unrelated to the ability to construct mental worlds
Ans: (c)
Option (B) and (D) are weekend by the word 'UNRELATED SKILLS'. Option (A) is weekend by the expression, no species posses the ability.
Hence answer is option (C) which reflects the information given in the passage.

Q12: A function, λ, is defined by

The value of the expression is: [GATE CE 2021 SET-1]
(a) -1
(b) 0
(c) 16/3
(d) 16
Ans: (b)
So, 1st definition will be applicable as p = q.
Hence, λ(1, 1) = (1 − 1)² = 0

Q13: 

Five line segments of equal lengths, PR, PS, QS, QT and RT are used to form a star as shown in the figure above.
The value of θ, in degrees, is ________   [GATE CE 2021 SET-1]
(a) 36
(b) 45
(c) 72
(d) 108
Ans: (a)
Sum of angle formed at the pentagon = 540º
Each angle of = 540/5 = 108º
∠x = 180 − 108 = 72º
Sum of angle of triangle = 180º
72º + 72º + θ = 180º
θ = 36º

Q14: Consider two rectangular sheets, Sheet M and Sheet N of dimensions 6cm x 4cm each.
Folding operation 1: The sheet is folded into half by joining the short edges of the current shape.
Folding operation 2: The sheet is folded into half by joining the long edges of the current shape.
Folding operation 1 is carried out on Sheet M three times.
Folding operation 2 is carried out on Sheet N three times.
The ratio of perimeters of the final folded shape of Sheet N to the final folded shape of Sheet M is ____.  [GATE CE 2021 SET-1]
(a) 0.546527778
(b) 0.126388889
(c) 0.295138889
(d) 0.217361111
Ans: (a)

(Perimeter)_M = 2(2 + 1.5) = 7
(Perimeter)_N = 2(0.5 + 6) = 13
Required ratio = 13/7

Q15: Statement: Either P marries Q or X marries Y
Among the options below, the logical NEGATION of the above statement is :  [GATE CE 2021 SET-1]
(a) P does not marry Q and X marries Y
(b) Neither P marries Q nor X marries Y
(c) X does not marry Y and P marries Q
(d) P marries Q and X marries Y
Ans: (b)
The statement says only one of these two action will happen, it's NEGATION should be a confirmed action, hence option (c) is the answer.

Q16: Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:  [GATE CE 2021 SET-1 ]
(a) 2
(b) 4
(c) 6
(d) 8
Ans: (c)
Following cases can be
PQSR, RQSP, QPSR, QRSP, RQPS and PQRS

Q17: ⊕ and ⊙ are two operators on numbers p and q such that p ⊕ q and p ⊙ q = p²/q;
If x ⊕ y = 2 ⊙ 2, then x =  [GATE CE 2021 SET-1]
(a) y/2
(b) y
(c) 3y/2
(d) 2y
Ans: (b)

(x - y)² = 0
x = y

Q18: In a company, 35% of the employees drink coffee, 40% of the employees drink tea and 10% of the employees drink both tea and coffee. What % of employees drink neither tea nor coffee?  [GATE CE 2021 SET-1]
(a) 15
(b) 25
(c) 35
(d) 40
Ans: (c)

Percent of employees drink neither tea nor coffee = 100 - 25 - 1 0 - 30 = 35

Q19: The mirror image of the above test about the X-axis is [GATE CE 2021 SET-1]
(a)
(b)
(c)
(d)
Ans: (b)

Q20: Getting to the top is _____ than staying on top.  [GATE CE 2021 SET-1]
(a) more easy
(b) much easy
(c) easiest
(d) easier
Ans: (d)
When the comparison is between two things we use the second degree of the adjective.The degree form of easy are: (easy - easier - easiest)

Q1: The monthly distribution of 9 Watt LED bulbs sold by two firms X and Y from January to June 2018 is shown in the pie-chart and the corresponding table. If the total number of LED bulbs sold by the two firms during April-June 2018 is 50000, then the number of LED bulbs sold by the firm Y during April-June 2018 is ________.
Percentage of 9 Watt LED bulbs sold by the firms X and Y from January 2018 to June, 2018  [GATE CE 2020 SET-2]
(a) 11250
(b) 9750
(c) 8750
(d) 8250
Ans: (c)
Marks to All As per IIT Key

Q2: In a school of 1000 students, 300 students play chess and 600 students play football. If 50 students play both chess and football, the number of students who play neither is _______   [GATE CE 2020 SET-2]
(a) 200
(b) 150
(c) 100
(d) 50
Ans: (b)

Q3: The ratio of 'the sum of the odd positive integers from 1 to 100' to 'the sum of the even positive integers from 150 to 200' is ________   [GATE CE 2020 SET-2]
(a) 45:95
(b) 01:02
(c) 50:91
(d) 01:01
Ans: (c)

Q4: For the year 2019, which of the previous year's calendar can be used?  [GATE CE 2020 SET-2]
(a) 2011
(b) 2012
(c) 2013
(d) 2014
Ans: (c)

Q5: Nominal interest rate is defined as the amount paid by the borrower to the lender for using the borrowed amount for a specific period of time. Real interest rate calculated on the basis of actual value (inflation-adjusted), is approximately equal to the difference between nominal rate and expected rate of inflation in the economy.
Which of the following assertions is best supported by the above information?  [GATE CE 2020 SET-2]
(a) Under high inflation, real interest rate is low and borrowers get benefited
(b) Under low inflation, real interest rate is high and borrowers get benefited
(c) Under high inflation, real interest rate is low and lenders get benefited
(d) Under low inflation, real interest rate is low and borrowers get benefited
Ans: (a)

Q6: If f(x) = x² for each x ∈ (−∞, ∞), then  is equal to ______ [GATE CE 2020 SET-2]
(a) (f(x))
(b) (f(x))²
(c) (f(x))³
(d) (f(x))⁴
Ans: (c)

Q7: After the inauguration of the new building, the Head of the Department (HoD) collated faculty preferences for office space. P wanted a room adjacent to the lab. Q wanted to be close to the lift. R wanted a view of the playground and S wanted a corner office.
Assuming that everyone was satisfied, which among the following shows a possible allocation?  [GATE CE 2020 SET-2]
(a)
(b)
(c)
(d)
Ans: (c)

Q8: Select the word that fits the analogy:
Partial : Impartial :: Popular: _______  [GATE CE 2020 SET-2]
(a) Impopular
(b) Dispopular
(c) Mispopular
(d) Unpopular
Ans: (d)

Q9: Select the most appropriate word that can replace the underlined word without changing the meaning of the sentence:
Now-a-days, most children have a tendency to belittle the legitimate concerns of their parents.  [GATE CE 2020 SET-2]
(a) disparage
(b) applaud
(c) reduce
(d) begrudge
Ans: (a) 

Q10: Rescue teams deployed _______disaster hit areas combat_______a lot of difficulties to save the people.  [GATE CE 2020 SET-2]
(a) with, at
(b) in, with
(c) with, with
(d) to, to
Ans: (b)

Q11: The total expenditure of a family, on different activities in a month, is shown in the pie-chart. The extra money spent on education as compared to transport (in percent) is ______.  [GATE CE 2020 SET-1]
(a) 5
(b) 33.3
(c) 50
(d) 100
Ans: (c)

Q12: The unit's place in 26591749¹¹⁰⁰¹⁶ is ______ [GATE CE 2020 SET-1]
(a) 1
(b) 3
(c) 6
(d) 9
Ans: (a)

Q13: Insert seven numbers between 2 and 34, such that the resulting sequence including 2 and 34 is an arithmetic progression. The sum of these inserted seven numbers is ______  [GATE CE 2020 SET-1]
(a) 120
(b) 124
(c) 126
(d) 130
Ans: (c)

Q14: Five friends P, Q, R, S and T went camping. At night, they had to sleep in a row inside the tent. P, Q and T refused to sleep next to R since he snored loudly. P and S wanted to avoid Q as he usually hugged people in sleep.
Assuming everyone was satisfied with the sleeping arrangements, what is the order in which they slept?  [GATE CE 2020 SET-1]
(a) RSPTQ
(b) SPRTQ
(c) QRSPT
(d) QTSPR
Ans: (a)

Q15: The sum of two positive numbers is 100. After subtracting 5 from each number, the product of the resulting numbers is 0. One of the original numbers is ____  [GATE CE 2020 SET-1]
(a) 80
(b) 85
(c) 90
(d) 95
Ans: (d)

Q16: If 0, 1, 2, . . . ,7, 8, 9 are coded as O, P, Q, . . . ,V, W, X, then 45 will be coded as ______  [GATE CE 2020 SET-1]
(a) TS
(b) ST
(c) SS
(d) SU
Ans: (d)

Q17: The American psychologist Howard Gardner expounds that human intelligence can be subcategorized into multiple kinds, in such a way that individuals differ with respect to their relative competence in each kind. Based on this theory, modern educationists insist on prescribing multi-dimensional curriculum and evaluation parameters that enable development and assessment of multiple intelligences.
Which of the following statements can be inferred from the given text?  [GATE CE 2020 SET-1]
(a) Howard Gardener insists that the teaching curriculum and evaluation needs to be multi-dimensional.
(b) Howard Gardener wants to develop and assess the theory of multiple intelligences.
(c) Modern educationists want to develop and assess the theory of multiple intelligences.
(d) Modern educationists insist that the teaching curriculum and evaluation needs to be multi-dimensional.
Ans: (d)

Q18: Select the word that fits the analogy:
Fuse : Fusion :: Use : ______  [GATE CE 2020 SET-1]
(a) Usage
(b) User
(c) Uses
(d) Usion
Ans: (a)

Q19: His hunger for reading is insatiable. He reads indiscriminately. He is most certainly a/an ______ reader.  [GATE CE 2020 SET-1]
(a) Aall-round
(b) precocious
(c) voracious
(d) wise
Ans: (c)

Q20: It is a common criticism that most of the academicians live in their ________ , so, they are not aware of their real life challenges.  [GATE CE 2020 SET-1]
(a) homes
(b) ivory towers
(c) glass palaces
(d) big flats
Ans: (b)

Q1: The Newspaper reports that over 500 hectares of tribal land spread across 28 tribal settlements in the Mohinitampuram forest division have already been "alienated". A top forest official said, "First the tribals are duped out of their landholdings. Second, the families thus rendered landless are often forced to encroach further into the forests". On the basis of the information available in the paragraph, ________ is/are responsible for duping the tribals.
(a) The Newspaper
(b) It cannot be inferred who
(c) Forest officials
(d) Landless families [2019: 2 Marks, Set-ll]
Ans: (b)
The Newspaper is just reporting the matter, it cannot be responsible for duping the tribals. A top forest official made the statement about tribals being duped hence officials can not be responsible for duping the tribals.

Q2:  An oil tank can be filled by pipe X in 5 hours and pipe Y in 4 hours, each pump working on its own. When the oil tank is full and the drainage hole is open, the oil is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how many hours will it take for the tank to be filled? (Assume that the rate of drainage is independent of the Head)
(a) 4.00
(b) 1.50
(c) 2.00
(d) 2.50 [2019: 2 Marks, Set-ll]

Ans: (d)
Let inlet pipes, A= 4 hours, B = 5 hours and outlet pipe, C = 20 hours.
In 1 hour (A + B + C) can fill = 1/4 + 1/5 - 1/20 = 8/20 = 2/5
(A + B + C) together = 5/2 = 2.5 hours

Q3: The population of state X increased by x% and the population of state Y increased by y% from 2001 to 2011. Assume that x is greater than y. Let P be the ratio of the population of state X to state Y in a given year. The percentage increase in P from 2001 to 2011 is _______.

   [2019: 2 Marks, Set-ll]

Ans: (b)
Let a, b be the initial population.
Given a/b = p (ratio earlier)

So, required % change,