GATE EC General Aptitude Previous Year Questions with Solutions

Key idea: Nocturnal means active at night; its opposite is active by day.

Official answer: B

Of the four options, only diurnal, active during the day, is about the time of day at all, so it is the antonym. The others (normal, abnormal, exceptional) have nothing to do with time of day.

Key idea: The top four scores all lie between 76 and 100, a spread of 24.

Official answer: A

Take (S1) and (S2) together. The four highest scores all lie between the fourth highest (76) and the highest (100).

So those four students are within 25 marks of each other, which is (S3). Option (A) holds.

The others fail: (S3) can come from any four students, so it fixes neither the highest score nor the fourth highest, and (S1) alone says nothing about the fourth score.

Key idea: Match each segment where it enters and leaves the hidden rectangle.

Official answer: D

Follow the stubs outside the rectangle:

• A segment comes in from the upper left through the top edge and leaves near corner Y, going down to the right.
• A segment comes in from the upper right through the top edge and leaves through the bottom edge near Z, going down to the left.
• A nearly horizontal segment enters low on the left edge and leaves higher on the right edge.

Only tile S has all three: two lines crossing from the top edge to the bottom corners, and one shallow line rising from left to right. Tile R has a line starting at corner X, which the stubs don't show. The answer is S, option (D).

Key idea: Taking the nth root of a base multiplies the logarithm by n.

Official answer: B

Change both logarithms to plain \log:

Since \log_p y \cdot \log_y p = 1, the product is n^2 = 16, so n = 4 (all quantities exceed 1, so n > 0). Option (B).

Key idea: Negating for every ... there exists gives there exists ... for every.

Official answer: B

Apply it to the statement: for every student becomes there exists a student, and there exists another student within 10 marks becomes every other student is more than 10 marks away.

That is option (B). Options (A) and (D) make claims about every student, and (C) says exactly one, neither of which follows from the negation.

Key idea: Solve the clues first, then rearrange the four first letters.

Official answer: A

• Synonym of recognize, 8 letters: IDENTIFY.
• A story long enough for a book, 5 letters: NOVEL.
• Two of something, 6 letters: COUPLE.
• One of two equal parts, 4 letters: HALF.

The first letters I, N, C, H rearrange to CHIN. Option (A).

Key idea: Teammates can't be parent and child, and a match can't hold two parent-child pairs.

Official answer: C

Look at who plays together in each match:

• Match 1 (P and X together): X is not P's parent.
• Match 3 (R and X together, Q and Y together): X is not R's parent, and Y is not Q's parent.

So X's child is Q, and Y's child is P or R.

Rule (ii) allows at most one parent-child pair in a match. Match 3 already has X against Q. If Y were R's parent, match 3 would also have Y against R: two pairs. So Y is P's parent, and R has no parent playing. Option (C).

Key idea: P_k = 4k, so the sum is 4 times the sum of 1 to 10.

Official answer: C

Option (C).

Key idea: Every ring's area is \pi(R^2 - r^2), so \pi cancels in the ratio.

Official answer: C

The boundaries are at radii 2.5, 3.5, 5.5, 7.5, 10.5 and 13.5. Every area is \pi times a difference of squares, so \pi cancels:

The ratio is 78.25 / 104 \approx 0.75. Option (C).

Key idea: The example is a reflection in a horizontal mirror.

Official answer: C

In the example, the two lines swap places and every character is flipped upside down, while each line still runs left to right. That is a reflection in a horizontal mirror.

Applied to the new block, the second line moves to the top and both lines appear upside down but in their original left-to-right order. Tile R shows exactly that. P also swaps the two words of one line, Q swaps the parts of the other line, and S does both, which the example never does. Option (C).

Key idea: The missing word has to be a stronger form of approval than the two after it.

Official answer: A

Group I goes from the harshest criticism to the mildest, so Group II must go from the warmest approval down to appreciation. To extol is to praise very highly, which fits before praise.

Prize means to value something, appropriate means to take or to be suitable, and espouse means to adopt a cause. None of them is a degree of praise. Option (A).

Key idea: A condition about the past that didn't happen takes a result with a modal plus have and a past participle.

Official answer: D

Had I learnt is the inverted form of if I had learnt: the speaker didn't learn acting as a child. The result of an unreal past condition is written with would have, could have or might have and a past participle, so could have been is right.

The other three are present or future forms, which don't match a condition that is already over. Option (D).

Key idea: A fixed ratio per step means the ratio over several steps is that factor raised to the number of steps.

Official answer: B

From C, the notes C#, D, D#, E, F and F# are six steps up. Six steps multiply the frequency by

The 130.8 Hz isn't needed, because a ratio doesn't depend on where the scale starts. Option (B).

Key idea: Find what one iteration does to the total length; a constant factor per iteration gives a power of n.

Official answer: B

Count the segments in the figure. Iteration 1 has 5 segments of \tfrac{1}{3}, so its length is \tfrac{5}{3}. Iteration 2 replaces each of those by 5 segments a third as long: 25 segments of \tfrac{1}{9}, length \tfrac{25}{9}.

Every iteration multiplies the number of segments by 5 and divides their length by 3, so the length grows by \tfrac{5}{3} each time:

Only (B) gives \tfrac{5}{3} at n = 1 and \tfrac{25}{9} at n = 2. Option (B).

Key idea: Treat positive and negative x separately, since |x| is x for one and -x for the other.

Official answer: A

For x > 0, |x| = x and f(x) = -1. For x < 0, |x| = -x and f(x) = +1. So the graph is the constant 1 left of the axis and the constant -1 right of it, with no value at x = 0.

That is plot (A). Plot (B) is the reverse, +|x|/x, and (C) and (D) aren't constant on either side. Option (A).

Key idea: Start with the sentence that refers back to nothing, then follow words such as this and such, which point to an earlier sentence.

Official answer: B

Q introduces the topic and leans on nothing before it, so it opens. S explains how adapting helps organisms survive as environments change.

R then names this process of adaptation as natural selection, and P, with such adaptations and over time, closes on the long-term result. The order Q, S, R, P is option (B).

The other orders put P or R, which both point back to something already said, ahead of Q.

Key idea: Three lengths with a fixed total make a triangle exactly when each one is less than half the total.

Official answer: D

The pieces are b_1, b_2 - b_1 and 1 - b_2, which add up to 1. Each must be shorter than the other two together, that is, shorter than 0.5:

Those are (A), (C) and (B). Condition (D) isn't needed: b_1 = 0.4 and b_2 = 0.7 give pieces of 0.4, 0.3 and 0.3, a valid triangle, yet b_1 + b_2 = 1.1. Option (D).

Key idea: A question given marks to all scores full marks for every candidate, whatever they answered.

Official answer: Marks to all

The final key awards marks to all for this question, and doesn't say why. We don't give an answer: as printed, the question doesn't say how far the students move in a round, or which way round the circle counts as behind, and the student who leaves each round depends on both.

In the exam this meant there was nothing to lose by answering it. As practice, treat it as an exercise in reading a puzzle's rules carefully before starting.

Ruling in the key: The final key gives marks to all (MTA) for this question: every candidate received its 2 marks.

Key idea: Every statement is about totals, so total each nation's medals first.

Official answer: C

Adding gold, silver and bronze:

• USA: 125
• Canada: 90
• France: 64
• Australia: 52
• Japan: 45
• All five: 376

(A) is true: France's 64 is third, ahead of Australia and Japan. (B) is true: the USA stays ahead of Canada. (D) is true: 90 is twice 45.

(C) is false: the USA and Canada have 215 of the 376 medals, about 57%, which is more than half. Option (C).

Key idea: With a slab rule, decide which slab the answer is in, then solve the single linear equation for that slab.

Official answer: B

At a fee of ₹5,00,000 the client pays 1.18 \times 1.2 \times 5{,}00{,}000 = 7{,}08{,}000 rupees, well under the limit, so the fee is in the upper slab. There, with the fee F in rupees, the overhead and the client's total are

The largest fee is ₹7,24,961. Option (B).

Key idea: The missing word must be a stronger kind of boredom than bored, but milder than weary.

Official answer: A

Each step in the first group is a stronger version of the same feeling. Jaded means tired and dulled by too much of something, which sits between being bored and being weary of it.

Baffled is confusion, dead isn't a degree of boredom, and worsted means defeated. Option (A).

Key idea: Anyone who shares a room in an acceptable allocation can't be the sibling pair.

Official answer: A

S and Q have no siblings, so the pair is two of P, R and T. Pairs that share a room in an acceptable allocation are ruled out: P and R (first allocation) and R and T (second).

That leaves P and T. Option (A).

Key idea: Write the two ratios as two linear equations in the present ages.

Official answer: B

With present ages a and f:

The first gives f = 4a - 15. Substituting, 5a + 25 = 8a - 20, so a = 15 and f = 45. The father was 45 - 15 = 30 when Aman was born. Option (B).

Key idea: 1/\log_b x = \log_x b, which turns the sum into a single logarithm.

Official answer: C

So x = 24. Option (C).

Key idea: Take out the common power of 3 first.

Official answer: A

The prime factors are 2, 3 and 13, so the greatest is 13. Option (A).

Key idea: Set up the claim before the incident that tests it, and end on the reply to the question.

Official answer: C

R states Shifu's belief, so it comes first. S is the incident, P is the student's challenge, which needs both R and S before it, and Q is Shifu's reply to P. The order is R, S, P, Q. Option (C).

Key idea: A tight band round circles in a square is four straight runs plus one full circle's worth of arcs.

Official answer: D

Around the bundle, the tape runs straight along each side for one diameter, 2r = 1 cm, between the outer sticks, and curves round each corner stick through a quarter turn. The four quarter turns make one full circle:

The tape is 10 cm wide, so its area is 10(4 + \pi) cm². Option (D).

Key idea: Read the eight values off the chart once, then compare each ratio across the two years.

Official answer: C

From the chart, 2003 has obese 15%, overweight 25%, normal 50% and underweight 10%; 2023 has 25%, 40%, 30% and 5%.

• (A) Overweight to normal: 0.5 in 2003, 1.33 in 2023. Increased: correct.
• (B) Underweight to normal: 0.2, then 0.17. Decreased: correct.
• (C) Obese to normal: 0.3, then 0.83. It increased, so this statement is INCORRECT.
• (D) Normal: 50%, then 30%. Decreased: correct.

Option (C).

Key idea: A mirror flips left to right and water flips top to bottom; together they turn the image through 180 degrees.

Official answer: A

Undoing both reflections means rotating the image 5:24 through 180°. The order of the characters reverses, and each turns upside down: 4 becomes an h, while 2 and 5 look the same rotated.

So the original reads h, 2, a colon, then 5, which is option (A).

Key idea: Each fold halves only the side perpendicular to the fold line.

Official answer: A

FO1 folds parallel to the 24 cm edge, so it halves the 16 cm side: after two folds A is 24 × 4 cm, perimeter 56 cm. FO2 halves the 24 cm side: B is 6 × 16 cm, perimeter 44 cm.

Option (A).

Key idea: The blank needs a noun for an inner moral sense, the thing that permits or forbids.

Official answer: C

A conscience is a person's sense of right and wrong, and it is what would or wouldn't permit supporting a proposal.

Conscious is an adjective, consensus is a group's agreement, not one person's, and consent is permission given, which doesn't itself permit anything. Option (C).

Key idea: Parliament is the body that makes up the legislature; find the branch that courts make up.

Official answer: A

Parliament belongs to the legislature, the law-making branch. Courts belong to the judiciary, the branch that interprets and applies the law. Option (A).

The executive is the third branch, and governmental and legal are adjectives, not branches.

Key idea: 0 to 9 add up to 45, so the digits must be 1 to 9 (a 0 adds nothing and can't lead), placed in rising order.

Official answer: C

The digits 0 to 9 add up to 45. A number with distinct digits summing to 45 must therefore use 1 to 9 (adding 0 only makes it longer, so bigger). The smallest arrangement puts them in rising order: 123456789.

(A) repeats the 5 and (D) repeats the 9, so neither has distinct digits, and (B) uses the right digits in a larger order. Option (C).

Key idea: Students who like at least one kind: n(R \cup C) = n(R) + n(C) - n(R \cap C).

Official answer: C

Taking away the 30 who like neither leaves 100 - 30 = 70 in the union. With n(C) = c and n(R) = 2c:

Option (C).

Key idea: Apart from the outer square, every rectangle is tilted: its sides lie on the three lines of each diagonal direction.

Official answer: C

Inside the square there are three parallel lines in each diagonal direction: the diagonal itself and the two sides of the inner tilted square. A tilted rectangle needs two lines from each direction, and every such choice has all four corners inside the outer square:

These are the four small squares, the four rectangles made of two small squares, and the inner tilted square. With the outer square, 9 + 1 = 10. Option (C).

Key idea: Clawed creatures exist and all of them are ferocious, so the two sets overlap.

Official answer: D

Creatures with claws exist, and every one of them is ferocious, so at least some ferocious creatures have claws: (D) follows.

(B) and (C) contradict "all creatures that have claws are ferocious", and (A) isn't stated: a clawed creature could be ferocious without being an animal. Option (D).

Key idea: The graph is symmetric about the y-axis and never negative, so f must be even and non-negative.

Official answer: A

Test each option for an even, non-negative function:

• (A) x^2 2^{-|x|}: even, zero at 0, positive elsewhere, and decays as |x| grows. It matches.
• (B) x\, 2^{-|x|} is odd: negative for x < 0.
• (C) |x|\, 2^{-x} grows without bound as x \to -\infty.
• (D) x\, 2^{-x} is negative for x < 0 and grows in size as x \to -\infty.

Option (A). Its peaks are where 2x - x^2 \ln 2 = 0, at x = \pm 2/\ln 2 \approx \pm 2.885.

Key idea: "When I was a kid" and the past tense mean the speaker is no longer a child.

Official answer: B

The narrator looks back ("When I was a kid", "I used to imagine"), so this is an adult remembering a childhood liking. Option (B).

(A) needs the speaker to be a child now. Partial to means fond of, not reading in parts, so (C) misreads it, and the passage draws no lesson, so (D) goes beyond it.

Key idea: The worst case puts every positive in a different group, so as many groups as possible need five more tests.

Official answer: A

There are 1000 / 5 = 200 groups, so 200 kits test the mixed samples. Each positive group then needs 5 more kits. The most positive groups there can be is 100, one positive in each:

Option (A).

Key idea: Each fold halves the 32 cm side, and in the end the creases split it into 1 cm strips.

Official answer: C

Five halvings take the 32 cm side to 32 / 2^5 = 1 cm. Unfolded, the sheet is divided into 32 strips of 1 cm, and 32 strips have 31 creases between them. Fold by fold, the creases add up as 1 + 2 + 4 + 8 + 16 = 31. Option (C).