Electronics and Communication Engineering
GATE ECE Quantitative Aptitude PYQs
Build your understanding with focused practice from past exam papers.
How to practice Quantitative Aptitude
Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.
Questions 1–10 of 52. Imported answers require independent review unless marked reviewed.
Question 2
Open questionGAMCQ1 markNeeds review
The statements (S1), (S2), and (S3) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is 150.
(S1) The highest score is 100.
(S2) The fourth highest score is 76.
(S3) There are at least four students whose scores are within 25 of each other.
Which one of the following options is necessarily correct?
Your answerChoose one option.
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Open questionGAMCQ1 markNeeds review
Real numbers
,
, and
(all greater than 1) satisfy
where the logarithms are taken to the bases
and
.The value of
is ________Your answerChoose one option.
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Open questionGAMCQ2 marksNeeds review
Let
represent the perimeter of a square with sides of length
. The value of the expression
is ________Your answerChoose one option.
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Open questionGAMCQ2 marksNeeds review
The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was 2.5 stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB). This was surrounded by two pairs of alternating rings of land and water. The first pair of land and water was two stades wide each (lengths DE and CD), and the outer pair is three stades wide each (lengths DE and EF).
The ratio of the surface area of the land to that of the water in the city of Atlantis is ________ (round off to two decimal places).
Your answerChoose one option.
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Open questionGAMCQ1 markNeeds review
The 12 musical notes are given as
,
,
,
,
,
,
,
,
,
,
, and
. Frequency of each note is
times the frequency of the previous note. If the frequency of the note C is 130.8 Hz, then the ratio of frequencies of notes
and
is:Your answerChoose one option.
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Open questionGAMCQ1 markNeeds review
The following figures show three curves generated using an iterative algorithm. The total length for the curve generated after ‘Iteration
’ is:Note: The figures shown are representative.
Iteration 0:
Iteration 1:
Length of each segment:
Iteration 2:
Length of each segment:
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Open questionGAMCQ1 markNeeds review
Which one of the following plots represents
, where
is a non-zero real number?Note: The figures shown are representative.
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Open questionGAMCQ2 marksNeeds review
A stick of length one meter is broken at two locations at distances of
and
from the origin (0), as shown in the figure. Note that
. Which one of the following is NOT a necessary condition for forming a triangle using the three pieces?Note: All lengths are in meter. The figure shown is representative.
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Open questionGAMCQ2 marksNeeds review
The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?
Nation | Gold | Silver | Bronze |
|---|---|---|---|
USA | 40 | 44 | 41 |
Canada | 39 | 27 | 24 |
Japan | 20 | 12 | 13 |
Australia | 17 | 19 | 16 |
France | 16 | 26 | 22 |
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Open questionGAMCQ2 marksNeeds review
An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to ₹ 5,00,000. For higher fees, the overhead is ₹ 1,00,000 plus 10% of the amount by which the fee exceeds ₹ 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than ₹ 10,00,000, what is the maximum consulting fee that the employee can charge?
Your answerChoose one option.
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