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Recent questions tagged geometry

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1 1 answer
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GATE Mechanical 2026 | GA | Question: 8
Consider a string P of length $l$ that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its diameter, as repres...
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0 0 answers
557
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GATE Mechanical 2025 | GA | Question: 9
Which one of the following options has the correct sequence of objects arranged in the increasing number of mirror lines (lines of symmetry)?Circle; Square; Equilateral t...
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2 2 answers
1.6k
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GATE Mechanical 2023 | Question: 38
The smallest perimeter that a rectangle with area of $4$ square units can have is __________ units. (Answer in integer)
4 4 votes
2 2 answers
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GATE Mechanical 2022 Set 2 | GA | Question: 10
Equal sized circular regions are shaded in a square sheet of paper of $1$ cm side length. Two cases, case $\text{M}$ and case $\text{N}$, are considered as shown in the f...
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4 4 votes
2 answers 2 answers
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GATE Mechanical 2022 Set 1 | GA | Question: 7
A rhombus is formed by joining the midpoints of the sides of a unit square.What is the diameter of the largest circle that can be inscribed within the rhombus?$\dfrac{1}{...
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3 3 votes
2 answers 2 answers
2.1k
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GATE Mechanical 2022 Set 1 | GA | Question: 8
An equilateral triangle, a square and a circle have equal areas.What is the ratio of the perimeters of the equilateral triangle to square to circle?$3\sqrt{3} : 2 : \sqrt...
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7 7 votes
4 answers 4 answers
1.2k
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GATE Mechanical 2021 Set 2 | GA | Question: 8
The ratio of the area of the inscribed circle to the area of the circumscribed circle of an equilateral triangle is ___________$\frac{1}{8}$$\frac{1}{6}$$\frac{1}{4}$$\fr...
6 6 votes
2 answers 2 answers
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GATE Mechanical 2021 Set 1 | GA | Question: 3
In the above figure, $\textsf{O}$ is the center of the circle and, $\textsf{M}$ and $\textsf{N}$ lie on the circle. The area of the right triangle $\textsf{MON}$ is $50\;...
2 2 votes
1 1 answer
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GATE ME 2012 | Question: 63
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y=2x-0.1x^2$ w...
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5 5 votes
3 answers 3 answers
511
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GATE Mechanical 2018 Set 2 | GA | Question: 7
A wire would enclose an area of $1936 \: m^2$, if it is bent to a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The lo...
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5 5 votes
3 answers 3 answers
860
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GATE Mechanical 2018 Set 2 | GA | Question: 4
The perimeters of a circle, a square, and an equilateral triangle are equal. Which one of the following statements is true?The circle has the largest areaThe square has t...
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7 7 votes
1 answers 1 answer
514
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GATE Mechanical 2018 Set 1 | GA | Question: 4
A rectangle becomes a square when its length and breadth are reduced by $10$ m and $5$ m, respectively. During this process, the rectangle loses $650 m^2$ of area. What i...
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15 15 votes
1 answers 1 answer
807
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GATE Mechanical 2017 Set 1 | GA | Question: 8
Let $S_{1}$ be the plane figure consisting of the points $(x, y)$ given by the inequalities $\mid x - 1 \mid \leq 2$ and $ \mid y+2 \mid \leq 3$. Let $S_{2}$ be the plan...
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14 14 votes
3 answers 3 answers
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GATE Mechanical 2017 Set 1 | GA | Question: 3
A right-angled cone (with base radius $5$ cm and height $12$ cm), as shown in the figure below, is rolled on the ground keeping the point $P$ fixed until the point $Q$ (a...
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0 0 answers
300
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GATE Mechanical 2016 Set 3 | GA | Question: 10
A wire of length $340$ $mm$ is to be cut into two parts. One of the parts is to be made into a square and the other into a rectangle where sides are in the ratio of $1:2$...
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12 12 votes
2 answers 2 answers
555
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GATE Mechanical 2016 Set 2 | GA | Question: 5
A window is made up of a square portion and an equilateral triangle portion above it. The base of the triangular portion coincides with the upper side of the square. If t...
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18 18 votes
2 answers 2 answers
647
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GATE Mechanical 2015 Set 3 | GA | Question: 9
Right triangle $PQR$ is to be constructed in $xy$-plane so that the right angle is at $P$ and line $PR$ is parallel to $x$-axis.The $x$ and $y$ coordinates of $P$, $Q$ an...
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9 9 votes
3 answers 3 answers
498
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GATE Mechanical 2015 Set 3 | GA | Question: 8
In the given figure $Q$ is a right triangle, $$PS:QS = 3:1$$ $$RT:QT = 5:2$$ $$PU:UR = 1:1$$ If area of triangle $QTS$ is $20$ $cm^2$, then the area of triangle $PQR$ in ...
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0 0 votes
0 0 answers
300
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GATE Mechanical 2015 Set 2 | GA | Question: 8
From a circular sheet of paper of radius $30$ $cm$, a sector of $10\%$ area is removed. If the remaining part is used to make a conical surface, then the ratio of radius ...
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