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Recent questions tagged geometry

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GATE Civil 2026 Set 1 | GA | Question: 7
In the given figure, $\overline{P Q}$ is the diameter of a circle with center $O$. Two points $R$ and $S$ are chosen on the circle such that $\angle R O S=80^{\circ}$. Wh...
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GATE Civil 2025 Set 2 | GA | Question: 10
Three villages $P, Q$, and $R$ are located in such a way that the distance $P Q=13 \mathrm{~km}$, $Q R=14 \mathrm{~km}$, and $R P=15 \mathrm{~km}$, as shown in the figur...
1 1 vote
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GATE Civil 2025 Set 1 | GA | Question: 9
​​​​​A circle with center at $(x, y)=(0.5,0)$ and radius $=0.5$ intersects with another circle with center at $(x, y)=(1,1)$ and radius $=1$ at two points. One of the poi...
0 0 votes
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GATE Civil 2025 Set 1 | Question: 25
Road $A$ and Road $B$ are joined by a circular horizontal curve of radius $200 \: \mathrm{m}$ as shown in the figure. Road $A$ and Road $B$ are tangential to the curve at...
3 3 votes
2 2 answers
GATE Civil 2024 Set 2 | GA | Question: 7
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...
7 7 votes
1 1 answer
GATE Civil 2024 Set 1 | GA | Question: 10
During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be $89.85^{\circ}$, the ratio of th...
12 12 votes
4 4 answers
GATE Civil 2023 Set 1 | GA | Question: 3
In the given figure, $\text{PQRSTV}$ is a regular hexagon with each side of length $5\mathrm{~cm}.$ A circle is drawn with its centre at $ \mathrm{V}$ such that it passes...
8 8 votes
2 2 answers
GATE Civil 2023 Set 1 | GA | Question: 10
A square of side length $4 \mathrm{~cm}$ 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...
4 4 votes
2 2 answers
GATE Civil 2022 Set 2 | GA | Question: 8
Consider the following equations of straight lines:$\text{Line L1}: 2x – 3y = 5$$\text{Line L2}: 3x + 2y = 8$$\text{Line L3}: 4x – 6y = 5$$\text{Line L4}: 6x – 9y = 6$Whi...
5 5 votes
2 2 answers
GATE Civil 2022 Set 1 | GA | Question: 5
In the following diagram, the point $\text{R}$ is the center of the circle. The lines $\text{PQ}$ and $\text{ZV}$ are tangential to the circle. The relation among the are...
16 16 votes
3 answers 3 answers
GATE Civil 2021 Set 2 | GA | Question: 9
In the figure shown above, $\text{PQRS}$ is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square a...
6 6 votes
2 answers 2 answers
GATE Civil 2021 Set 2 | GA | Question: 10
In an equilateral triangle $\text{PQR}$, side $\text{PQ}$ is divided into four equal parts, side $\text{QR}$ is divided into six equal parts and side $\text{PR}$ is divid...
15 15 votes
3 answers 3 answers
GATE Civil 2021 Set 1 | GA | Question: 8
Five line segments of equal lengths, $\text{PR, PS, QS, QT}$ and $\text{RT}$ are used to form a star as shown in the figure above.The value of $\theta$, in degrees, is __...
6 6 votes
2 answers 2 answers
GATE Civil 2019 Set 1 | GA | Question: 3
On a horizontal ground, the base of a straight ladder is $6$ m away from the base of a vertical pole. The ladder makes an angle of $45^{\circ}$ to the horizontal. If the ...
4 4 votes
1 answers 1 answer
GATE Civil 2019 Set 1 | GA | Question: 9
A square has side $5$ cm smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger squ...
5 5 votes
2 answers 2 answers
GATE Civil 2019 Set 2 | GA | Question: 3
Suresh wanted to lay a new carpet in his new mansion with an area of $70\times 55$ sq.mts. However an area of $550$ sq. mts. had to be left out for flower pots. If the co...
13 13 votes
2 answers 2 answers
GATE Civil 2016 Set 2 | GA | Question: 9
A square pyramid has a base perimeter $x$, and the slant height is half of the perimeter. What is the lateral surface area of the pyramid?$x^{2}$$0.75 \: x^{2}$$0.50 \: x...
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GATE Civil 2016 Set 1 | GA | Question: 5
A cube is built using $64$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the b...
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GATE Civil 2014 Set 1 | GA | Question: 8
The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is $3:4:5:6.$ The larg...
1 1 vote
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GATE Civil 2014 Set 1 | GA | Question: 4
If $y=5x^{2}+3,$then the tangent at $x=0,y=3$passes through $x=0,y=0$has a slope of $+1$is parallel to the $x$-axishas a slope of $-1$
0 0 votes
1 1 answer
GATE Civil 2012 | Question: 61
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}...
10 10 votes
5 answers 5 answers
GATE Civil 2018 Set 1 | GA | Question: 4
Tower A is $90$ m tall and tower B is $140$ m tall. They are 100 m apart. A horizontal skywalk connects the floors at $70$ m in both the towers. If a taut rope connects t...
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