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Recent questions tagged geometry

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1 1 answer
331
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GATE ECE 2026 | GA | Question: 9
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 represe...
11 11 votes
2 2 answers
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GATE ECE 2024 | GA | Question: 7
​​​​​Four identical cylindrical chalk-sticks, each of radius $r=0.5 \mathrm{~cm}$ and length $l=10 \mathrm{~cm}$, are bound tightly together using a duct tape as shown in...
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6 6 votes
2 2 answers
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GATE ECE 2024 | GA | Question: 10
​​​Two identical sheets $\text{A}$ and $\text{B}$, of dimensions $24 \mathrm{~cm} \times 16 \mathrm{~cm}$, can be folded into half using two distinct operations, $\text{F...
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1 1 vote
0 0 answers
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GATE ECE 2024 | Question: 26
​​​​​Consider the Earth to be a perfect sphere of radius $\text{R}$. Then the surface area of the region, enclosed by the $60^{\circ} \mathrm{N}$ latitude circle, that co...
0 0 votes
0 0 answers
420
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TIFR ECE 2023 | Question: 5
Let $\mathrm{B}$ denote the unit ball in $\mathbb{R}^{2}$, and $\mathrm{Q}$ a square of side length $2$. Let $\mathrm{K}$ be the set of all vectors $z$ such that for some...
1 1 vote
0 0 answers
363
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TIFR ECE 2014 | Question: 15
You are allotted a rectangular room of a fixed height. You have decided to paint the three walls and put wallpaper on the fourth one. Walls can be painted at a cost of Rs...
1 1 vote
0 0 answers
317
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TIFR ECE 2021 | Question: 2
Given a fixed perimeter of $1,$ among the following shapes, which one has the largest area?SquareA regular pentagonA regular hexagonA regular septagonA regular octagon
1 1 vote
0 0 answers
334
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TIFR ECE 2021 | Question: 8
The maximum area of a parallelogram inscribed in the ellipse (i.e. all the vertices of the parallelogram are on the ellipse) $x^{2}+4 y^{2}=1$ is:$2$$4$$1$$5$$3$
1 1 vote
0 0 answers
431
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TIFR ECE 2021 | Question: 12
An ant does a random walk in a two dimensional plane starting at the origin at time $0.$ At every integer time greater than $0,$ it moves one centimeter away from its ear...
1 1 vote
0 0 answers
270
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TIFR ECE 2021 | Question: 13
Consider a unit Euclidean ball in $4$ dimensions, and let $V_{n}$ be its volume and $S_{n}$ its surface area. Then $S_{n} / V_{n}$ is equal to:$1$$4$$5$$2$$3$
1 1 vote
0 0 answers
344
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TIFR ECE 2020 | Question: 6
For all values of $r>0$, the area of the set of all points outside the unit square whose Euclidean distance to the unit square is less than $r$ is:$=\pi r^{2}+4 r$$<4 \pi...
1 1 vote
0 0 answers
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TIFR ECE 2019 | Question: 8
Let $K$ be a cube of side $1$ in $\mathbb{R}^{3}$, with its centre at the origin, and its sides parallel to the co-ordinate axes. For $t \geq 0$, let $K_{t}$ be the set o...
5 5 votes
4 answers 4 answers
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GATE ECE 2022 | GA | Question: 3
A trapezium has vertices marked as $\text{P, Q, R}$ and $\text{S}$ (in that order anticlockwise). The side $\text{PQ}$ is parallel to side $\text{SR}.$Further, it is give...
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7 7 votes
3 answers 3 answers
1.9k
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GATE ECE 2021 | GA | Question: 10
​​Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the...
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15 15 votes
5 answers 5 answers
4.4k
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GATE ECE 2020 | GA | Question: 8
A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$,...
18 18 votes
3 answers 3 answers
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GATE ECE 2016 Set 3 | GA | Question: 9
Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant.$14.95$$15.25$$15.70$$20.35$
21 21 votes
2 answers 2 answers
802
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GATE ECE 2016 Set 3 | GA | Question: 10
A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ and has a slope of $-0.02$. What is the value of $y$ at $...
13 13 votes
1 answers 1 answer
634
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GATE ECE 2016 Set 2 | 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 $1:2$. ...
13 13 votes
1 answers 1 answer
758
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GATE ECE 2015 Set 3 | 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 the radiu...
8 8 votes
2 answers 2 answers
787
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GATE ECE 2018 | GA | Question: 5
A $1.5$ m tall person is standing at a distance of $3$ m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is tw...
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