Register

Recent questions tagged geometry

0 0 votes
1 1 answer
357
357 views
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
2.8k
2.8k views
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...
User Avatar
6 6 votes
2 2 answers
2.0k
2.0k views
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...
User Avatar
1 1 vote
0 0 answers
2.0k
2.0k views
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
427
427 views
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
371
371 views
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
322
322 views
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
343
343 views
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
439
439 views
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
278
278 views
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
351
351 views
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$$<4 \pi...
1 1 vote
0 0 answers
300
300 views
TIFR ECE 2019 | Question: 8
Let $K$ be a cube of side $1$ in $\mathbb{R}^{3}$, with its centre at the origin, and its sides parallel to the co-ordinate axes. For $t \geq 0$, let $K_{t}$ be the set o...
5 5 votes
4 answers 4 answers
3.8k
3.8k views
GATE ECE 2022 | GA | Question: 3
A trapezium has vertices marked as $\text{P, Q, R}$ and $\text{S}$ (in that order anticlockwise). The side $\text{PQ}$ is parallel to side $\text{SR}.$Further, it is give...
User Avatar
7 7 votes
3 answers 3 answers
2.0k
2.0k views
GATE ECE 2021 | GA | Question: 10
​​Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular convex hexagon to the...
User Avatar
15 15 votes
5 answers 5 answers
4.6k
4.6k views
GATE ECE 2020 | GA | Question: 8
A circle with centre $\text{O}$ is shown in the figure. A rectangle $\text{PQRS}$ of maximum possible area is inscribed in the circle. If the radius of the circle is $a$,...
18 18 votes
3 answers 3 answers
1.6k
1.6k views
GATE ECE 2016 Set 3 | GA | Question: 9
Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant.$14.95$$15.25$$15.70$$20.35$
21 21 votes
2 answers 2 answers
881
881 views
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
693
693 views
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
859
859 views
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
839
839 views
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...
To see more, click for the full list of questions or popular tags.