Recent questions tagged geometry / GO Electronics

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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 the following figure. The width of the duct tape is equal to the length of the chalk-stick. The area ... to wrap the bundle of chalk-sticks once, is $20(4+\pi)$ $20(8+\pi)$ $10(8+\pi)$ $10(4+\pi)$

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 a...

Arjun

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Arjun asked Feb 16

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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, $\text{FO1}$ or $\text{FO2}$. In $\text{FO1}$, the axis of folding remains parallel to the initial ... of the perimeters of the final shapes of $\text{A}$ and $\text{B}$ is $14:11$ $11: 14$ $18:11$ $11: 18$

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, $\...

Arjun

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Arjun asked Feb 16

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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 contains the north pole in its interior is $\_\_\_\_\_\_$. $(2-\sqrt{3}) \pi R^{2}$ $\frac{(\sqrt{2}-1) \pi R^{2}}{2}$ $\frac{2 \pi R^{2}}{3}$ $\frac{(2+\sqrt{3}) \pi R^{2}}{8 \sqrt{2}}$

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 circl...

admin

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admin asked Feb 16

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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. $10$ per meter and the wall paper can be put at the rate of Rs $20$ per meter for that ... $200$ square meter room? $400 \times \sqrt{3} $ $400$ $400 \times \sqrt{2}$ $200 \times \sqrt{3}$ $500$

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...

admin

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admin asked Dec 14, 2022

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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? Square A regular pentagon A regular hexagon A regular septagon A regular octagon

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

admin

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admin asked Nov 30, 2022

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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: $2$ $4$ $1$ $5$ $3$

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$

admin

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admin asked Nov 30, 2022

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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 earlier position in a random direction independent of its past. After $4$ steps, what is the expected square of the distance (measured in centimeters) from its starting point? $4$ $1$ $2$ $\pi$ $0$

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...

admin

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admin asked Nov 30, 2022

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1 answer

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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 given that, $\text{PQ = 11 cm, QR = 4 cm, RS = 6 cm}$ and $\text{SP = 3 cm.}$ What is the shortest distance between $\text{PQ}$ and $\text{SR (in cm)}?$ $1.80$ $2.40$ $4.20$ $5.76$

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...

Arjun

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Arjun asked Feb 15, 2022

1 votes

1 answer

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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 area of the original equilateral triangle is $2:3$ $3:4$ $4:5$ $5:6$

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...

Arjun

6.6k points

587 views

Arjun asked Feb 19, 2021

1 votes

1 answer

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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 $a$, then the area of the shaded portion is _______. $\pi a^{2}-a^{2}$ $\pi a^{2}-\sqrt{2}a^{2}$ $\pi a^{2}-2a^{2}$ $\pi a^{2}-3a^{2}$

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 $a$,...

go_editor

1.9k points

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go_editor asked Feb 13, 2020

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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. $14.95$ $15.25$ $15.70$ $20.35$

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$

Milicevic3306

16.0k points

108 views

Milicevic3306 asked Mar 27, 2018

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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 $x=5$ from the fit? $-0.030$ $-0.014$ $0.014$ $0.030$

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 $...

Milicevic3306

16.0k points

118 views

Milicevic3306 asked Mar 27, 2018

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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 $1:2$. What is the length of the square (in mm) such that the combined area of the square and the rectagle is a $\textbf{MINIMUM?}$ $30$ $40$ $120$ $180$

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 $1:2$. ...

Milicevic3306

16.0k points

100 views

Milicevic3306 asked Mar 27, 2018

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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 radius and height of the cone is ________.

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...

Milicevic3306

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Milicevic3306 asked Mar 27, 2018

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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 twice her height. What is the height of the lamp post in meters? $1.5$ $3$ $4.5$ $6$

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...

gatecse

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gatecse asked Feb 19, 2018