Recent questions tagged geometry

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31

Best Open Video Playlist for Geometry Topic | Quantitative Aptitude
Please list out the best free available video playlist for Geometry Functions from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then select the best playlist and add to GO classroom video ... ones are more likely to be selected as best. For the full list of selected videos please see here

Please list out the best free available video playlist for Geometry Functions from Quantitative Aptitude as an answer here (only one playlist per answer). We'll then sele...

164 views

makhdoom ghaya asked Aug 26, 2022

4 votes

1 answer

32

GO Classes Weekly Quiz 1 | General Aptitude | Question: 9
Consider the following right-angled triangle, in which the angle between the side $\text{AC}$ and $\text{CB}$ is a right angle. Let $a,b,c$ be the length of the sides $\text{BC, AC, AB}$ respectively. Assume $a,b,c$ are integers. ... $a,b$ must be of odd length. $c$ must be of even length. It is possible that the length of every side is odd.

Consider the following right-angled triangle, in which the angle between the side $\text{AC}$ and $\text{CB}$ is a right angle. Let $a,b,c$ be the length of the sides $\t...

565 views

GO Classes asked May 1, 2022

1 votes

1 answer

33

GATE Civil 2022 Set 2 | GA Question: 8
Consider the following equations of straight lines: $\text{Line L1}: 2x - 3y = 5$ $\text{Line L2}: 3x + 2y = 8$ $\text{Line L3}: 4x - 6y = 5$ $\text{Line L4}: 6x - 9y = 6$ Which one among the following is the correct statement? $\text{L1}$ ... $\text{L2}$ $\text{L4}$ is perpendicular to $\text{L2}$ and $\text{L4}$ is parallel to $\text{L3}$

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 =...

376 views

Arjun asked Feb 15, 2022

1 votes

1 answer

34

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 areas of the squares, $\text{PXWR, RUVZ}$ and $\text{SPQT}$ is Area of $\text{SPQT}$ ... $\text{RUVZ}$ Area of $\text{PXWR}$ = Area of $\text{RUVZ}$ - Area of $\text{SPQT}$

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...

674 views

Arjun asked Feb 15, 2022

1 votes

1 answer

35

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 figures below. In the case $\text{M}$ ... of case $\text{M}$ to that of case $\text{N}$? $2 : 3$ $1 : 1$ $3 : 2$ $2 : 1$

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...

690 views

Arjun asked Feb 15, 2022

1 votes

1 answer

36

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? $\dfrac{1}{\sqrt{2}}$ $\dfrac{1}{2\sqrt{2}}$ $\sqrt{2}$ $2 \sqrt{2}$

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}{...

929 views

Arjun asked Feb 15, 2022

1 votes

1 answer

37

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? $3\sqrt{3} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : \sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 4 : 2\sqrt{\pi}$ $\sqrt{\left ( 3 \sqrt{3} \right )} : 2 : 2\sqrt{\pi}$

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...

512 views

Arjun asked Feb 15, 2022

1 votes

1 answer

38

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...

1.3k views

Arjun asked Feb 15, 2022

15 votes

3 answers

39

GATE CSE 2022 | GA Question: 9
The corners and mid-points of the sides of a triangle are named using the distinct letters $\text{P, Q, R, S, T}$ and $\text{U,}$ but not necessarily in the same order. Consider the following statements: The line joining $\text{P}$ and $\text{R}$ is ... $\text{U}$ cannot be placed at a mid-point $\text{R}$ cannot be placed at a corner

The corners and mid-points of the sides of a triangle are named using the distinct letters $\text{P, Q, R, S, T}$ and $\text{U,}$ but not necessarily in the same order. C...

6.8k views

Arjun asked Feb 15, 2022

3 votes

1 answer

40

GATE Overflow Test Series | Mock GATE | Test 6 | Question: 3
If the area of each of the $6$ faces of a cuboid is grown by a factor of $16$, the volume of the cuboid will grow by a factor of ______.

If the area of each of the $6$ faces of a cuboid is grown by a factor of $16$, the volume of the cuboid will grow by a factor of ______.

159 views

Arjun asked Jan 30, 2022

1 votes

1 answer

41

TIFR CSE 2021 | Part A | Question: 2
What is the area of a rectangle with the largest perimeter that can be inscribed in the unit circle (i.e., all the vertices of the rectangle are on the circle with radius $1$)? $1$ $2$ $3$ $4$ $5$

What is the area of a rectangle with the largest perimeter that can be inscribed in the unit circle (i.e., all the vertices of the rectangle are on the circle with radius...

soujanyareddy13

624 views

soujanyareddy13 asked Mar 25, 2021

12 votes

2 answers

42

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 and centers at $S$ and $Q$. The probability that any point picked randomly within the square falls in the ... ____________ $4-\frac{\pi }{2}$ $\frac{1}{2}$ $\frac{\pi }{2}-1$ $\frac{\pi }{4}$

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...

3.4k views

go_editor asked Mar 1, 2021

4 votes

1 answer

43

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 divided into eight equals parts. The length of each subdivided part in $\text{cm}$ is an integer. ... triangle $\text{PQR}$ possible, in $\text{cm}^{2}$, is $18$ $24$ $48\sqrt{3}$ $144 \sqrt{3}$

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...

1.2k views

go_editor asked Mar 1, 2021

4 votes

2 answers

44

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 ___________ $\frac{1}{8}$ $\frac{1}{6}$ $\frac{1}{4}$ $\frac{1}{2}$

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...

1.2k views

go_editor asked Mar 1, 2021

4 votes

1 answer

45

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 $50\;\text{cm}^{2}$. What is the area of the circle in $\text{cm}^{2}?$ $2\pi$ $50\pi$ $75\pi$ $100\pi$

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\;...

1.9k views

gatecse asked Feb 22, 2021

9 votes

2 answers

46

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 _______________ $36$ $45$ $72$ $108$

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 __...

2.6k views

Arjun asked Feb 19, 2021

3 votes

1 answer

47

GATE Electrical 2021 | GA Question: 7
In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown, in $\text{cm}^{2}$ is: $12.50$ $6.25$ $3.125$ $1.5625$

In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest square (shaded) as shown...

2.2k views

Arjun asked Feb 19, 2021

5 votes

1 answer

48

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...

3.0k views

Arjun asked Feb 19, 2021

2 votes

1 answer

49

CMI-2020-DataScience-B: 4
In the figure shown below, the circle has diameter $5$. Moreover, $AB$ is parallel to $DE.$ If $DE=3$ and $AB=6,$ what is the area of triangle $ABC?$

In the figure shown below, the circle has diameter $5$. Moreover, $AB$ is parallel to $DE.$ If $DE=3$ and $AB=6,$ what is the area of triangle $ABC?$

soujanyareddy13

342 views

soujanyareddy13 asked Jan 29, 2021

3 votes

1 answer

50

GATE Electrical 2020 | GA Question: 9
Given a semicircle with $\text{O}$ as the centre, as shown in the figure, the ratio $\dfrac{\overline{AC}+\overline{CB}}{\overline{AB}}$ is _______, where $\overline{AC}$, $\overline{CB}$ and $\overline{AB}$ are chords. $\sqrt{2}$ $\sqrt{3}$ $2$ $3$

Given a semicircle with $\text{O}$ as the centre, as shown in the figure, the ratio $\dfrac{\overline{AC}+\overline{CB}}{\overline{AB}}$ is _______, where $\overline{AC}$...

717 views

go_editor asked Feb 28, 2020

4 votes

2 answers

51

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 $a$,...

2.2k views

go_editor asked Feb 13, 2020

10 votes

2 answers

52

GATE CSE 2020 | Question: GA-8
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ number of circles can be painted, then the unpainted area available in ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$

The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching t...

5.6k views

Arjun asked Feb 12, 2020

15 votes

4 answers

53

GATE CSE 2020 | Question: GA-9
Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is ________. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$

Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, t...

8.1k views

Arjun asked Feb 12, 2020

1 votes

1 answer

54

TIFR CSE 2020 | Part A | Question: 13
What is the area of the largest rectangle that can be inscribed in a circle of radius $R$? $R^{2}/2$ $\pi \times R^{2}/2$ $R^{2}$ $2R^{2}$ None of the above

What is the area of the largest rectangle that can be inscribed in a circle of radius $R$?$R^{2}/2$$\pi \times R^{2}/2$$R^{2}$$2R^{2}$None of the above

670 views

admin asked Feb 10, 2020

0 votes

1 answer

55

ISI2014-DCG-55
If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then $\lambda < \frac{4}{3}$ $\lambda > \frac{5}{3}$ $\lambda \in \big( \frac{4}{3}, \frac{5}{3}\big)$ $\lambda \in \big( \frac{1}{3}, \frac{5}{3}\big)$

If $a,b,c$ are sides of a triangle $ABC$ such that $x^2-2(a+b+c)x+3 \lambda (ab+bc+ca)=0$ has real roots then$\lambda < \frac{4}{3}$$\lambda \frac{5}{3}$$\lambda \in \bi...

381 views

Arjun asked Sep 23, 2019

1 votes

1 answer

56

ISI2014-DCG-56
Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is $4$ $3$ $-4$ $-3$

Two opposite vertices of a rectangle are $(1,3)$ and $(5,1)$ while the other two vertices lie on the straight line $y=2x+c$. Then the value of $c$ is$4$$3$$-4$$-3$

434 views

Arjun asked Sep 23, 2019

2 votes

1 answer

57

ISI2014-DCG-58
Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of one of the vertices of this square are $(2, -2)$ $(2\sqrt{2},-2)$ $(-2, 2\sqrt{2})$ $(2\sqrt{2}, -2\sqrt{2})$

Consider a circle with centre at origin and radius $2\sqrt{2}$. A square is inscribed in the circle whose sides are parallel to the $X$ an $Y$ axes. The coordinates of on...

515 views

Arjun asked Sep 23, 2019

1 votes

1 answer

58

ISI2014-DCG-60
The equation of any circle passing through the origin and with its centre on the $X$-axis is given by $x^2+y^2-2ax=0$ where $a$ must be positive $x^2+y^2-2ax=0$ for any given $a \in \mathbb{R}$ $x^2+y^2-2by=0$ where $b$ must be positive $x^2+y^2-2by=0$ for any given $b \in \mathbb{R}$

The equation of any circle passing through the origin and with its centre on the $X$-axis is given by$x^2+y^2-2ax=0$ where $a$ must be positive$x^2+y^2-2ax=0$ for any giv...

505 views

Arjun asked Sep 23, 2019

2 votes

1 answer

59

ISI2015-MMA-18
The set of complex numbers $z$ satisfying the equation $(3+7i)z+(10-2i)\overline{z}+100=0$ represents, in the complex plane, a straight line a pair of intersecting straight lines a point a pair of distinct parallel straight lines

The set of complex numbers $z$ satisfying the equation $$(3+7i)z+(10-2i)\overline{z}+100=0$$ represents, in the complex plane,a straight linea pair of intersecting straig...

1.2k views

Arjun asked Sep 23, 2019

1 votes

1 answer

60

ISI2015-MMA-28
In a triangle $ABC$, $AD$ is the median. If length of $AB$ is $7$, length of $AC$ is $15$ and length of $BC$ is $10$ then length of $AD$ equals $\sqrt{125}$ $69/5$ $\sqrt{112}$ $\sqrt{864}/5$

In a triangle $ABC$, $AD$ is the median. If length of $AB$ is $7$, length of $AC$ is $15$ and length of $BC$ is $10$ then length of $AD$ equals$\sqrt{125}$$69/5$$\sqrt{11...

620 views

Arjun asked Sep 23, 2019

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