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41
NIELIT 2017 DEC Scientist B - Section A: 59
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure $9, 40$ and $41$? $6$ $4$ $24.5$ $20.5$
Lakshman Patel RJIT
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Mar 30, 2020
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Lakshman Patel RJIT
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nielit2017dec-scientistb
geometry
circles
triangle
1
vote
1
answer
42
CAT 2019 Set-2 | Question: 72
Two circles, each of radius $4$ cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is $\sqrt{2}$ $\frac{\pi }{3}$ $\frac{1}{\sqrt{2}}$ $1$
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Mar 20, 2020
by
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cat2019-2
quantitative-aptitude
geometry
1
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1
answer
43
CAT 2019 Set-2 | Question: 82
In a triangle $\text{ABC}$, medians $\text{AD}$ and $\text{BE}$ are perpendicular to each other, and have lengths $12$ cm and $9$ cm, respectively. Then, the area of triangle $\text{ABC}$, in sq cm. is $68$ $72$ $78$ $80$
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
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297
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cat2019-2
quantitative-aptitude
geometry
1
vote
1
answer
44
CAT 2019 Set-2 | Question: 98
Let $\text{A}$ and $\text{B}$ be two regular polygons having $\text{A}$ and $\text{B}$ sides, respectively. If $b= 2a$ and each interior angle of $\text{B}$ is $3/2$ times each interior angle of $\text{A}$, then each interior angle, in degrees, of a regular polygon with $a + b$ sides is ________
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Mar 20, 2020
by
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13.4k
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387
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cat2019-2
quantitative-aptitude
geometry
numerical-answer
1
vote
1
answer
45
CAT 2019 Set-2 | Question: 93
Let $\text{ABC}$ be a right-angled triangle with hypotenuse $\text{BC}$ of length $20$ cm. If $\text{AP}$ is perpendicular on $\text{BC}$, then the maximum possible length of $\text{AP}$, in cm, is $10$ $6\sqrt{2}$ $8\sqrt{2}$ $5$
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
252
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cat2019-2
quantitative-aptitude
geometry
3
votes
1
answer
46
CAT 2018 Set-2 | Question: 73
A chord of length $5$ cm subtends an angle of $60^\circ$ at the centre of a circle. The length, in cm, of a chord that subtends an angle of $120^\circ$ at the centre of the same circle is $8$ $6\sqrt2$ $5\sqrt3$ $2\pi$
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
303
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cat2018-2
quantitative-aptitude
geometry
2
votes
1
answer
47
CAT 2018 Set-2 | Question: 72
On a triangle $\text{ABC}$, a circle with diameter $\text{BC}$ is drawn, intersecting $\text{AB}$ and $\text{AC}$ at points $\text{P}$ and $\text{Q}$, respectively. If the lengths of $\text{AB, AC}$, and $\text{CP}$ are $30$ cm, $25$ cm, and $20$ cm respectively, then the length of $\text{BQ}$, in cm, is __________
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
250
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cat2018-2
quantitative-aptitude
geometry
numerical-answer
3
votes
1
answer
48
CAT 2018 Set-2 | Question: 86
A parallelogram $\text{ABCD}$ has area $48$ sqcm. If the length of $\text{CD}$ is $8$ cm and that of $\text{AD}$ is $s$ cm, then which one of the following is necessarily true? $s\geq6$ $s\neq6$ $s\leq6$ $5\leq s\leq7$
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Mar 20, 2020
by
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13.4k
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392
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cat2018-2
quantitative-aptitude
geometry
2
votes
1
answer
49
CAT 2018 Set-2 | Question: 96
From a rectangle $\text{ABCD}$ of area $768$ sq cm, a semicircular part with diameter $\text{AB}$ and area $72\pi$ sq cm is removed. The perimeter of the leftover portion, in cm, is $80 + 16\pi$ $86+8\pi$ $82+24\pi$ $88+12\pi$
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Mar 20, 2020
by
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13.4k
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305
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cat2018-2
quantitative-aptitude
geometry
3
votes
1
answer
50
CAT 2018 Set-2 | Question: 94
The area of a rectangle and the square of its perimeter are in the ratio $1:25$. Then the lengths of the shorter and longer sides of the rectangle are in the ratio $1:4$ $2:9$ $1:3$ $3:8$
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
335
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cat2018-2
quantitative-aptitude
geometry
2
votes
1
answer
51
CAT 2018 Set-2 | Question: 97
A triangle $\text{ABC}$ has area $32$ sq units and its side $\text{BC}$, of length $8$ units, lies on the line $x =4$. Then the shortest possible distance between $\text{A}$ and the point $(0,0)$ is $4$ units $8$ units $4\sqrt2$ units $ 2\sqrt2$ units
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
260
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cat2018-2
quantitative-aptitude
geometry
2
votes
1
answer
52
CAT 2018 Set-1 | Question: 73
In a circle, two parallel chords on the same side of a diameter have lengths $4$ cm and $6$ cm. If the distance between these chords is $1$ cm, then the radius of the circle, in cm, is $\sqrt{12}$ $\sqrt{14}$ $\sqrt{13}$ $\sqrt{11}$
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Quantitative Aptitude
Mar 20, 2020
by
go_editor
13.4k
points
139
views
cat2018-1
quantitative-aptitude
geometry
2
votes
1
answer
53
CAT 2018 Set-1 | Question: 76
Given an equilateral triangle $\text{T1}$ with side $24$ cm, a second triangle $\text{T2}$ is formed by joining the midpoints of the sides of $\text{T1}$. Then a third triangle $\text{T3}$ is formed by joining the midpoints of the sides of $\text{T2}$. If this ... many such triangles $\text{T1, T2, T3}, \dots$ will be $164\sqrt 3$ $188\sqrt 3$ $248\sqrt 3$ $192\sqrt 3$
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by
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13.4k
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224
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cat2018-1
quantitative-aptitude
geometry
2
votes
1
answer
54
CAT 2018 Set-1 | Question: 80
Points $\text{E, F, G, H}$ lie on the sides $\text{AB, BC, CD}$, and $\text{DA}$, respectively, of a square $\text{ABCD}$. If $\text{EFGH}$ is also a square whose area is $62.5\%$ of that of $\text{ABCD}$ and $\text{CG}$ is longer than $\text{EB}$, then the ratio of length of $\text{EB}$ to that of $\text{CG}$ is $2:5$ $4:9$ $3:8$ $1:3$
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Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
370
views
cat2018-1
quantitative-aptitude
geometry
2
votes
1
answer
55
CAT 2018 Set-1 | Question: 90
In a circle with center $\text{O}$ and radius $1$ cm, an arc $\text{AB}$ makes an angle $60$ degrees at $\text{O}$. Let $\text{R}$ be the region bounded by the radii $\text{OA, OB}$ and the arc $\text{AB}$. If $\text{C}$ and $\text{D}$ ... $\bigg(\dfrac{\pi}{6} \bigg)^\frac{1}{2} \\$ $\bigg(\dfrac{\pi}{4\sqrt 3} \bigg)^\frac{1}{2}$
go_editor
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Mar 20, 2020
by
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13.4k
points
329
views
cat2018-1
quantitative-aptitude
geometry
2
votes
1
answer
56
CAT 2018 Set-1 | Question: 88
Let $\text{ABCD}$ be a rectangle inscribed in a circle of radius $13$ cm. Which one of the following pairs can represent, in cm, the possible length and breadth of $\text{ABCD}?$ $24,10$ $25,9$ $24,12$ $25,10$
go_editor
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in
Quantitative Aptitude
Mar 20, 2020
by
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13.4k
points
160
views
cat2018-1
quantitative-aptitude
geometry
2
votes
1
answer
57
CAT 2018 Set-1 | Question: 89
In a parallelogram $\text{ABCD}$ of area $72$ sq cm, the sides $\text{CD}$ and $\text{AD}$ have lengths $9$ cm and $16$ cm, respectively. Let $\text{P}$ be a point on $\text{CD}$ such that $\text{AP}$ is perpendicular to $\text{CD}$. Then the area, in sq cm, of triangle $\text{APD}$ is $18\sqrt 3$ $24\sqrt 3$ $32\sqrt 3$ $12\sqrt 3$
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Mar 20, 2020
by
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13.4k
points
180
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cat2018-1
quantitative-aptitude
geometry
1
vote
1
answer
58
CAT 2017 Set-2 | Question: 84
$\text{ABCD}$ is a quadrilateral inscribed in a circle with centre $\text{O}$. If $\angle \text{COD} =120$ degrees and $\angle \text{BAC} = 30$ degrees, then the value of $\angle \text{BCD}$ (in degrees) is $89$ $87$ $86$ $90$
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Mar 16, 2020
by
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13.4k
points
144
views
cat2017-2
quantitative-aptitude
geometry
1
vote
1
answer
59
CAT 2017 Set-2 | Question: 82
The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths $10$ cm and $20$ cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is $12$ cm. If the ... $1300$ $1340$ $1480$ $1520$
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Quantitative Aptitude
Mar 16, 2020
by
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13.4k
points
235
views
cat2017-2
quantitative-aptitude
geometry
2
votes
1
answer
60
CAT 2017 Set-2 | Question: 81
Let $\text{ABCDEF}$ be a regular hexagon with each side of length $1$ cm. The area (in sq cm) of a square with $\text{AC}$ as one side is $3\sqrt{2}$ $3$ $4$ $\sqrt{3}$
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Quantitative Aptitude
Mar 16, 2020
by
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13.4k
points
195
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cat2017-2
quantitative-aptitude
geometry
1
vote
1
answer
61
CAT 2017 Set-2 | Question: 86
Let $\text{P}$ be an interior point of a right-angled isosceles triangle $\text{ABC}$ with hypotenuse $\text{AB}$. If the perpendicular distance of $\text{P}$ from each of $\text{AB, BC},$ and $\text{CA}$ is $4\left ( \sqrt{2} -1\right )$cm, then the area, in sq cm, of the triangle $\text{ABC}$ is $16$ $15$ $14$ $12$
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Quantitative Aptitude
Mar 16, 2020
by
go_editor
13.4k
points
188
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cat2017-2
quantitative-aptitude
geometry
1
vote
1
answer
62
CAT 2017 Set-2 | Question: 85
If three sides of a rectangular park have a total length $400$ ft, then the area of the park is maximum when the length (in ft) of its longer side is $299$ $200$ $201$ $399$
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Quantitative Aptitude
Mar 16, 2020
by
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13.4k
points
222
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cat2017-2
quantitative-aptitude
geometry
1
vote
1
answer
63
CAT 2017 Set-1 | Question: 86
Let $\text{ABC}$ be a right-angled triangle with $\text{BC}$ as the hypotenuse. Lengths of $\text{AB}$ and $\text{AC}$ are $15$ km and $20$ km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from $\text{A}$ at a speed of $30$ km per hour is $23$ $22$ None of these $24$
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Quantitative Aptitude
Mar 13, 2020
by
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13.4k
points
219
views
cat2017-1
quantitative-aptitude
geometry
1
vote
1
answer
64
CAT 2017 Set-1 | Question: 83
Let $\text{ABC}$ be a right-angled isosceles triangle with hypotenuse $\text{BC}$. Let $\text{BQC}$ be a semi-circle, away from A, with diameter $\text{BC}$. Let $\text{BPC}$ be an arc of a circle centered at $\text{A}$ and lying between $\text{BC}$ ... the area, in sq cm, of the region enclosed by $\text{BPC}$ and $\text{BQC}$ is $9 \pi-18$ $18$ $9\pi$ $9$
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Quantitative Aptitude
Mar 13, 2020
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13.4k
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300
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cat2017-1
quantitative-aptitude
geometry
0
votes
0
answers
65
CAT 2017 Set-1 | Question: 82
From a triangle $\text{ABC}$ with sides of lengths $40$ ft, $25$ ft and $35$ ft, a triangular portion $\text{GBC}$ is cut off where $\text{G}$ is the centroid of $\text{ABC}$. The area, in sq ft, of the remaining portion of triangle $\text{ABC}$ is $225 \sqrt{3} \\$ $\dfrac{500}{ \sqrt{3}} \\$ $\dfrac{275 }{\sqrt{3}} \\$ $\dfrac{250 }{\sqrt{3}} $
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Quantitative Aptitude
Mar 13, 2020
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13.4k
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110
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cat2017-1
quantitative-aptitude
geometry
1
vote
1
answer
66
CAT 2017 Set-1 | Question: 95
Let $\text{AB, CD, EF, GH}$, and $\text{JK}$ be five diameters of a circle with center at $\text{O}$. In how many ways can three points be chosen out of $\text{A, B, C, D, E, F, G, H, J, K,} $ and $\text{O}$ so as to form a triangle? $160$ $159$ $169$ $150$
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Quantitative Aptitude
Mar 13, 2020
by
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13.4k
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206
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cat2017-1
quantitative-aptitude
geometry
0
votes
0
answers
67
CAT 2016 | Question: 67
Direction for questions: Answer the questions based on the following information. In a locality, there are five small cities: $\text{A, B, C, D}$ and $\text{E}$ ... is to be set up within $3 \text{ km }$ of each city, how many ration shops will be required? $1$ $2$ $3$ $4$
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Mar 11, 2020
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13.4k
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216
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cat2016
quantitative-aptitude
geometry
1
vote
1
answer
68
CAT 2016 | Question: 71
From a circular sheet of paper with a radius $20\:\text{cm}$, four circles of radius $5\:\text{cm}$ each are cut out. What is the ratio of the uncut to the cut portion? $1:3$ $4:1$ $3:1$ $4:3$
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13.4k
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cat2016
quantitative-aptitude
geometry
1
vote
1
answer
69
CAT 2016 | Question: 69
If $\text{ABCD}$ is a square and $\text{BCE}$ is an equilateral triangle, what is the measure of $\angle \text{DEC}?$ $15^{\circ}$ $30^{\circ}$ $20^{\circ}$ $45^{\circ}$
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Quantitative Aptitude
Mar 11, 2020
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13.4k
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330
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cat2016
quantitative-aptitude
geometry
1
vote
1
answer
70
CAT 2016 | Question: 76
The figure shows a circle of diameter $\text{AB}$ and radius $6.5$ cm. If chord $\text{CA}$ is $5$ cm long, find the area of $\triangle \text{ABC}$ __________
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cat2016
quantitative-aptitude
geometry
numerical-answer
1
vote
1
answer
71
CAT 2016 | Question: 79
In $\triangle \text{ABC},\:\angle \text{B}$ is a right angle, $\text{AC} = 6$ cm, and $\text{D}$ is the mid-point of $\text{AC}$. The length of $\text{BD}$ is ___________
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13.4k
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cat2016
quantitative-aptitude
geometry
numerical-answer
1
vote
1
answer
72
CAT 2016 | Question: 90
The points of intersection of three lines $2\text{X} + 3\text{Y} – 5 = 0, 5\text{X} – 7\text{Y} + 2 = 0$ and $9\text{X} – 5\text{Y} – 4= 0$ form a triangle are on lines perpendicular to each other are on lines parallel to each other are coincident
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13.4k
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cat2016
quantitative-aptitude
geometry
cartesian-coordinates
0
votes
0
answers
73
CAT 2015 | Question: 73
From a circular sheet of paper with a radius $20$ cm, four circles of radius $5$ each are cut out. What is the ratio of the uncut to the cut portion? $1: 3$ $4: 1$ $3: 1$ $4: 3$
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Quantitative Aptitude
Mar 9, 2020
by
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13.4k
points
132
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cat2015
quantitative-aptitude
geometry
0
votes
1
answer
74
CAT 2015 | Question: 72
$\text{PQRS}$ is a square. $\text{SR}$ is a tangent (at point $\text{S})$ to the circle with centre $\text{O}$ and $\text{TR = OS}$. Then the ratio of area of the circle to the area of the square is $\pi /3$ $11/7$ $3 /\pi$ $7/11$
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Quantitative Aptitude
Mar 9, 2020
by
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13.4k
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147
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cat2015
quantitative-aptitude
geometry
0
votes
1
answer
75
CAT 2015 | Question: 71
$\text{ABCD}$ is a square of area $4$ with diagonals $\text{AC}$ and $\text{BD}$, dividing square into $4$ congruent triangles. Figure looks like four non-over lapping triangles. Then the sum of the perimeters of the triangles is $8\left ( 2+\sqrt{2} \right )$ $8\left ( 1+\sqrt{2} \right )$ $4\left ( 1+\sqrt{2} \right )$ $4\left ( 2+\sqrt{2} \right )$
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cat2015
quantitative-aptitude
geometry
0
votes
1
answer
76
CAT 2015 | Question: 80
$\text{ABCD}$ is a rhombus with the diagonals $\text{AC}$ and $\text{BD}$ intersecting at the origin on the $x\text{-}y$ plane. The equation of the straight line $\text{AD}$ is $x + y = 1$. What is the equation of $\text{BC}?$ $x + y = -1$ $x - y = -1$ $x + y = 1$ None of these
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13.4k
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188
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cat2015
quantitative-aptitude
geometry
0
votes
1
answer
77
CAT 2015 | Question: 76
The figure shows the rectangle $\text{ABCD}$ with a semicircle and a circle inscribed inside in it as shown. What is the ratio of the area of the circle to that of the semicircle? $\left ( \sqrt{2}-1 \right )^{2}:1$ $2\left ( \sqrt{2}-1 \right )^{2}:1$ $\left ( \sqrt{2}-1 \right )^{2}:2$ None of these
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13.4k
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132
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cat2015
quantitative-aptitude
geometry
0
votes
0
answers
78
CAT 2015 | Question: 83
In the figure above, $\text{AB = BC = CD = DE = EF = FG = GA}$. Then $\angle \text{DAE}$ is approximately $15^{\circ}$ $20^{\circ}$ $30^{\circ}$ $25^{\circ}$
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cat2015
quantitative-aptitude
geometry
0
votes
0
answers
79
CAT 2011 | Question: 5
On a plate in the shape of an equilateral triangle $\text{ABC}$ with area $16\sqrt 3\;\text{sq cm}$, a rod $\text{GD}$, of height $8\:\text{cm}$, is fixed vertically at the centre of the triangle. $\text{G}$ ... of the triangle $\text{CGD}\:\text{(in sq cm)}$. $3 \sqrt {19}$ $4 \sqrt {19}$ $12 \sqrt {3}$ None of these
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Krithiga2101
268
points
446
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cat2011
quantitative-aptitude
geometry
0
votes
0
answers
80
CAT 2011 | Question: 14
In the figure alongside, $\text{O}$ is the centre of the circle and $\text{AC}$ is the diameter. The line $\text{FEG}$ is tangent to the circle at $\text{E}$. If $\angle \text{GEC}= 52^{\circ}$, find the value of $\angle e+\angle c.$ $154^{\circ}$ $156^{\circ}$ $166^{\circ}$ $180^{\circ}$
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253
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