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Recent questions tagged geometry

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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 $41$? $6$ $4$ $24.5$ $20.5$
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$
1 votes
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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$
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, the...
1 votes
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$
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 tria...
1 votes
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$
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 lengt...
3 votes
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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$
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 t...
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$
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...
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$
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...
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$
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...
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
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{...
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 $\sqrt{12}$ $\sqrt{14}$ $\sqrt{13}$ $\sqrt{11}$
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 cir...
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 $\text{ABCD}?$ $24,10$ $25,9$ $24,12$ $25,10$
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...
1 votes
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 $89$ $87$ $86$ $90$
$\text{ABCD}$ 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...
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 $3\sqrt{2}$ $3$ $4$ $\sqrt{3}$
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$$\sqrt{3}$
1 votes
1 answer
62
CAT 2017 Set-2 | Question: 85
If three sides of a rectangular park have a total length $400$ ft, then the area of the park is maximum when the length (in ft) of its longer side is $299$ $200$ $201$ $399$
If three sides of a rectangular park have a total length $400$ ft, then the area of the park is maximum when the length (in ft) of its longer side is$299$$200$$201$$399$
1 votes
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? $160$ $159$ $169$ $150$
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...
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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? $1$ $2$ $3$ $4$
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 $\text{E}$. The dista...
1 votes
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? $1:3$ $4:1$ $3:1$ $4:3$
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...
1 votes
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 $\angle \text{DEC}?$ $15^{\circ}$ $30^{\circ}$ $20^{\circ}$ $45^{\circ}$
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}$
1 votes
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 $\triangle \text{ABC}$ __________
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 $\triangle \text{ABC}$ __________
1 votes
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 ___________
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 ___________...
1 votes
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
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 triangleare on l...
0 votes
1 answer
73
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 $\pi /3$ $11/7$ $3 /\pi$ $7/11$
$\text{PQRS}$ 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 ...
0 votes
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74
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? $1: 3$ $4: 1$ $3: 1$ $4: 3$
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$$4:...
0 votes
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78
CAT 2015 | Question: 83
In the figure above, $\text{AB = BC = CD = DE = EF = FG = GA}$. Then $\angle \text{DAE}$ is approximately $15^{\circ}$ $20^{\circ}$ $30^{\circ}$ $25^{\circ}$
In the figure above, $\text{AB = BC = CD = DE = EF = FG = GA}$. Then $\angle \text{DAE}$ is approximately $15^{\circ}$$20^{\circ}$$30^{\circ}$$25^{\circ}$
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