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121
CAT 2003 | Question: 2-76
The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are $c, t,$ and $s,$ respectively. Then, $s > t > c$ $c > t > s$ $c > s > t$ $s > c > t$
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cat2003-2
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geometry
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122
CAT 2003 | Question: 2-71
Let $\text{ABCDEF}$ be a regular hexagon. What is the ratio of the area of the triangle $\text{ACE}$ to that of the hexagon $\text{ABCDEF}?$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$ $\frac{5}{6}$
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cat2003-2
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123
CAT 2003 | Question: 2-68
Answer the question on the basis on the basis of the information given below. Consider three circular parks of equal size with centres at $A_1,\:\: A_2,\:\:$ and $A_3$ respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). ... $A_3, \: C_3$ $A_3, \: C_2$ Somewhere between $A_2$ and $A_3$, Somewhere between $C_3$ and $C_1$
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cat2003-2
quantitative-aptitude
geometry
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124
CAT 2003 | Question: 2-67
Answer the question on the basis on the basis of the information given below. Consider three circular parks of equal size with centres at $A_1,\:\: A_2,\:\:$ and $A_3$ respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). ... finishes her sprint? $B_1, \: C_1$ $B_3, \: C_3$ $B_1, \: C_3$ $B_1$, Somewhere between $C_3$ and $C_11$
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Quantitative Aptitude
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526
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cat2003-2
quantitative-aptitude
geometry
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125
CAT 2003 | Question: 2-66
Answer the question on the basis on the basis of the information given below. Consider three circular parks of equal size with centres at $A_1,\:\: A_2,\:\:$ and $A_3$ respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed ... $b= \frac{a+c}{2}=2(1+\sqrt{3})r$ $c=2b-a=(2+\sqrt{3}r$
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Quantitative Aptitude
May 4, 2016
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cat2003-2
quantitative-aptitude
geometry
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126
CAT 2003 | Question: 2-55
A square tin sheet of side $12$ inches is converted into a box with open top in the following steps - The sheet is placed horizontally. Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent ... . If $x$ is an integer, then what value of $x$ maximizes the volume of the box? $3$ $4$ $1$ $2$
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Quantitative Aptitude
May 4, 2016
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187
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cat2003-2
quantitative-aptitude
geometry
1
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1
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127
CAT 2003 | Question: 2-51
A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a $35\%$ reduction in the length of the hypotenuse of the triangle. If the area of the original triangle ... the cut, what is the area (in square inches) of the smaller triangle? $16.665$ $16.565$ $15.465$ $14.365$
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Quantitative Aptitude
May 4, 2016
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cat2003-2
quantitative-aptitude
geometry
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0
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128
CAT 2006 | Question: 64
Below question is on the basis of information given below: A punching machine is used to punch a circular hole of diameter $2$ units from a square sheet of aluminium of width $2$ units, as shown below. The hole is punched such that circular hole touches one corner P of the square sheet and the diameter of ... $(\pi - 1) /2$ $(\pi - 1) /4$ $(\pi - 2) /2$ $(\pi - 2) /4$
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Quantitative Aptitude
May 3, 2016
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cat2006
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geometry
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1
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129
CAT 2004 | Question: 58
Answer the question on the basis of the information given below: In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line P ... of SO is $8 \sqrt{3}$ cm $10 \sqrt{3}$ cm $12 \sqrt{3}$ cm $14 \sqrt{3}$ cm
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Quantitative Aptitude
May 3, 2016
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cat2004
quantitative-aptitude
geometry
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130
CAT 2004 | Question: 57
Answer the question on the basis of the information given below: In the adjoining figure, I and II are circles with centres P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets ... that the length of PO is $28$ cm. What is the radius of the circle II? 2 cm 3 cm 4 cm 5 cm
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Quantitative Aptitude
May 3, 2016
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426
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cat2004
quantitative-aptitude
geometry
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131
CAT 2003 | Question: 1-125
Choose $1$ if the question can be answered by one of the statements alone but not by the other. Choose $2$ if the question can be answered by using either statement alone. Choose $3$ if the question can be answered by using both the statements together, but cannot be answered by ... $=1$ cm and perimeter of DEF $=3$ cm Perimeter of ABC $=6$ cm, AB $=2$ cm, and AC $=2$ cm
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Quantitative Aptitude
May 3, 2016
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13.4k
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314
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cat2003-1
quantitative-aptitude
geometry
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132
CAT 2003 | Question: 1-123
Choose $1$ if the question can be answered by one of the statements alone but not by the other. Choose $2$ if the question can be answered by using either statement alone. Choose $3$ if the question can be answered by using both the statements together, but ... of the circle? AB is not a diameter of the circle. The distance between AB and the tangent at E is $5$ cm.
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Quantitative Aptitude
May 3, 2016
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221
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cat2003-1
quantitative-aptitude
geometry
0
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133
CAT 2002 | Question: 89
Answer the question based on the diagram In the diagram below Angle $\text{ABC} = 90^{\circ} = \text{Angle DCH = Angle DOE = Angle EHK = Angle FKL = Angle GLM = Angle LMN,}$ $\text{AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN}$ The ratio of the areas of the two quadrangles $\text{ABCD}$ and $\text{DEFG}$ is $1:2$ $2:1$ $12:7$ None of these
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Quantitative Aptitude
May 2, 2016
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431
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cat2002
quantitative-aptitude
geometry
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134
CAT 2001 | Question: 41
A rectangular pool $20$ metres wide and $60$ metres long is surrounded by a walkway of uniform width. If the total area of the walkway is $516$ square metres, how wide, in metres, is the walkway? $43$ m $4.3$ m $3$ m $3.5$ m
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Quantitative Aptitude
Apr 1, 2016
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13.4k
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148
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cat2001
quantitative-aptitude
geometry
0
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135
CAT 2001 | Question: 40
Based on the figure below, what is the value of $x,$ if $y = 10?$ $0$ $11$ $12$ None of these
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Quantitative Aptitude
Apr 1, 2016
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13.4k
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137
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cat2001
quantitative-aptitude
geometry
1
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2
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136
CAT 2001 | Question: 34
In $\triangle \text{DEF}$ shown below, points $\text{A, B,}$ and $\text{C}$ are taken on $\text{DE, DF}$ and $\text{EF}$ respectively such that $\text{EC = AC}$ and $\text{CF = BC}.$ If $\measuredangle \text{D} = 40^{\circ}$, then what is $\measuredangle \text{ACB}$ in degrees? $140$ $70$ $100$ None of these
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Quantitative Aptitude
Mar 31, 2016
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cat2001
quantitative-aptitude
geometry
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137
CAT 2001 | Question: 29
Euclid has a triangle in mind, Its longest side has length $20$ and another of its sides has length $10.$ Its area is $80.$ What is the exact length of its third side? $\sqrt{260}$ $\sqrt{250}$ $\sqrt{240}$ $\sqrt{270}$
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Quantitative Aptitude
Mar 31, 2016
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13.4k
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150
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cat2001
quantitative-aptitude
geometry
0
votes
1
answer
138
CAT 2001 | Question: 23
Two sides of a plot measure $32$ metres and $24$ metres and the angle between them is a perfect right angle. The other two sides measure $25$ metres each and the other three are not right angles. What is the area of the plot? $768$ $534$ $696.5$ $684$
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Quantitative Aptitude
Mar 31, 2016
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13.4k
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262
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cat2001
quantitative-aptitude
geometry
0
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139
CAT 2001 | Question: 8
In the above diagram, $\text{ABCD}$ is a rectangle with $\text{AE = EF = FB}.$ What is the ratio of the area of the triangle $\text{CEF}$ and that of the rectangle? $\frac{1}{6}$ $\frac{1}{8}$ $\frac{1}{9}$ None of these
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13.4k
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257
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cat2001
quantitative-aptitude
geometry
0
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0
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140
CAT 2001 | Question: 7
A certain city has a circular wall around it, and this wall has four gates pointing north, south, east and west. A house stands outside the city, three km north of the north gate, and it can just be seen from a point nine km east of the south gate. What is the diameter of the wall what surrounds the city? $6$ km $9$ km $12$ km None of these
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Quantitative Aptitude
Mar 31, 2016
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13.4k
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455
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cat2001
quantitative-aptitude
geometry
0
votes
1
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141
CAT 2001 | Question: 2
A square, whose side is $2$ metres, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres is $\frac{\sqrt{2}}{\sqrt{2}+1}$ $\frac{2}{\sqrt{2}+1}$ $\frac{2}{\sqrt{2} - 1}$ $\frac{\sqrt{2}}{\sqrt{2}-1}$
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Quantitative Aptitude
Mar 31, 2016
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248
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cat2001
quantitative-aptitude
geometry
0
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142
CAT 2000 | Question: 110
A farmer has decided to build a wire fence along one straight side of his property. For this, he planned to place several fence-posts at six metre intervals, with posts fixed at both ends of the side. After he bought the posts and wire, he found that the number of posts ... many posts did he buy? $100$ metres, $15$ $100$ metres, $16$ $120$ metres, $15$ $120$ metres, $16$
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Quantitative Aptitude
Mar 30, 2016
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274
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cat2000
quantitative-aptitude
geometry
0
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answers
143
CAT 2000 | Question: 106
ABCDEFGH is a regular octagon. A and E are opposite vertices of the octagon. A frog starts jumping from vertex to vertex, beginning from A. From any vertex of the octagon except E, it may jump to either of the two adjacent vertices. When it reaches E, the frog stops ... n jumps ending in E. Then what is the value of $a_{2n - 1}$? Zero Four $2n - 1 $ Cannot be determined
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Quantitative Aptitude
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368
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cat2000
quantitative-aptitude
geometry
0
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144
CAT 2000 | Question: 102
In the figure above, $\text{AB = BC = CD = DE = EF = FG = GA}.$ Then $\measuredangle \text{DAE}$ is approximately $15^{\circ}$ $20^{\circ}$ $30^{\circ}$ $25^{\circ}$
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Quantitative Aptitude
Mar 29, 2016
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cat2000
quantitative-aptitude
geometry
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145
CAT 2000 | Question: 101
If $a, b, c$ are the sides of a triangle, and $a^2 + b^2 + c^2 = bc + ca + ab$, then the triangle is equilateral isosceles right angled obtuse angled
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cat2000
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geometry
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146
CAT 2000 | Question: 97
Consider a circle with unit radius. There are $7$ adjacent sectors, $\text{S}_1, \text{S}_2, \text{S}_3,\dots, \text{S}_7$ in the circle such that their total area is $(1/8)$th of the area of the circle. Further, the area of the $j$-th sector is twice that of the ... $\frac{\pi}{508}$ $\frac{\pi}{2040}$ $\frac{\pi}{1016}$ $\frac{\pi}{1524}$
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cat2000
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geometry
0
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1
answer
147
CAT 2000 | Question: 96
$\text{ABCD}$ is a rhombus with the diagonals $\text{AC}$ and $\text{BD}$ intersecting at the origin on the $x-y$ 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 the above
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148
CAT 2002 | Question: 88
Answer the question based on the diagram In the diagram below Angle $\text{ABC} = 90^{\circ} = \text{Angle DCH = Angle DOE = Angle EHK = Angle FKL = Angle GLM = Angle LMN,}$ $\text{AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN}$ The magnitude of Angle $\text{FGO =}$ $30^{\circ}$ $45^{\circ}$ $60^{\circ}$ None of these
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Mar 2, 2016
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399
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cat2002
quantitative-aptitude
geometry
0
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answers
149
CAT 2002 | Question: 81
The area of the triangle with the vertices $(a,a), (a+1, a)$ and $(a, a+2)$ is $a^3$ $1$ $0$ None of these
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Quantitative Aptitude
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163
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cat2002
quantitative-aptitude
geometry
0
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0
answers
150
CAT 2002 | Question: 74
There is a common chord of $2$ circles with radius $15$ and $20.$ The distance between the two centres is $25.$ The length of the chord is $48$ $24$ $36$ $28$
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Quantitative Aptitude
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cat2002
quantitative-aptitude
geometry
0
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151
CAT 2002 | Question: 71
In the figure given below, find the distance $\text{PQ}.$ $7$ m $4.5$ m $10.5$ m $6$ m
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Quantitative Aptitude
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180
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cat2002
quantitative-aptitude
geometry
0
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152
CAT 2002 | Question: 70
The internal bisector of an angle $\text{A}$ in a triangle $\text{ABC}$ meets the side $\text{BC}$ at point $\text{D. AB = 4, AC = 3}$ and angle $\text{A} = 60^{\circ}$. Then what is the length of the bisector $\text{AD}?$ $\frac{12 \sqrt{3}}{7}$ $\frac{12 \sqrt{13}}{7}$ $\frac{4 \sqrt{13}}{7}$ $\frac{4 \sqrt{3}}{7}$
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cat2002
quantitative-aptitude
geometry
0
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153
CAT 2002 | Question: 64
In order to cover less distance, a boy – rather than going along the longer and the shorter lengths of the rectangular path, goes by the diagonal. The boy finds that he saved a distance equal to half the longer side. The ration of the length and breadth is $1/2$ $2/3$ $3/4$ $7/15$
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Quantitative Aptitude
Mar 2, 2016
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cat2002
quantitative-aptitude
geometry
0
votes
1
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154
CAT 2002 | Question: 58
In the following figure, the area of the isosceles right triangle $\text{ABE}$ is $7$ sq.cm. If $\text{EC = 3BE},$ then the area of rectangle $\text{ABCD}$ id (insq.cm.) $64$ $82$ $26$ $56$
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Quantitative Aptitude
Mar 1, 2016
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13.4k
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457
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cat2002
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geometry
0
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answers
155
CAT 2003 | Question: 1-142
In the figure below, the rectangle at the corner measures $10\;\text{cm} \times 20\;\text{cm}.$ The corner A also the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm? $10\;\text{cm}$ $40\;\text{cm}$ $50\;\text{cm}$ None of these
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Quantitative Aptitude
Feb 10, 2016
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cat2003-1
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156
CAT 2003 | Question: 1-141
In the figure given below, $\text{AB}$ is the chord of a circle with centre $\text{O. AB}$ is extended to $\text{C}$ such that $\text{BC = OB}.$ The straight line $\text{CO}$ is produced to meet the circle at $\text{D}.$ ... $x=ky,$ then the value of $k$ is $3$ $2$ $1$ None of these
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Quantitative Aptitude
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13.4k
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177
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cat2003-1
quantitative-aptitude
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0
answers
157
CAT 2003 | Question: 1-136
In a triangle $\text{ABC, AB= 6, BC= 8}$ and $\text{AC=10}.$ A perpendicular dropped from $\text{B}$, meets the side $\text{AC}$ at $\text{D}.$ A circles of radius $\text{BD}$ (with centre $\text{B})$ is drawn. If the circle cuts $\text{AB}$ and $\text{BC}$ at $\text{P}$ and $\text{Q}$ respectively, then $\text{AP : QC}$ is equal to $1:1$ $3:2$ $4:1$ $3:8$
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0
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0
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158
CAT 2003 | Question: 1-137
In the diagram given below, $\measuredangle \text{ABD} = \measuredangle \text{CDB} = \measuredangle \text{PQD} = 90^{\circ}$. If $\text{AB : CD} = 3:1,$ the ratio of $\text{CD : PQ}$ is $1:0.69$ $1:0.75$ $1:0.72$ None of these
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146
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cat2003-1
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159
CAT 2003 | Question: 1-133
In the figure below, $\text{ABCDEF}$ is a rectangular hexagon and $\measuredangle \text{AOF} = 90^{\circ}$ is parallel to $\text{ED}.$ What is the ratio of the area of the triangle $\text{AOF}$ to that of the hexagon $\text{ABCDEF}?$ $\frac{1}{12}$ $\frac{1}{6}$ $\frac{1}{24}$ $\frac{1}{18}$
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13.4k
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264
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quantitative-aptitude
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0
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0
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160
CAT 2003 | Question: 1-132
Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with center at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centres at P and R ... the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to $20$ $28$ $36$ $40$
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