# Free CAT Questions

### Geometry for CAT 2011

Hi Guys, Geometry, Algebra and Number system form the major chunk of our QA section for CAT. Proficiency in these three sections would definitely boost our Quants scores. Contents of Geometry 1\. Plane Geometry - Basics and Tri... Read More »
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Hi Guys,

Geometry, Algebra and Number system form the major chunk of our QA section for CAT.

Proficiency in these three sections would definitely boost our Quants scores.

Contents of Geometry
1. Plane Geometry - Basics and Triangles
3. Circle
4. Mensuration
5. Trignometry
6. coordinate Geome

i tried to dowmload it..but was nt able to do so:-(...help..my email id is bhavyamehta1421@gmail.com
regards
bhavya
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same here dude..were u able to do it later..plz reply..regards bhavya
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vibhormittal360 Says
There are 3 balls in a plane touching each other equally and above it another ball placed touching all the balls equally, we have the find the distance of the bottom of the above ball to the ground...how can this problem be solved???

Three balls touching each other can placed like
:-(:-(
:-(
consider these connected to each other, And a ball is above in the center,

now the ball center from earth above earth is radius of any ball.

now the centers of 3 balls makes the equilateral triangle.
try to imagine a ball above it...
if you keep a ball above it

it will take a shape like pyramid. base is Equi. triangle and top is in middle
if we draw a perpendicular on the triangle it will meet centroid. so centroid is 2/3 of perpendicular inside the triangle.

Now you need to again apply one time for hight.
I hope I am pretty clear on that.

Thanks
Ashish
• 1 Like
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There are 3 balls in a plane touching each other equally and above it another ball placed touching all the balls equally, we have the find the distance of the bottom of the above ball to the ground...how can this problem be solved???
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Guys which book is best for Geometry and trigo preparation? Please help me as I am going to start my prep.
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Hi Puys,

I have a geometry Q which I'm stuck with. Please post the solution if u are able to solve it.
Q) In a cyclic quadrilateral ABCD, AB = 2, BC = 3, CD = 4 and AD = 5. What is the ratio of the lengths of the diagonals?
a) 7:11
b) 11:13
c) 10:11
d) 13:15
e) 15:7

Sandeep

In a cyclic quadrilateral ABCD the ratio of the diagonals equals the ratio of the sums of products of the sides that share the diagonals' end points. In other words,

(1) AC / BD = (ABAD + BCCD) / (ABBC + ADCD).
Proof

Triangles PAD and PBC are similar, so that
which can be also written as
BCCD/PC = ADCD/PD, In the same manner, the similarity of triangles PAB and PDC implies
which shows that four expressions
(4) ABAD/PA, ABBC/PB, BCCD/PC, and ADCD/PD are all equal. (1) follows by combining the first and the thrid terms and also the second and the fourth.
• 6 Likes
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Hi Puys,

I have a geometry Q which I'm stuck with. Please post the solution if u are able to solve it.
Q) In a cyclic quadrilateral ABCD, AB = 2, BC = 3, CD = 4 and AD = 5. What is the ratio of the lengths of the diagonals?
a) 7:11
b) 11:13
c) 10:11
d) 13:15
e) 15:7

Sandeep
• 1 Like
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sorry the data was missing
Q is the point of intersection of AC and DB inside the circle
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wat is point Q dude ??? i mean how is AQB forming...data missing i guess
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puys i have a question in which i am stuck :help

C and D are points on the circle with diameter AB such that (angle AQB) =2*(angle COD), where O the center of the circle. Q is the point of intersection of AC and DB inside the circle.The tangents at C and D meet at P. The circle has radius 1. The distance of P from its center is:
(a) (sqrt2)/3
(b) 2/(sqrt3)
(c) 3/(sqrt2)
(d) 1
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OK...i am losing the track here...in the question,it is not specified that he has to cover all the cities.Is that we are taking into account while solving??

From top city,3 routes are possible

Since there are 3 edges leading from each city and also the figure is perfectly symmetrical, these 3 routes are possible from each edge.

So,total number of routes = 4 * 3 = 12.

ps : one more ceo from Delhi
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Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without traveling on the same road more than once
10,12,14,15
I am getting 13 as the answer..that too by calculating manually all the routes.Is there any shortcut for such questions??
Image is attached.

From top city,3 routes are possible

Since there are 3 edges leading from each city and also the figure is perfectly symmetrical, these 3 routes are possible from each edge.

So,total number of routes = 4 * 3 = 12.

ps : one more ceo from Delhi
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If x, y, z are the angles of a triangle where x, y, z are integers, what is the number if values that x-y-z can take?
1. 90
2. 355
3. 178
4. 177

Please provide me with a solution.....

Quote:Solution I found on PG :
Originally Posted by quantphobic
If x, y, z are the angles of the triangle ABC, where x, y, z are integers, then what isthe number of values that x - y - z can take?

x-y-z = 180-2(y+z)

y+z -> 2 to 179

So, 178 values...
• 2 Likes
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Four cities are connected by a road network as shown in the figure. In how many ways can you start from any city and come back to it without traveling on the same road more than once

10,12,14,15

I am getting 13 as the answer..that too by calculating manually all the routes.Is there any shortcut for such questions??

Image is attached.
##### Attachments
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