Official Quant thread for CAT 2013

MBA CAT 2022
1481

Aryabhatta had a triangle in mind. Its longest side was 10 cm and one of its sides has a length of 5 cm. What is the exact length of the third side if the area of the triangle is 20 cm^2?


1) root(65)
2) root(60)
3) root(120)
4) root(175)

Please explain with approach
1482
@soumitrabengeri said:
Aryabhatta had a triangle in mind. Its longest side was 10 cm and one of its sides has a length of 5 cm. What is the exact length of the third side if the area of the triangle is 20 cm^2?1) root(65)2) root(60)3) root(120)4) root(175)Please explain with approach
1)

look trianlge will be obtuse as it has 10 as longest side

now : 10

also 10^2 > x^2 + 5^2

ie x

so we get 2 options

i checkd with 1 and got ans 😃
1483
@soumitrabengeri said:
Aryabhatta had a triangle in mind. Its longest side was 10 cm and one of its sides has a length of 5 cm. What is the exact length of the third side if the area of the triangle is 20 cm^2?1) root(65)2) root(60)3) root(120)4) root(175)Please explain with approach
let the side 10 be the base...

now area of triangle will be= 1/2*10*(perpendicular)=20

from here lenghth of perpedicular= 4

as other side is 5...apply pythagoras theorm= _/(5^2- 4^2) =3

now other part of base will be= 10-3 =7

now apply pyth in other part of triangle to get third side = _/(4^2+7^2)=65

1484
@soumitrabengeri said:
Aryabhatta had a triangle in mind. Its longest side was 10 cm and one of its sides has a length of 5 cm. What is the exact length of the third side if the area of the triangle is 20 cm^2?1) root(65)2) root(60)3) root(120)4) root(175)Please explain with approach
let say the angle between the two sides (with length 10 and 5) is A
1/2*10*5* Sin A=20
=> Sin A=4/5

==> Cos A=3/5

==> 2*5*10*3/5=5^2+10^2-a^2
==> a^2=65
==> a=root(65) option (1)

Good morning All __/\__

@Brooklyn : last page pe 1 question daala h wo karo. Its a good question :)

1485
@vijay_chandola said:
Isosceles triangle ABC has the property that, if D is a point on AC such that BD bisects angle ABC, then triangle ABC and BCD are similar. If BC has length of one unit, then what is the length of AB?P.S. No OA available
sin72/ sin36 aa rha he mera
@vijay_chandola
1486
@rkshtsurana said:
sin72/ sin36 aa rha he mera@vijay_chandola
Similarity se,
AB/BC=BC/CD
=> AB=1/CD----(1)

Bisector property se,
AB/BC=AD/CD
=> AB=AD/CD---(2)

==> from 1 and 2,
AD=1

Now, AB cannot be equal to BC, and BC cannot be equal to CA
==> AB=AC

==> DC=AB-1

from (1),
AB=1/(AB-1)

By solving this quadratic equation, AB={1+sqrt(5)}/2

@rkshtsurana :thumbsup:
wolfram se check kiya, sin 72/sin 36={1+sqrt(5)}/2 :D
1487
@soumitrabengeri said:
Aryabhatta had a triangle in mind. Its longest side was 10 cm and one of its sides has a length of 5 cm. What is the exact length of the third side if the area of the triangle is 20 cm^2?1) root(65)2) root(60)3) root(120)4) root(175)Please explain with approach
LET base of triangle be 10 => ht = 4

Base is divided in to 7 cm & 3 cm

Applying Pytha we get _/65...

OA ?

PS: was struggling to find this thread since last 3-4 days....

Bhai log thread ka naam kuch aur rakho.... (CAT 2013)
1488
@karan20 said:
LET base of triangle be 10 => ht = 4Base is divided in to 7 cm & 3 cmApplying Pytha we get _/65...OA ?PS: was struggling to find this thread since last 3-4 days....Bhai log thread ka naam kuch aur rakho.... (CAT 2013)
your answer is correct..aur kya naam rakhenge bhai thread ka??
1489

A geometric progression of infinite terms has its first term as 2. If each of the terms is cubed, each term in the progression would be 7 times the sum of the terms following it. Find the sum to infinity formed by squaring each of the terms


1) 8/3
2) 10/3
3) 16/3
4) 20/3

Please explain with approach
1490
@vijay_chandola said:
Isosceles triangle ABC has the property that, if D is a point on AC such that BD bisects angle ABC, then triangle ABC and BCD are similar. If BC has length of one unit, then what is the length of AB?P.S. No OA available
sin72/ sin36 ??? iske aage nhi aa rha :banghead:
1491
@soumitrabengeri said:
A geometric progression of infinite terms has its first term as 2. If each of the terms is cubed, each term in the progression would be 7 times the sum of the terms following it. Find the sum to infinity formed by squaring each of the terms1) 8/32) 10/33) 16/34) 20/3Please explain with approach
option 3


a = 2

sum of the cubed series from the second term = 7 * (a^3 * r^3)/(1 - r^3) = a^3
7r^3 = 1 - r^3
8r^3 = 1
r = 1/2

sum to infinity of squared terms = a^2/(1-r^2) = 4/(3/4) = 16/3
1492
@Brooklyn said:
sin72/ sin36 ??? iske aage nhi aa rha
sin72/ sin36=2*Sin 36*cos 36/sin 36=2*cos 36
ab ho jayega. :)
1493
cos 18 cos 36 cos 72 cos 144 = ?
1494
@soumitrabengeri dekh bhai .this might help u badi muskil se banaya hai yeh paint mein 😛 root (7^2+4^2)=root(65)
1495
@sauravd2001 said:
@soumitrabengeri dekh bhai .this might help u badi muskil se banaya hai yeh paint mein root (7^2+4^2)=root(65)
Thank you so much bhai..appreciate it..
1496

1/4{(2 cos18 cos72)(2 cos36 cos144)}

=1/4{(cos90 + cos54)(cos8 + cos180)}
=1/4{cos54(-1 + cos8)}

options kya hai?


@rkshtsurana said:
cos 18 cos 36 cos 72 cos 144 = ?
1497
@Messy_19 said:
1/4{(2 cos18 cos72)(2 cos36 cos144)}=1/4{(cos90 + cos54)(cos8 + cos180)}=1/4{cos54(-1 + cos8)}options kya hai?
1/16 (rt { 5 + 2rt5})
-1/16( rt { 5 + 2rt5})
-1/16(rt( rt5 + 1))
1/16(rt (rt5 + 1))

a standard method to solve such ques is der
1498
@rkshtsurana bhai answere option 2 hai kya ? dekh bhai option 1 and 4 directly reject karde kyunki cos 144 de rakha hai toh answeer defintely negative hoga n baki karke maine 2 nikala hai
1499
@sauravd2001 said:
@rkshtsurana bhai answere option 2 hai kya ? dekh bhai option 1 and 4 directly reject karde kyunki cos 144 de rakha hai toh answeer defintely negative hoga n baki karke maine 2 nikala hai
ans is 2..plz share approach..
1500
The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?