Official Quant thread for CAT 2013

@bodhi_vriksha said:
In a right circular cone of radius 4cm and height 10cm, largest cube is inscribed whose base rests at base of the cone. A sphere is then inserted between top of cube and the vertex of cone. What can be the maximum radius of the sphere?Team BV--Pratik Gauri
aprox. near 1.5 cm?? options would be helpful to eliminate and use..
@amresh_maverick said:
approx 2.06 by any chance
@pratskool said:
aprox. near 1.5 cm?? options would be helpful to eliminate and use..
approach ? I dunt know the answer :)

Team BV--Pratik Gauri
@bodhi_vriksha said:
approach ? I dunt know the answer Team BV--Pratik Gauri
the side of the cube came out to be 40/9 cm which is the diameter of the cone in which sphere in inscribed, next sphere is like an inscribed circle in the triangle of the cone.... found the inradius of the triangle...
@heylady said:
What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?
60/143 ?

[9! / ( 5! 4! ) * 5! / ( 3! 2 !) ] = 14 ! / ( 8! 6!)
@heylady said:
What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?
60/143
@heylady said:
What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?
Approach: Total ways to reach from 0,0 to 8,6 = 14!/8!*6!

No. of ways to reach 0,0 to 5,4 and then to 8,6 = 9!/5!*4! X 5!/3!*2!

Req prob = 60/143
@techgeek2050 said:
what i mean to say is thisif one of a,b,c>=10let a = a' + 10 , the equation becomesa' + b + c + k = 6similarly for b and c, a + b' + c + k = 6 , and a + b + c' + k = 6for each solution = 9C3so total = 3*9C3 ways are there wherein one of a,b,c is >=10 , so that is what should be subracted. P.S - bhai don't call me sir.. m just a noob.
my brain not working in this particular problem, i would try understanding and getting back to you, would tag you here if i am able to do so...
@bodhi_vriksha said:
approach ? I dunt know the answer Team BV--Pratik Gauri
similar to @pratskool sir,

the side of the cube will be 40/9 cm . Found R which is in radius
@bodhi_vriksha said:
In a right circular cone of radius 4cm and height 10cm, largest cube is inscribed whose base rests at base of the cone. A sphere is then inserted between top of cube and the vertex of cone. What can be the maximum radius of the sphere?Team BV--Pratik Gauri
around 1.5 , exactly getting 100/9*1/(2+root(29)) ??
@amresh_maverick said:
similar to @pratskool sir,the side of the cube will be 40/9 cm . Found R which is in radius
correct approach :)

Team BV--Pratik Gauri
@pratskool said:
the side of the cube came out to be 40/9 cm which is the diameter of the cone in which sphere in inscribed, next sphere is like an inscribed circle in the triangle of the cone.... found the inradius of the triangle...
How can it be 40/9? 3D figure hai...will be less...

regards
scrabbler

please solve it Question 18

@scrabbler said:
How can it be 40/9? 3D figure hai...will be less...regardsscrabbler
sirjee , itna visualisation mujhse nei hota,,, maine toh triangle main square ghusa ke kar diya...
@scrabbler said:
How can it be 40/9? 3D figure hai...will be less...regardsscrabbler
use similar triangles ..
10-x/x=10/8 .. from this we get upper triangle's height :)

Team BV--Pratik Gauri
@heylady said:
What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?
60/3...finally
@scrabbler said:
How can it be 40/9? 3D figure hai...will be less...regardsscrabbler
maine to aajtak 3D mein film bhi nahi dekhi

How many integers b/w 1 and 10000 have the sum of their digits equal to 18 ?

PS: @bodhi_vriksha sir ur method to solve above type of q's got over my head , bouncer
@pratskool said:
sirjee , itna visualisation mujhse nei hota,,, maine toh triangle main square ghusa ke kar diya...
Wohi to...instead of quad with sides x and x it will be a quad with sides x and xrt2 (the horizontal one). Bahut painful number aata hai...

regards
scrabbler

@scrabbler said:
Wohi to...instead of quad with sides x and x it will be a quad with sides x and xrt2 (the horizontal one). Bahut painful number aata hai...regardsscrabbler

isn't it fine if we consider a cross section of 3D figure and solve it...
like in ths case , sabse middle wala cross section with max area ?
@heylady said:
What is the probability that a path from (0,0) to (8,6) pass through (5,4), assuming that all paths move along grid lines and that movement must be either the positive x or the positive y direction?
60/143 ?

9c5*5c2/14c6 = 60/143
@amresh_maverick said:
maine to aajtak 3D mein film bhi nahi dekhiHow many integers b/w 1 and 10000 have the sum of their digits equal to 18 ?PS: @bodhi_vriksha sir ur method to solve above type of q's got over my head , bouncer
There would be one 2 digit no ie. 99
coming to 3 digit nos .. abc --> a+b+c=18
a' +b+c=17 --> C(19,2) solutions... subtract cases when b or c >9
b and c greater than 9 ..cases are --> C(9,2)*2
a greater than 9 -->C(10,2)

so total 3 digit no--> C(19,2)-2*C(9,2)-C(10,2)

similarly find 4 digit no cases and add :)

Team BV--Pratik Gauri