Official Quant thread for CAT 2013

MBA CAT 2024
24488
@nramachandran said:
A person walking takes 26 steps to come down on a escalator and it takes 30 seconds for him for walking. The same person while running takes 18 second and 34 steps. How many steps are there ?
46
24489
@amresh_maverick said:
On giving 3 pencils free with every 5 pens bought, a shopkeeper makes a profit of 20% and on giving 6 pencils free with every 2 pens bought, he suffers a loss of 25%. Find the approximate profit percent made by the shopkeeper when he gives 4 pencils free with every 6 pens bought. (Assume that the pencils are identical and the same applies to the pens.)
18%
24490
What is the number of distinct triangles with integral valued sides and perimeter 14?
24491

guys pls help me with this---->
what is the coefficient of x^2*y^3*z^5 in (x+y+z)^10?

24492
@vishcat
10C5 * 5C2??
24493
@imvipk the options are-
1)2!3!5!
2)10!/(2!3!5!)
3)10c2*8c3*5c5
4)all of them
5)none.


your ans may be right so pls explain it
24494
@vishcat
option 2??
24495
@imvipk yes its right .do explain that
24496
The total number of Integer solutions of x³y²z⁴=9720000
24497
@vishcat said:
guys pls help me with this---->what is the coefficient of x^2*y^3*z^5 in (x+y+z)^10?
10! / (2! 3! 5!)

In general, for (x+y+z)^n, the coefficient of x^a y^b z^c is given by n!/ (a!.b!.c!) , where n=a+b+c

Note: The number of terms in the expansion of (x+y+z)^n is given by (n+1)(n+2)/2. This is true only for a trinomial.

So, in this particular case -> 11*12/2 = 66

Vineet, Team BV
24498
@bodhi_vriksha plz help


(1 + x + x^5)^15 - no of terms ?
24499
@DeAdLy can you please share ur solution
24500
@vishcat said:
guys pls help me with this---->what is the coefficient of x^2*y^3*z^5 in (x+y+z)^10?
10!/2! *3!*5!
24501
@bodhi_vriksha so do we have to remember this .....isn't there a proof for this?
24502
@saurav205 how??pls explain this
24503
@amresh_maverick said:
@bodhi_vriksha plz help(1 + x + x^5)^15 - no of terms ?
Is it 133..?
24504
@jain4444 said:
The total number of Integer solutions of x³y²z⁴=9720000
Sir OA kya hai...
M getting only one solution....
3,24,5
Bad feeling about this one...kuch miss hua hai....
9720000=2^6*3^5*5^4

24505
@vishcat said:
@saurav205 how??pls explain this
Bhai refer to BT...
Explanation difficult as of now...in office yar....time lagega.....
24506
@vishcat
general term of any binomial expression is nCr*x^r*y^(n-r)

split the above equation in two parts: x+y=a and z=b
nw u get (x+y+z)^15= (a+b)^15
solve the equation as binomial expression...
for z^5, it will be 10C5* a^5 * b^5......1

again expand a, it will be 5C2* x^2 * y*3....2

substitute equation 2 in 1..
hence answer..
24507
@sbharadwaj said:
Is it 133..?
detail mein post karo soln, TIA