Official Quant thread for CAT 2013

@Dexian said:
7^20 - 7
Each prize can be won by 20 players hence 20^7 ways, this includes the ways in which a single player getting all the 20 prizes. hence 20 such cases.

so 20^7 - 20 OA
@Koushik98 said:
In the figure given below, ABCD is a rectangle, DE : EC = 5 : 4 and CF : FD = 8 : 1. If the area of the quadrilateral APFD is 49 square units, then find the area of the quadrilateral BPEC (in square units). a 86 b 87 c 88 d 85
@albiesriram said:
Each prize can be won by 20 players hence 20^7 ways, this includes the ways in which a single player getting all the 20 prizes. hence 20 such cases.so 20^7 - 20 OA
lekin..... if there are 7 ppl........ then there are 7 cases wen all d prizes are wid one guy...
so -7 hona chahiye...
@Dexian said:
lekin..... if there are 7 ppl........ then there are 7 cases wen all d prizes are wid one guy...so -7 hona chahiye...
oh yes.. i made a mistake while copying the question from that book...

ur OA is correct according the question i uploaded... sorry bhai just now checked the question.. i I solved the question as if there are 20 players and 7 prizes... was

The probability that the randomly selected chord of a circle has length lies between 1/4 and 4/5 of the diameter is?

@albiesriram said:
The probability that the randomly selected chord of a circle has length lies between 1/4 and 4/5 of the diameter is?
3/5??
@Subhashdec2 said:
3/5??
approach dhigyae.. have a doubt in OA !
@albiesriram said:
approach dhigyae.. have a doubt in OA !
bhai gandi approach h

i took 20 as diameter and thought 5 to 16 12 chords aayenge
12/20
@Subhashdec2 said:
bhai gandi approach hi took 20 as diameter and thought 5 to 16 12 chords aayenge12/20
My doubt is there will be Two unique chords for any one diameter...
@albiesriram said:
My doubt is there will be Two unique chords for any one diameter...
wo kaise?
and what is the OA?
@Subhashdec2 said:
wo kaise?
iTwo different segments mein two chords hoga na?. But only diameter . geometric probabiliy hein aur area use karna chhiyae..

@Subhashdec2 said:
and what is the OA?

self framed.. Original question carried the chance between 1/4 times to 3/4 times.. they used symmetry to say its 1/2 chance.
@albiesriram said:
iTwo different segments mein two chords hoga na?. But only diameter . geometric probabiliy hein aur area use karna chhiyae..self framed.. Original question carried the chance between 1/4 times to 3/4 times.. they used symmetry.
what was the OA for the one which had 1/4 and 3/4

and how did they do it?
could u explain

OA was 1/2

their method is like this..

Let P be the length of the chord S be the midpoint of the chord from the center and r the radius of the given circle then,

S= rcosx
P = 2rsinx

Now, 1/4(2r)

=> 1/4
=> (_/7 /4 ).r

Now R1 = rt 7 /4 .r
R2 = rt15 /4 . r

reqd. probability = area of circular annulus

R2^2 - R1^2
P = ____________

r^2
= 1/2

231/400 shayad OA hoga..


chalo lets
@albiesriram said:
The probability that the randomly selected chord of a circle has length lies between 1/4 and 4/5 of the diameter is?
@ravihanda when 13^71 divided by 57 remainder is r. what is the unit digit of the quotient?
What is the 50th smallest positive integer that can be written as the sum of distinct non-negative integer powers of 3?
@erm said:
@ravihandawhen 13^71 divided by 57 remainder is r. what is the unit digit of the quotient?
13^71 mod 57

E(57) = 36

13^36k mod 57 = 1

let 13^71 mod 57 = r

r*13 mod 57 = 1

57k + 1 = 13r
=> k = 5 and r = 22

57*Q + 22 = 13^71
unit digit of 13^71 is 7

57*Q + 22 = xxxx7

so , unit digit of Q = 5
@jain4444 said:
What is the 50th smallest positive integer that can be written as the sum of distinct non-negative integer powers of 3?
Jain bhai 354 ???
@simplydevesh said:
@Dexian@Shray14 said:The latest registration no issued by registration authority is DL-5S-2234. If all the numbers and alphabets before this have been used up, then find how many vehicles have a registration number starting with DL-5??192234192225172227NOTB 192225plz explain ur approach??
@Dexian @mailtoankit @Subhashdec2

Sorry for the late replying..its ans among the options is NOT.

My approach..
5A no varies from 0001 to 9999=10*10*10*9
and till 5s=10*10*10*9*18
till 5S-2234 it will be 10*10*10*9*18+2235..
How many positive integers n≤1000 cannot be written in the form a^2āˆ’b^2āˆ’c^2 where a,b and c are non-negative integers subject to a ≄ b+c?