@vbhvgupta said:Q
Let x=k^a
Now substitute and get
2a/(a+1) + 3a/(2a+1) = 0
Solve and get a single value of a
Hence (1)
Now substitute and get
2a/(a+1) + 3a/(2a+1) = 0
Solve and get a single value of a
Hence (1)
@Marchex said:5 PASSENGERS ARE ON A TRAIN AND 6 STATIONS are there continuously,what is the probability that 5 passengers step down at different stations?
5/54
@next_big_thing said:This is a question from CAT 2010 paper. Can anyone plz solve it coz I am at a loss ??? -->A triangular garden is to be enclosed inside 3 straight fences. Raju started running at an uniform speed on the three sides of the proposed boundary of the garden & discovered that he was taking 48min, 102min, 90min to traverse the garden's three sides. However, in the latest colony meet, it was decided that the coverage area of the park should be reduced to accomodate a parking lot. Since the fence on the shortest boundary was already constructed, the length of the boundary covered by Raju in 90min was reduced by 60% & the longest was modified accordingly so that the park still remained triangular in shape.1) How much time will Raju take to run along the boundary of the garden thus formed? 120min, 148min, 128min, 160min, 144min2) If Raju's speed was 15metres/min, what is the approx area of the parking lot (in km^2)? 0.39, 0.28, 0.29, 0.45, 0.52Plz post the solution as well or else it wont be of any help.
1.D= S*T ==> T1 : T2: T3 = D1:D2 : D3 ;
48 : 102 : 90 ==> 8:17 : 15 ( Right angle Triangle ) ;
Now after modifications ==> the new boundaries are 48 : 36 : 60 ==> total = 144 ;
2. A = 1/2 * b*h ; base = b = 15 * 48; h = 15 * 36 ; A = 0.5 * 225 * 48*36
48 : 102 : 90 ==> 8:17 : 15 ( Right angle Triangle ) ;
Now after modifications ==> the new boundaries are 48 : 36 : 60 ==> total = 144 ;
2. A = 1/2 * b*h ; base = b = 15 * 48; h = 15 * 36 ; A = 0.5 * 225 * 48*36
@vbhvgupta said:Q
solving the eqn
2log x /( 1 + log x) + 3logx / (1 + 2log x) =0
log x = 0 , -5/7 (base is k. can't be 0)
so 1 value
@Marchex said:5 PASSENGERS ARE ON A TRAIN AND 6 STATIONS are there continuously,what is the probability that 5 passengers step down at different stations?
Total ways of stopping = 6^5
Total ways of stopping at different stations = 6!
Hence 6!/6^5 = 5/54
Total ways of stopping at different stations = 6!
Hence 6!/6^5 = 5/54
@albiesriram said:Its basically an application of catalan numbers Total arrangements 68 !/ 34!*34 !Reqd valid arrangements = 1/ n+1 * C(2n,n)Here,n = 34wolfram gives the answer as 1/35 , so a+b = 36 may be wrong for more refer this.http://mathcircle.berkeley.edu/BMC6/pdf0607/catalan.pdf
Thanks dost. Didn't know this funda!
But yeah, Catalan numbers is way beyond the scope of CAT
regards
scrabbler
But yeah, Catalan numbers is way beyond the scope of CAT
regards
scrabbler
@ravi.theja said:1.D= S*T ==> T1 : T2: T3 = D12 : D3 ;48 : 102 : 90 ==> 8:17 : 15 ( Right angle Triangle ) ;Now after modifications ==> the new boundaries are 48 : 36 : 60 ==> total = 144 ;2. A = 1/2 * b*h ; base = b = 15 * 48; h = 15 * 36 ; A = 0.5 * 225 * 48*36
1st one is correct butfor second one u have calculated the whole area....
just calculate area of triangle whose sides are 102*15,54*15,60*15
@Tusharrr said:@albiesriram Yup ITs correctAnswer 36
Whats the source dude.? 
The level is notch higher than CAT 
@scrabbler These in next commentuesions are from different math questions sites
I m liking the comments of correct answers and can tell just correct answer unsolved questions solutions are not there.
I am posting another question
If you all want IN next commEnt
ABC is an acute triangle with ∠BCA=35∘. Denote the circumcenter of ABC as O and the orthocenter of ABC as H. If AO=AH, what is the value of ∠ABC(in degrees)?
@catahead True.. small numbers makes it easier to get... the concept.
Will post more challenging stuff as and when I get it.
@harshit12 @abhishek.2011 @pratskool @Buck.up
1) Please please try & solve 1 last question from the same paper---->
An escalator is moving at 3 steps/second. Harish walks in the same direction as a moving escalator at 2 steps/second, takes 3 seconds less to get out of the escalator than when he was moving on the stationary escalator. How many steps are there in the stationary escalator??
16, 10, 25, 20, data insufficient.
2) In the previous question that u solved, while finding the area of the parking lot, all of u have considered the 48min side & (90-36)min side [i.e. the 60% decrease]. Can u plz explain y you considered (90-36) & NOT 36 only??
@next_big_thing said:@[email protected]@[email protected]) Please please try & solve 1 last question from the same paper---->An escalator is moving at 3 steps/second. Harish walks in the same direction as a moving escalator at 2 steps/second, takes 3 seconds less to get out of the escalator than when he was moving on the stationary escalator. How many steps are there in the stationary escalator??16, 10, 25, 20, data insufficient.
Length of escalator=l
e=3steps/sec
harish=2 steps/sec
When both moving, net speed=3+2=5 steps/sec
Now acc to condition,
l/5 +3 =l/2
l(1/2-1/5)=3
l=10 steps
@next_big_thing said:2) In the previous question that u solved, while finding the area of the parking lot, all of u have considered the 48min side & (90-36)min side [i.e. the 60% decrease]. Can u plz explain y you considered (90-36) & NOT 36 only??
Parking lot was the area of park devoid of new parking area.
Initial area=1/2 *48*90
After boundary, Park area reduced to=1/2 *48 * 36
So parking area=Initial area-After boundary, Park area=1/2 *48*90-1/2 *48 * 36=1/2*48*(90-36) ?
The remainder of 11^11^11/9 ?
P.S. Method other than Euler will be appreciated 
there are 2 1s, 2 2s, 2 3s, in how many ways can these be arranged so that two same digits are not adjacent to each other?