Please solve these quants questions

[amit_in1976]

Hi,
Please solve the following

1. Two circles of unit radius intersect one another. The distance between their centres is 3^.5 (root 3) and AB is the common chord. P is a point on the circumference of one of the circles. Then measure of angle APB = ?

2. In Delhi metro circular train track, there are 5 stations and 10 sub stations. No two stations are consecutive and atmost 3 substations are consecutive. In how many ways can these stations and substations be arranged?

Ans 1: 30 or 150
Ans 2: 51

[Evanescence]

if point P is on the that part of the circle which is on the othe side of AB (the region where the circles dont intersect) then angleAPB is 30 degree.

the line joining the centres (say XY)is perpendicular bisector to AB. Also this line segment XY itself is bisected by AB. let the intersection pont of AB and XY be R. Then XR is root3/2 and XA=1(radius) so angle AXR is 30 degree. so angle AXB is 60. angle APB is half of AXB and hence it is 30 degree.

but if the point P is on the other segment, then it is obviously 180-30=150 degrees.

so unless the location of the point is given we cannot arrive at an answer.

[Evanescence]

dude, was it a DS ques? or a normal one with a 'cannot be determined' as an option? if it was a DS ques, phew! God save us!!!

[amit_in1976]

No...it was not a DS question...it was in one of the CL FLTs. The options were

a) 30 b)150 c) either a or b d) insufficient data

But this could easily be a DS question also

[Evanescence]

so whats d answer? its tricky man.

choices 3 as well as 4 seem to qualify as the right answer.

i mean data regarding location of point P isnt given. so you can say insufficient data. on the other hand the answer could be 30 or 150. damn, its so ambiguous.

[newguy]

Guys,

I am sorry if I am breaking some kind of flow here but I was looking for where to put my question and this one seemed the most recent thread on Quant Problem...

The question goes like :

An unknown polynomial f(x) of degree 37 yields a remainder of 1 when divided by x-1, a remainder of 3 when divided by x-3, a remainder of 21 when divided by x-5.
Find the remainder when f(x) is divided by (x-1)(x-3)(x-5).

Thanks,

[spaceman spiff]

well I'm not providing a solution to any of the problems, but raising one of my own...

in questions in ds like
who among a,b,c is the tallest ?
a) a is not shorter than b.
b) c is shorter than b

from a alone a>=b ...so can we say we have an answer?time and ims have different takes on this.
a and b might be of same height...but the question asks 'tallest' and it has to be just one.

can I have an authoritative answer on this ?

[Evanescence]

a>=b and hence u cannot conclude who among a and b is tallest.
all we can say is that c is definitely the shortest.
a unique answer cannot be got for tallest ... so answer must be choice (4) cannot be determined

[MrAnderson]

hi all,
need help ..
plz tell me how to solve probs of this kind..
1.Find no of common roots btw 2 eqns.
a)x^3+3x^2+4x+5=0
b)x^3+2x^2+7x+3=0

thnx in advance
MrAnderson.

[methuselah]

One qn from P&C

A student has to answer 9 qns out of 12 qns in a qn paper such that he has to answer atleast 3 qns from the first 4 qns . In how many ways can he do this ?

My Soln...
------------
He can choose the 3 qns out of the first 4 in 4C3 ways ...

and the qns left out now are 9 and he has to answer any 6 of those in 9C6 ways...

Therefore number of ways = 4C3 * 9C6
= 4 *84
= 336

Soln Given ...
-------------

Case 1 : He attempts 3 qns out of the first 4 and the other 6 qns from the rest
No of ways = 4C3 * 8C6

Case 2: He attempts all the 4 qns out of the first 4 qns and the other 5 from the rest
No of ways = 4C4 * 8C5

Total no of ways = 4C3*8C6 + 4C4*8C5
= 4*28 + 56
= 168

Which soln is correct and why ?? What's the diff between the both of them ??

Thanks in advance