Official Quant thread for CAT 2013

@Dexian said:
in this circle centered at (1, -2) with radius= root(24)........... wat does y/x representis it the slope of the tangent...???
yup thts the thng whenever u face a prob of y/x i mark 0/1 without solving although it actually goes from infinity to -infinity bt always there is sum or the othr condition making it most likely zero or 1 ....:D :D
@piyushrohella12 said:
yup thts the thng whenever u face a prob of y/x i mark 0/1 without solving although it actually goes from infinity to -infinity bt always there is sum or the othr condition making it most likely zero or 1 ....
lekin infinity to answer nahi hona chahiye... kuchh to number aayega i guess... i m not sure if my concept is clear abt slope of tangent and all ......... wait for GODs to come...
@techgeek2050 said:
simply y/x y cordinate / x cordinate
Well, obviously if we put x=0 then y/x = infinity..
If we can't put x = 0

Then, maximum of y can be at the lowest point of the circle if sign(+ or -) is not taken into consideration otherwise it's the uppermost point in a circle of radius, R = 2_/6
and centre ( 1, -2)

We can calculate the coordinates of uppermost and lowermost point easily since we know R=2_/6

Oter than this I don't know anything about it's solution :splat:
@techgeek2050 said:
Find the largest value of y/x if x ˛ + y ˛ - 2x + 4y - 19 = 0.
2(sqrt(6)-1)
My questionďťż
@ScareCrow28 said:
Well, obviously if we put x=0 then y/x = infinity..If we can't put x = 0Then, maximum of y can be at the lowest point of the circle if sign(+ or -) is not taken into consideration otherwise it's the uppermost point in a circle of radius, R = 2_/6 and centre ( 1, -2)We can calculate the coordinates of uppermost and lowermost point easily since we know R=2_/6Oter than this I don't know anything about it's solution
sir, the highest point of the circle is at x = 1, where y is approx = 3
y/x = 3 (approx)

and dy/dx >0 for 0

so as x becomes less than 1, y is still > 1, so y /x should go on increasing.
is it possible to find the maximum value then?


@DarkHorse25 said:
2(sqrt(6)-1)
approach?
@techgeek2050 said:
sir, the highest point of the circle is at x = 1, where y is approx = 3y/x = 3 (approx)and dy/dx >0 for 0 so as x becomes less than 1, y is still > 1, so y /x should go on increasing.is it possible to find the maximum value then?
Actually, I really don't think that we can find a global maxima of the function y/x with the given domain!
At least I can't find a solution to it 😞 Others may well!

(x-1)^2 + (y-2)^2 = 24
Suppose y/x = k

(1-1/x)^2 + (k-2/x)^2 = 24/x^2

k = [ 2 + _/(24 - (x-1)^2 ] / x

To maximise k, put limit: x->0

Even then I couldn't solve it!

May be @bodhi_vriksha sir would help!
Out of 120 students in a school, 87 plays hockey, 76 plays football, 65 plays tennis and 19 plays carrom.
What can be minimum number of students who play at least two of the three games?

don't have the OA
@samratroy_1990 said:
My question
is it 0.892?
@samratroy_1990 said:
My question
73/99
@techgeek2050 said:
Out of 120 students in a school, 87 plays hockey, 76 plays football, 65 plays tennis and 19 plays carrom.What can be minimum number of students who play at least two of the three games?don't have the OA
bhai idhar toh 4 games hai
@techgeek2050 said:
Out of 120 students in a school, 87 plays hockey, 76 plays football, 65 plays tennis and 19 plays carrom.What can be minimum number of students who play at least two of the three games?don't have the OA
I + II + III + IV= 120
I + 2II + 3III +4IV = 247

Minimise (II + III + IV) OR Maximise I

Also, II + 2III + 3IV = 127
Put, II = 0
WE get, III = 2 and IV = 41

Hence minimum number of students playing at least 2 games = 0 + 2 + 41 = 43 ?..
@ScareCrow28 said:
Actually, I really don't think that we can find a global maxima of the function y/x with the given domain! At least I can't find a solution to it Others may well!(x-1)^2 + (y-2)^2 = 24Suppose y/x = k(1-1/x)^2 + (k-2/x)^2 = 24/x^2k = [ 2 + _/(24 - (x-1)^2 ] / xTo maximise k, put limit: x->0Even then I couldn't solve it! May be @bodhi_vriksha sir would help!
cant we simply put (x-1)^2=0 ?
@DarkHorse25 said:
cant we simply put (x-1)^2=0 ?
That would give the maximum value of y not y/x.
@ScareCrow28 said:
That would give the maximum value of y not y/x.
but then only we can minimize the value of (x-1)^2. hence maximizing the value of y/x bcoz min value of x-1 will be 0
@samratroy_1990 said:
My question
86/99?
@iLoveTorres said:
86/99?
1- 2*13/99=73/99
@DarkHorse25 said:
but then only we can minimize the value of (x-1)^2. hence maximizing the value of y/x bcoz min value of x-1 will be 0
But, when x --> 0 then y/x is an increasing function, so we can't say that if we put x=1 that will give y/x as maximum
@DarkHorse25 said:
73/99
approach??

i simply used the formula, area of regular octagon = 2a^2 (1+rt2)
the figure will form a regular octagon of side 43/99
a =43/99

correct me if i am wrong. :)