Official Quant thread for CAT 2013

If the value of a purchase is less than rs 3200,the customer gets a discount of 14%.The customer gets a discount of 16% on a purchase between rs 3200-6300.The customer gets a discount of certain % on a purchase above rs 6300.A customer gets a total discount of rs 1520 which is equal to 16% of the purchase value.How much discount does the customer get for amount exceeding rs 6300?

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Determining how the charges distribute on the surface of a conductor is, in general, a very difficult problem. We know that if we charge a conductor the charges go to the surface and redistribute so that the electric field in the conductor vanishes. One of the few shapes for which this distribution can be determined analytically is the ellipsoid.
x^2/a^2 + y^2/b^2 + z^2/c^2=1.
Here, a, b and c are the ellipsoid's semi-axes. One can prove that for an ellipsoidal conductor the surface charge density is given by

σ(x,y,z)=Q/(4 pi abc) X 1/root(x^2/a^4 + y^2/b^4 + z^2/c^4)
where Q is the the net charge of the conductor. Note that if we set a=b=c=R we obtain the uniform charge distribution Q/(4 pi R^2), corresponding to a spherical conductor. Suppose that we measure the electric field near the surface of a charged ellipsoid with Q=1nC, a=2cm,b=5cmand c=3cm. What is the maximum value in in volts per meter of the electric field?

Details and assumptions
k=1/(4 pi ϵ0) =9×10^9m/F


@albiesriram said:
radius of bigger circle 9cm
radius of smaller circle 3cm
KN =2cm
@ChirpiBird said:
sry, didnt get you? answer is 3/2?this is how i did,roots of the first eq are 8,2.for next eq. roots will be R = (+ 4r +/- rt 16r^2- 64)/2R= 2r +/-2 rt r^2-4twice of 8 or 2 must be equal to this root.taking 2 . 4-2r = 2rt r^2-42-r = rt R^2-4sq it8 = 4rr=2.correct me if i am wrong.
@albiesriram said:
is it 6/pi-1
option d
@albiesriram said:
OA:-


@albiesriram said:
6/pi - 1 ?
@RDN said:
substitute a=1,c=2 => b =-4.52x2 - 9x + 4 (2x - 1)(x - 4) => E= 0.5 , F = 4 or E=4 , F=0.5Answer - option 1 ?
yar didn't got ur method..
@vbhvgupta said:
If the equation X^3-4X^2+X+6=0 and X^3-3X^2-4X+K=0 have a common root. which of the following be the value of k1. 122. 63. -124. -3
12!!
@albiesriram said:
(1 + k^2)^3/k^2 ?

ab^2 + bc^2 = ac^2
(-k*bc)^2 + bc^2 = ac^2
ac^2 = (k^2 + 1)*bc^2

ac^2 + cd^2 = ad^2
(k^2 + 1)*bc^2 + cd^2 = ad^2
(k^2 + 1)*bc^2 + k^2*ac^2 = ad^2
(k^2 + 1)*bc^2 + k^2*(k^2 + 1)*bc^2 = ad^2
(k^2 + 1)^2*bc^2 = ad^2

ad^2 + de^2 = ae^2
ad^2(1 + 1/k^2) = ae^2
(k^2 + 1)^2*bc^2*(1 + 1/k^2) = ae^2
(ae/bc)^2 = (1 + k^2)^3/k^2
@mohitjain said:
12!!
approach

please give approach if u find time guys..

@vbhvgupta said:
approach
get d roots of the 1st equation wich comes out 2 be 3,2 and -1 ..den since they have a common root put dese values in d oder eq.,we get k as 12. by puttin x=3
@vbhvgupta said:
If the equation X^3-4X^2+X+6=0 and X^3-3X^2-4X+K=0 have a common root. which of the following be the value of k1. 122. 63. -124. -3
SHud be 12
@albiesriram
@mailtoankit

C

take triangle 1 : square root 3 :2 ... which means 30 : 60 : 90 k = square root 3

or take triangle 1:1 : square root 2 = which means 45 45 90 k= 1 :P

easy for those who hate equations like me
@albiesriram 120??
@Tusharrr said:
@albiesriram 120??
nope..