Official Quant thread for CAT 2013

MBA CAT 2024
5201
@soham2208 said:
@freebull Chill man I think, marginal revenue = 0 =>Change in revenue with addition of new people per trip is zeroSo, if g(x) = Number of people * Fare = x*(54 - x/32)^2g'(x) = 0=> (54-x/32)^2 - (x/16)*(54-x/32) = 0 => x = 1728(rejected) or 54-x/32 - 2x/32 = 0=> 3x = 32*54 => x = 576 ..So, is it 576 ?
yup !!
5202
@freebull said:
see the attachement plz !! instead of scanning whole lot of unwanted theory i wanted just the relevant part..tht's why i asked it here.otherwise i too know for wht purpose google has been put up there. hope i didn't waste much of ur precious time.thanks anyway !!
From the definition of marginal revenue, when revenue will be maximum, marginal revenue will be zero.

Revenue=x*(54-x/32)^2
Now, by differentiating the revenue function, we get maximum value of function at x = 576

hence, number of people per trip=576
5203
@freebull said:
see the attachement plz !! instead of scanning whole lot of unwanted theory i wanted just the relevant part..tht's why i asked it here.otherwise i too know for wht purpose google has been put up there. hope i didn't waste much of ur precious time.thanks anyway !!

For zero marginal revenue, the derivative of the revenue function should be equated to zero. In general it also means that for zero marginal revenue, addition of new passangers wont result in an increase in revenue.
EDIT

PS. Bro..you should have posted the question and then asked the query..sorry for any offences.
5204
@vijay_chandola said:
In a square PQRS, T is the midpoint of PQ and U is any variable point on QR. What is the minimum possible value of €˜SU + UT €™ (in cm) if the side of the square is 2 cm?(a) 2_/2 (b) _/5 +_/2 (c) 1+2_/2 (d) _/13
SP^2+PT^2=ST^2
2^2+3^2=ST^2
4+9=ST^2
ST=rt(13)
5205
@vijay_chandola said:
If the roots of the equation ax3 + bx2 + cx + d = 0 are in Geometric Progression, then which of the following relations is true?(a) a*c^2 = b^2*d(b) a*c^3 = b^3*d (c) a^2*c = b*d^2 (d) a^3*c = b*d^3
b?
5206
@vijay_chandola g.p series : first term= a^15 common ratio=a ==> sumation = a^15 ( a^36-1)/a-1 ==> a^15=1==> a^35=1 ===> a^36=a ==> sumatn =1
5207

This is Quant thread, and so Dead ! 😐 Not Good :nono:


There are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines
5208
@vijay_chandola said:
If the roots of the equation ax3 + bx2 + cx + d = 0 are in Geometric Progression, then which of the following relations is true?

(a) a*c^2 = b^2*d
(b) a*c^3 = b^3*d
(c) a^2*c = b*d^2
(d) a^3*c = b*d^3
b)
5209
@soham2208 said:
This is Quant thread, and so Dead ! Not Good

There are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines

not sure
but getting
2y=x
and
2y =x +10
approach
circle is at centre at -3,1 with radius =5
as the tangents are prependicular to 2x +y=4
=> they are parallell .
their equation 2y=x+K1, 2y=x+K2
The line passing through centre and prependiular to tangents is diameter with equation 2x+y=K
put -3,1 to get K as -5
substitute the value of y =-2x-5 in the equation of circle to get quadration
5x^2+30x+40=0
to get x=-2,-4 and corespondingly y=-1,3
substitute in the eqautions of tangent the x and y pair to get
2y=x
2y=x+10
to check if these are right distance between them should be 2 sqrt(5)
distance between them =10-0 /sqrt(2^2+1^2)=2sqrt(5)
5210
@soham2208 said:
This is Quant thread, and so Dead ! Not GoodThere are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines
x-2y=0
x-2y+10=0
5211
@soham2208 said:
This is Quant thread, and so Dead ! Not GoodThere are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines
y=x/2
2y=x+10..yehi hai kya??
5212
@vijay_chandola said:
OA: a) 9

Solution:

For these kind of questions
, form the numbers in form of 4K or 4K +1 or 4K + 2 or 4K + 3
(as all numbers are of the form 4K or 4K +1 or 4K + 2 or 4K + 3)

Coins available: 4, 8, 13 and 18
1) We can make every number of the form 4K
2) We can make every number of the form 4K + 1 starting with 13
3) We can make every number of the form 4K + 2 starting with 18
4) We can make every number of the form 4K + 3 starting with (18 + 13) = 31

Hence, largest number should be less than 31, which is 27.
bhai ek aur aisa question post kar do agar hai practice ke liye. New concept for me
5213
@vijay_chandola said:If the roots of the equation ax3 + bx2 + cx + d = 0 are in Geometric Progression, then which of the following relations is true?
(a) a*c^2 = b^2*d
(b) a*c^3 = b^3*d
(c) a^2*c = b*d^2
(d) a^3*c = b*d^3

Option: b
5214

Some more questions to save the thread :splat:


find the equation of the locus of the midpoint of a line segment of length 4 units which moves with its ends always on the coordinate axes .
5215
@soham2208 said:
This is Quant thread, and so Dead ! Not GoodThere are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines
x-2y=0 and x-2y+10=0 ???
5216

is it

x^2 +y^2 =4

@soham2208 said:
Some more questions to save the thread

find the equation of the locus of the midpoint of a line segment of length 4 units which moves with its ends always on the coordinate axes .

5217
@soham2208 said:
This is Quant thread, and so Dead ! Not GoodThere are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines
(x+3)^2 + (y-1)^2 = 5 => circle with center (-3,1) and radius rt(5)

eqn of line passing through center and perpendicular to 2x+y=4 is given by 2(y-1)=(x+3)

i.e x-2y+5=0.........(i)

parallel tangents required would be parallel to above line at a distance equal to radius

say the line is x-2y+c=0

=>|c-5|/rt(1^2+2^2) = rt(5)
=>|c-5| = 5
=>c=10 or c=0

hence eqn of required tangents x-2y+10=0 and x-2y=0

ATDH.
5218
@soham2208 said:
This is Quant thread, and so Dead ! Not GoodThere are two lines tangent to the circle x^2 +y^2 + 6x €“2y + 5 = 0 that are perpendicular to the line 2x + y = 4. Give the equations of these two lines
x^2 + y^2 + 6x - 2y + 5= 0
(x+3)^2 + (y-1)^2 = 5; C(-3,1), R = root(5)

Line perpendicular to 2x+y-4= 0 will be y-2x+k= 0
Now, |{1-2(-3)+k}/root(5)| = root(5)
So, k = -2,-12

The equation of two lines will be: y-2x-2=0 and y-2x-12=0.

5219
@soham2208 said:
Some more questions to save the threadfind the equation of the locus of the midpoint of a line segment of length 4 units which moves with its ends always on the coordinate axes .
circle..x^2+y^2=2^2??
5220

a circle which has a diameter of 10 cm,and two diam of the same circle intersect at O,let P be a point in the first quadrant and the foot of the perp drawn to x axis be A and foot of perp drawn to y-axis be B,calculate the max value of hypotenuse so formed.