Official Quant thread for CAT 2013

@techsurge said:
@rubikmath@Torque024@vijay_chandolaOA 31Find the coefficient of x^30 in expasnion of (1-x^5)^6 * (1+x^3)^10a) -5038b)5038c) -5040d) 5039
x^30 from
x^0*x^30
x^15*x^15
x^30*x^0

x^0*x^30=>1*10!/10!=1
x^15*x^15=>-6*5*4/6*10*9*8*7*6/120=-5040
x^30*x^0=>1

-5038
@techsurge said:
@rubikmath@Torque024@vijay_chandolaNew QuestionFind the coefficient of x^30 in expasnion of (1-x^5)^6 * (1+x^3)^10a) -5038b)5038c) -5040d) 5039OA 31 for below
a) ? -5038?
@maddy2807 said:
A milkman has 16 lt of pure milk in a container. At first house he sells 1 lt of milk and adds water to fill the container. At every subsequent house he sells twice the volume of the solution as he did at the previous house and adds water to fill the container. If he claims to sell at the cost price . Find his overall profit, when container is empty.
15/16*100 = 93.75
@maddy2807 said:
A milkman has 16 lt of pure milk in a container. At first house he sells 1 lt of milk and adds water to fill the container. At every subsequent house he sells twice the volume of the solution as he did at the previous house and adds water to fill the container. If he claims to sell at the cost price . Find his overall profit, when container is empty.
93.75??

15/16*100
@maddy2807 said:
A milkman has 16 lt of pure milk in a container. At first house he sells 1 lt of milk and adds water to fill the container. At every subsequent house he sells twice the volume of the solution as he did at the previous house and adds water to fill the container. If he claims to sell at the cost price . Find his overall profit, when container is empty.
buying volume=16 liters
selling volume=1+2+4+8+16=31 liters

==> profit=(31-16)/16*100=93.75%
@maddy2807 said:
A milkman has 16 lt of pure milk in a container. At first house he sells 1 lt of milk and adds water to fill the container. At every subsequent house he sells twice the volume of the solution as he did at the previous house and adds water to fill the container. If he claims to sell at the cost price . Find his overall profit, when container is empty.
SP=1x+2x+4x+8x+16x
CP=16x
Profit=15x
%= 1500/16
@techsurge said:
@rubikmath
@Torque024

@vijay_chandola

New Question

Find the coefficient of x^30 in expasnion of

(1-x^5)^6 * (1+x^3)^10

a) -5038

b)5038

c) -5040

d) 5039

OA 31 for below

OA = -5038
1+1 -5040
Q Find the equation of tangent to the curve y=x^3 -2x^2+6x-4 =0 at x=1 in the X-Y plane
A) y+5x+4=0
B)y-5x+4=0
C)y-2x+4=0
D)y+2x+4=0
Solved by options but dont know the right way to solve it
@techsurge B option..by options
@techsurge b? tangent
@techsurge aese
dy/ dx = 3x^2 -4x + 6
dy/dx ( x=1) = 5
equation of tangent : y = 5x + c
at x = 1 y =1
1 = 5 +c
c =-4
y = 5x -4
or y-5x + 4
@techsurge said:
OA = -5038 1+1 -5040Q Find the equation of tangent to the curve y=x^3 -2x^2+6x-4 =0 at x=1 in the X-Y planeA) y+5x+4=0B)y-5x+4=0C)y-2x+4=0D)y+2x+4=0Solved by options but dont know the right way to solve it
its option B.

y-5x+4=0
@maddy2807 said:
A milkman has 16 lt of pure milk in a container. At first house he sells 1 lt of milk and adds water to fill the container. At every subsequent house he sells twice the volume of the solution as he did at the previous house and adds water to fill the container. If he claims to sell at the cost price . Find his overall profit, when container is empty.
93.75
@techsurge said:
OA = -5038 1+1 -5040Q Find the equation of tangent to the curve y=x^3 -2x^2+6x-4 =0 at x=1 in the X-Y planeA) y+5x+4=0B)y-5x+4=0C)y-2x+4=0D)y+2x+4=0Solved by options but dont know the right way to solve it
option b
@techsurge said:
@rubikmath@Torque024@vijay_chandolaNew QuestionFind the coefficient of x^30 in expasnion of (1-x^5)^6 * (1+x^3)^10a) -5038b)5038c) -5040d) 5039OA 31 for below
-5038
@techsurge said:
OA = -5038
1+1 -5040
Q Find the equation of tangent to the curve y=x^3 -2x^2+6x-4 =0 at x=1 in the X-Y plane
A) y+5x+4=0
B)y-5x+4=0
C)y-2x+4=0
D)y+2x+4=0
Solved by options but dont know the right way to solve it
yup OA b)

@rkshtsurana 's approach is right

although options can eliminate the same

Q) Bhanu and Ria start running simultaeously on a linear track with same speeds and cover first 280 m in t seconds. After covering every 280 m , Bhanu decreases its speed by fraction of half and Ria decreases her speed by fraction of 2/3 . bhanu takes 1.5 t minutes less than the time taken by Ria to cover the entire distance. Find the distance which in metres is an integral multiple of 280

A) 2800

B) 1400

C) 1680

D) 2240

@techsurge said:
yup OA b)@rkshtsurana 's approach is rightalthough options can eliminate the sameQ) Bhanu and Ria start running simultaeously on a linear track with same speeds and cover first 280 m in t seconds. After covering every 280 m , Bhanu decreases its speed by fraction of half and Ria decreases her speed by fraction of 2/3 . bhanu takes 1.5 t minutes less than the time taken by Ria to cover the entire distance. Find the distance which in metres is an integral multiple of 280A) 2800B) 1400C) 1680D) 2240
b 1400
1.5t minutes --> 90 t secs .
t+3t+9t+27t+81t - t+2t+4t+8t+16t = 90t
--> 5 * 280 --> 1400

@techsurge said:
yup OA b)@rkshtsurana 's approach is rightalthough options can eliminate the sameQ) Bhanu and Ria start running simultaeously on a linear track with same speeds and cover first 280 m in t seconds. After covering every 280 m , Bhanu decreases its speed by fraction of half and Ria decreases her speed by fraction of 2/3 . bhanu takes 1.5 t minutes less than the time taken by Ria to cover the entire distance. Find the distance which in metres is an integral multiple of 280A) 2800B) 1400C) 1680D) 2240
t+2t+4t..+nt+1.5*60t=t+3t+9t+..+nt
=>t(3^n-1)/2-t(2^n-1)=90t
=>3^n/2-2^n=91.5

n=5 comes closest

so 280*5=1400
@krum said:
t+2t+4t..+nt+1.5*60t=t+3t+9t+..+nt
=>t(3^n-1)/2-t(2^n-1)=90t
=>3^n/2-2^n=91.5

n=5 comes closest

so 280*5=1400
@techsurge said:
yup OA b)@rkshtsurana 's approach is rightalthough options can eliminate the sameQ) Bhanu and Ria start running simultaeously on a linear track with same speeds and cover first 280 m in t seconds. After covering every 280 m , Bhanu decreases its speed by fraction of half and Ria decreases her speed by fraction of 2/3 . bhanu takes 1.5 t minutes less than the time taken by Ria to cover the entire distance. Find the distance which in metres is an integral multiple of 280A) 2800B) 1400C) 1680D) 2240
1400
time inv. prop to speed
how many 3 digit natural numbers have less than 5 prime factors?