[vivekimmortal]

a composite no. has 720 factors, if the no of distint prime factors is max possible, what is the no of pairs of factors which are coprime to each otherand whose product is the given no.

a...8
b...64
c...32
d...16
e...4

[hsemu]

Originally Posted by shashankmishra

C S Inequality was stated earlier on this thread or try Wiki .......

Here CS is not required .....

x + y + z = 5

x^2 + y^2 + z^2 + 2*(xy + yz + zx) = 25

x^2 + y^2 + z^2 = 19

For (x^2)to be max (y^2 + z^2) to be Min

y^2 + z^2 = (y + z)^2 -2yz => For this to be Min "yz" should be Max which is for y = z

So x + y + z = 5 or
x + 2y = 5
y = (5-x)/2...............(i)
Also
xy + yz + zx = 3 or
2xy + y^2 = 3
Substitute the value of y from eqn(i) you will have x = 13/3 as Max

my approach..............
x + y + z = 5
x^2 + y^2 + z^2 + 2*(xy + yz + zx) = 25
x^2 + y^2 + z^2 = 19
2(y^2+z^2)>=(y+z)^2
=> 2(19-x^2)>=(5-x)^2
=>38-2x^2>=25+x^2 -10x
=>3x^2 -10x-13=<0
=>3x^2-13x+3x-13=<0
=>(x+1)(3x-13)=<0
-1=<x<=13/3
or
y=z
2y+x=5
2y^2+x^2=19
[(5-x)^2]/2 +x^2=19
this equation would also give x=13/3 on calculation

[convalesce]

Originally Posted by vivekimmortal

a composite no. has 720 factors, if the no of distint prime factors is max possible, what is the no of pairs of factors which are coprime to each otherand whose product is the given no.

a...8
b...64
c...32
d...16
e...4

my take is 4

[vivekimmortal]

Originally Posted by convalesce

my take is 4

ans is option b-->>64

[shashankmishra]

Originally Posted by vivekimmortal

a composite no. has 720 factors, if the no of distint prime factors is max possible, what is the no of pairs of factors which are coprime to each otherand whose product is the given no.

a...8
b...64
c...32
d...16
e...4

720 = 2*2*2*2*3*3*5

For Max distinct prime factors, Number = a * b * c * d * (e^2) * (f^2) * (g^4) {Where a,b,c,d,e,f,g are Prime numbers}

So Required Ans = 2^(7-1) = 64

[burning_desire]

here,s a prb---
lagaan is leveid on 60% of d cultivated land.the revenue dep. collected a total of rs. 384000 through d lagaan frm d village of SUKHIYA,sukhiya, avery rich farmer paid only rs.480 as lagaan.THE PECENTAGE OF TOTAL LAND OF SUKHIYA OVER D TOTAL TAXABLE LAND OF D VILLAGE IS....
a.0.15%
b.15%
c.0.125%
d.none of these
plz post d soln as well......

[pk_gt1]

Originally Posted by burning_desire

here,s a prb---
lagaan is leveid on 60% of d cultivated land.the revenue dep. collected a total of rs. 384000 through d lagaan frm d village of SUKHIYA,sukhiya, avery rich farmer paid only rs.480 as lagaan.THE PECENTAGE OF TOTAL LAND OF SUKHIYA OVER D TOTAL TAXABLE LAND OF D VILLAGE IS....
a.0.15%
b.15%
c.0.125%
d.none of these
plz post d soln as well......

---snipped--

[burning_desire]

Originally Posted by pk_gt1

i'm getting
option c

d ans. Is 'd'....0.20833%....evn i dnt knw d soln...lets see maybe some1 else can get d right soln.....

[pk_gt1]

.. a car is climbing up the hill at 90kmph . a rabbit is sitting at the top of the hill spots the car when it is 1170 km away and start running down towards the car at 140 kmph. as soon as it meets the car it turns back to the top of hill at 120kmph. the rabbit continues to do this till the car reaches the top. the total distance travelled by the rabbits is......

[pk_gt1]

Originally Posted by burning_desire

d ans. Is 'd'....0.20833%....evn i dnt knw d soln...lets see maybe some1 else can get d right soln.....

bro my fault.. i did a mistake..(actually watching football and doing sums don't go hand in hand..my fault..)

ans is .20833%

480 is taxable amt from suknas point of view,in net he ought o give

480/60=800

so 800/384000=.20833%