@rubikmath said:let x = m! ; y = n!1/x + 1/y =1/20--> (x-20)(y-20) =400one f the solns . is 4 * 100 --> x=24; y=100--> m=4;n=5
great method dude........
@bullseyes said:X is a three-digit number. The sum of all its distinct prime factors is 17. What is the value of X?I. X > 420II. The total number of factors of X is 24. X ‰¤ 630if statement I alone is sufficient and statement II alone is not sufficient to answer the questionif statement II alone is sufficient and statement I alone is not sufficient to answer the question.if each statement alone is sufficient to answer the question.if statements I and II together are sufficient but neither statement alone is sufficient to answer the question.if the two statements I and II together are not sufficient to answer the question and additional data is needed.
1 and 2 both but not alone
from 1 x=210
from 2 x=420 and 630
x>420
therefore x=630
p,q,r are sides of triangle such that p^2+ q^2/ r^2 > K
FIND K
0.25
0.5
0.55
0.75
FIND K
0.25
0.5
0.55
0.75
@Cat.Aspirant123 said:p,q,r are sides of triangle such that p^2+ q^2/ r^2 > KFIND K0.250.50.550.75
0.55
@krum said:0.55
approach ?
x + y + 2z = 4 and x^2 + y^2 + 2z^2 = 20, for the real quantities x, y and z.
How many integral values can z take?
OPTIONS
1) 0
2) 1
3) 2
4) 3
5) More than 3
How many integral values can z take?
OPTIONS
1) 0
2) 1
3) 2
4) 3
5) More than 3
@Cat.Aspirant123 said:p,q,r are sides of triangle such that p^2+ q^2/ r^2 > KFIND K0.250.50.550.75
0.55??
@sujamait said:approach ?x + y + 2z = 4 and x^2 + y^2 + 2z^2 = 20, for the real quantities x, y and z.How many integral values can z take?OPTIONS1) 0 2) 1 3) 2 4) 3 5) More than 3
@Brooklyn said:0.55??
my appraoch:
we need to take obtuse triangle.
for obtuse triangle, r^2 > p^2 + q^2
so take an example: 2,1,3
u get 5/9 = 0.55
@Brooklyn said:my appraoch:we need to take obtuse triangle.for obtuse triangle, r^2 > p^2 + q^2so take an example: 2,1,3u get 5/9 = 0.55
but in a triangle sum of 2 sides > 3rd ??
2+1=3 yaha toh eqaul ho rha hi ..
@sujamait said:but in a triangle sum of 2 sides > 3rd ??2+1=3 yaha toh eqaul ho rha hi ..
yup that is why it is >0.55 and not equal to and > 0.55
coz u can take 2.99999 so on which would tend to 3 , i hope u get my logic :)
@Brooklyn said:my appraoch:we need to take obtuse triangle.for obtuse triangle, r^2 > p^2 + q^2so take an example: 2,1,3u get 5/9 = 0.55
bro 2,1,3 is not a triangle...its a straight line. (2+1=3)
@surajmenonv said:bro 2,1,3 is not a triangle...its a straight line. (2+1=3)
2,1,2.999 is read the post above your post :)
@Brooklyn said:yup that is why it is >0.55 and not equal to and > 0.55coz u can take 2.99999 so on which would tend to 3 , i hope u get my logic
aah mene bhi 213 hee liya tha..but precisely yehi par confuse ho gaya tha...sahi hai 0.55 seems fine I guess :)
Find the coefficient of x12 in the expansion of (1-x6)4 (1-x)-4
pls show solution steps..thank u
method pls@Brooklyn said:2,1,2.999 is read the post above your post
is there an elegant solution so that its proved with particular examples? try! m trying too \m/
there will be three case 1) when we take x^0 from (1-x^6)4 and x^12 from (1-x)^-4
in this case coefficient will be
(-4*-5*...........*-15)/ 12! = 455
2) when x^6 from both
(-4)(-4*-5*........*-9)/6! = -336
3) when we take x^12 from(1-x^6)4
4C2 = 6
so coefficient of x^12 is the whole expansion will be = 455 -336-6 = 125
@mahalgoldn
in this case coefficient will be
(-4*-5*...........*-15)/ 12! = 455
2) when x^6 from both
(-4)(-4*-5*........*-9)/6! = -336
3) when we take x^12 from(1-x^6)4
4C2 = 6
so coefficient of x^12 is the whole expansion will be = 455 -336-6 = 125
@mahalgoldn
@mahalgoldn said:Find the coefficient of x12 in the expansion of (1-x6)4 (1-x)-4pls show solution steps..thank u
(1-4x^6+6x^12)(1-x)^-4
no we have to find out the coeff of x^12 that can be made from...
1.coeff of (1)(x^12)=====> 455
2. coeff of (x^6)(x^6)======> -336
3. coeff of (x^12)(1)=======> 6
so ans =125
Note :> Coeff of x^r in (1-x)^-n = C(n+r-1,n-1)
What is the number of ways to arrange 4 red and 6 green balls in a circle? Given that balls of same color are considered same!
@kingsleyx said:What is the number of ways to arrange 4 red and 6 green balls in a circle? Given that balls of same color are considered same!
21 ?