Champs... this one is still pending. Go ahead and nail it!
(a) f(2) = f(4) (b) f(3) = f(7) (c) f(4) = f(10) (d) Atleast 2 of the foregoing
(a) f(2) = f(4) (b) f(3) = f(7) (c) f(4) = f(10) (d) Atleast 2 of the foregoing
@maroof10 said:Total no. of people in a community =100No. of people who like amy =83No. of people who like bill =88No. of people who like candy = 51No. of people who like dany =371.Find the max no. of persons who like exactly one out of the four?2.Find the max no. of persons who like exactly two out of four?3.Find the min no. of person who like atleast three out of four?Kindly share the approach.Suggest some good links for practising such questions.
You can try this question using lines....if two lines overlap that means those many people like 2 of the given 4 things.....
And the length of the lines should be between 0 to 100.....
To maximise/minimise the lines you can break the lines in parts but ensure that the fragmented parts do add up to the values provided in the question.....
Cant solve it right now...in bus...
@sameersapre23 said:Fifty white marbles are placed in a row. What is the minimum number of black marbles that need tobe placed between the white marbles such that each marble (white or black) has at least oneneighbour of the other colour?(a) 24 (b) 49 (c) 25 (d) 48
25 ?
@sameersapre23 said:How many different terms does the product (a + b + c+ d + e + f)(c + d + e + f + g) have?1130252429
6*5 - 4c2 = 24 ?
@bodhi_vriksha said:Champs... this one is still pending. Go ahead and nail it!Let f: R -> R and f(x+2) = 1/2 + (f(x) - (f(x))^2)^1/2. Then which among the following is always true?(a) f(2) = f(4) (b) f(3) = f(7) (c) f(4) = f(10) (d) Atleast 2 of the foregoing
(2f(x+2)-1)^2 = 4*(f(x) - f(x)^2)
=>f(x) + f(x+2) = f(x)^2 + f(x+2)^2 +1..........................(i)
=>f(x+2) + f(x+4) = f(x+2)^2 + f(x+4)^2 + 1..................(ii)
subtracting we get (ii) from (i) we get
f(x)-f(x+4) = {f(x) - f(x+4)} * {f(x) + f(x+4)}
=> either f(x) = f(x+4) or f(x)+f(x+4) = 1
if f(x) + f(x+4) = 1 then option (b) is true.
however, if f(x)+f(x+4) = 1 => f(x) = 1- f(x+4)
replacing this in (i)
f(x+4)+1 + f(x+2) = {1-f(x+4)}^2 + f(x+2)^2 + 1
replacing x+2 by x we get
f(x+2) + f(x) + 1 = f(x+2)^2 -2f(x+2) + 1 + f(x)^2 +1
=>3f(x+2) + f(x) = f(x+2)^2 + f(x)^2 + 1...................(iii)
using (i) and (iii) we get f(x) + f(x+2) = 3f(x+2) + f(x)
=>f(x+2) = 0
=>f(x) = 0 and this does not satisfy the original equation.
hence only option (B) is true.
@bodhi_vriksha : thanks for pointing out the calculation error earlier. Have corrected the solution accordingly. I hope this one is fine.
ATDH.
find the value of a:b where a/b is an improper fraction satisfying the equation 16a2 - 26 ab + 9b2
please share the approach.
please share the approach.
@Subhashdec2 said:yaar iska explanation btana
(a + b + c + d+ e + f)---> 6 terms
(c + d + e + f + g)----> 5 terms
total terms = 6*5 = 30
now (c + d + e + f) --> 4 terms are repeating twice
so total terms by these 4 = 4c2
total no. of distinct terms = 6*5 - 4c2 = 24
@impluse said:find the value of a:b where a/b is an improper fraction satisfying the equation 16a2 - 26 ab + 9b2 please share the approach.
16a^2/b^2 - 26a/b +9=0
16x^2-26x+9=0
16x^2-8x-18x+9=0
(8x-9)(2x-1)=0
x=9/8 or 1/2
3/2sqrt(2) or 1/sqrt(2)
so it will be 3/2sqrt(2)
@mailtoankit said:(a + b + c + d+ e + f)---> 6 terms(c + d + e + f + g)----> 5 termstotal terms = 6*5 = 30now (c + d + e + f) --> 4 terms are repeating twiceso total terms by these 4 = 4c2total no. of distinct terms = 6*5 - 4c2 = 24
what if we had something like (a+b+c+d)(c+d+e+f)(a+c+f)
@sameersapre23 said:Fifty white marbles are placed in a row. What is the minimum number of black marbles that need tobe placed between the white marbles such that each marble (white or black) has at least oneneighbour of the other colour?(a) 24 (b) 49 (c) 25 (d) 48
25 required??
1)consider 4 W marbles
den WBWWBW = 2 B marbles required
2)consider 6 W marbles
WBWWBWWBW = 3 B marbles required
so for 50 W marbles ,,25 B marbles required??
1)consider 4 W marbles
den WBWWBW = 2 B marbles required
2)consider 6 W marbles
WBWWBWWBW = 3 B marbles required
so for 50 W marbles ,,25 B marbles required??
@sameersapre23
25
Since every pair of white marbles need one black marble. So, 25 pairs of white marbles need 25 black marbles.
@Subhashdec2 said:what if we had something like (a+b+c+d)(c+d+e+f)(a+c+f)
12
did it by taking a = 1 , b = 2....like this....
.....pehele waale method se nahi ho raha..
.....pehele waale method se nahi ho raha..@mailtoankit said:12 did it by taking a = 1 , b = 2....like this.........pehele waale method se nahi ho raha..
ye wala method hee bta 1,2,3... aise rakhke kaise kara
thoda explain kar
there are two numbers m and n. which of the following must be added to two numbers m and n such that their ratio becomes x:y
a) mx+ny/y=x
a) mx+ny/y=x
b)my+nx/y-x
c)my-nx/x-y
d)my+nx/y+x
please share the approach
please share the approach
@Subhashdec2 said:ye wala method hee bta 1,2,3... aise rakhke kaise karathoda explain kar
bhai a = 1 b = 2 c = 3 d = 4 e = 5 f = 6..le kar eqn mein daal do.....fir expand karo.....kaafi terms common aaygi...calculation kaafi karni padegi is method mein....sure bhi nahi hoon sahi hai ki nahi..
...sure bhi nahi hoon sahi hai ki nahi..@mailtoankit said:bhai a = 1 b = 2 c = 3 d = 4 e = 5 f = 6..le kar eqn mein daal do.....fir expand karo.....kaafi terms common aaygi...calculation kaafi karni padegi is method mein....sure bhi nahi hoon sahi hai ki nahi..
chal thik h
thanks man
@impluse said:there are two numbers m and n. which of the following must be added to two numbers m and n such that their ratio becomes x:ya) mx+ny/y=xb)my+nx/y-xc)my-nx/x-yd)my+nx/y+xplease share the approach
(m+p)/(n+p) = x/y
=> m*y+p*y=n*x+p*x
=> p*(y-x) = n*x-m*y
=> p=(m*y-n*x)/(x-y)