crux of the problem: if the total work to be done is constant then if the rate of working decreases then time taken increases.i.e R*T=W (Work: filling of the tank)also, if rate of work decreases by 1/x then time taken increases by 1/(x-1)i.e R(1-1/x)*T(1 + 1/x-1) = W.Application to the given problem: divide tank in three parts, base to h->v1, h to 2h-> V2 and 2h to 3h -> v3. if outlet pipes were not there then all the parts would be filled in time T= 4 hr each. Say rate of A is R. Rate of C is R/x and B is 2R/xEffective rate while v2 is getting filled = R-R/x = R(1-1/x) [rate has decreased by 1/x] hence time must increase by 1/(x-1) i.e new time = 4*(1+1/x-1) = 4x/(x-1)Effective rate while v3 is getting filled = R-R/x -2R/x = R{1-1/(x/3) } [rate has decreased by 1/(x/3)] hence time must increase by 1/(x/3-1) i.e new time = 4*{1+1/(x/3 -1)} = 4x/(x-3 )Calculations:(This is the point where you would start from in real exam if above concept is known, so observe how quick and simple things are from here on) =>total time to fill = time for v1 + time v2 + time v3 =16hr48 min=> 4 + 4x/(x-1) + 4x/(x-3) = 16 + 4/5=> x/(x-1) + x/(x-3) = 16/5=> x = 6hence rate of B = 2R/6 = R/3 hence it will take 3 time the time of A i.e 12*3 = 36 hrsThe good thing about this method is that it deals in single variable so we do not get lost in multiple eqns.ATDH.
Bhai ye batao ki agar 25^86 ko change kare (5^2*86 ) - (5^171) = 5^172-5^171 =5.. Is tarah karna galat hoga kya??
5^172-5^171 =5....................dis is not correct as 5^2-5=5(5-1)=5x4 5^3-5^2=5^2(5-1)=5^2 x 4 5^4-5^3=5^3(5-1)=5^3 x 4 in d same way 5^172 -5^171=5^171 x 4 i hope u got it.......
5^172-5^171 =5....................dis is not correct as 5^2-5=5(5-1)=5x45^3-5^2=5^2(5-1)=5^2 x 45^4-5^3=5^3(5-1)=5^3 x 4in d same way 5^172 -5^171=5^171 x 4i hope u got it......
agar directly 5^171*4 aur fir base change karo toh kya galat hai
constant term in d expression (x^2+y+1/y+1/x^2)^8 =???
I tried like this.. confirm the answer if correct.
Constant term will be the sum of coefficients of terms where powers of four terms are such that they cancel out in numerator and denominator.
The coefficient of a term in this expression will be 8!/(a!b!c!d!) where a, b, c and d are powers of x^2, y, 1/y and 1/x^2 respectively.
So possible combinations of such a b c and d where terms cancel out are.. 2 2 2 2 => coefficient is 8!/(2!)^4 = 2520 1 3 3 1 => coefficient is 8!/(3!)^2 = 1120 3 1 1 3 => coefficient is 8!/(3!)^2 = 1120 0 4 4 0 => coefficient is 8!/(4!)^2 = 70 4 0 0 4 => coefficient is 8!/(4!)^2 = 70
In a family, there are four members. the father is of 38 years older than his son, and the mother is 26 years older than her daughter. The sum of their ages today is 82. All members are at least one year old. Eight years ago, the sum of their ages was 57. Which of these is a possible value for the age of the son in 10 years ?18192021
A positive integer is equal to the square of the number of factors it has. How many such integers are there?(a) 1(b) 2 (c) 3 (d) InfinitePlease explain with approach
2???
1,9 are nos
sirf odd no hi aise ho skte hai... baki hit and trial
small doubt.....In a family, there are four members. the father is of 38 years older than his son, and the mother is 26 years older than her daughter. The sum of their ages today is 82. All members are at least one year old. Eight years ago, the sum of their ages was 57. Which of these is a possible value for the age of the son in 10 years ? sum of their ages today is 82..then eight years ago ,it should be 50 rite??? correct me if i am wrong...
it can be more than 50 also... if any of their child has age less than 8
A positive integer is equal to the square of the number of factors it has. How many such integers are there?(a) 1(b) 2 (c) 3 (d) InfinitePlease explain with approach
Let N=a^p * b^q ( a and b are different prime nos)
Also, N= [(p+1)(q+1)]^2 = a^p * b^q
Since N is a perfect square hence p and q are even nos.
small doubt.....In a family, there are four members. the father is of 38 years older than his son, and the mother is 26 years older than her daughter. The sum of their ages today is 82. All members are at least one year old. Eight years ago, the sum of their ages was 57. Which of these is a possible value for the age of the son in 10 years ? sum of their ages today is 82..then eight years ago ,it should be 50 rite??? correct me if i am wrong...
