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2^48Mod 100 = 2^46Mod25 ; using euler @(N)=4 => 2^44Mod25=1 =>Rem(16) What's wrong in this

In a video lecture which is related to inequalities chapter.......for an example problem g(x)=|x-2|+|x-3|+|x-6|. find the least possible value of g(x)....it has been in the second step of the solution that 2<=x<=3, g(x)=7-x, minimum at x=3 and g(x)=4....please explain me about this step and other steps also.......thank you

a-b varies directly with a+b, a^2-b^2 will vary directly with

find the unit digit of 82^83^84^85..can u explain its solution..i.e how it is simplified in the form of 4k+1

say dry 42 96 get 39 kite 67

how to solve para jumbles

In the concept theory of factors and cyclicity,there is description as: 172^143 mod 100 = 172*172^142mod 100 = 4*(43*172^142mod25) = 4*(43*22^142mod25) = 4*(43*484^71mod 25)...So how the value of 43*172^142mod 25 has been simplified to 43*22^142mod25 and futher..Can u please elaborate this step..

On a square cardboard of length 10 cm, two identical circles of radius 2 cm are drawn such that the two centres and the two points of intersection of the circle form a square. Find the total area of the cardboard covered by the two circles?

The factorial of a number n is exactly divisible by (2^11×11^2) then the least posible value of n is?

a.22 b.25 c. does not exist d.none of this

The sum of 4 prime no of two digit is 204.The sum of 1st and last i.e (p1+p4)is same as the sum of second no p2 and third number p3 i.e (p2+p3)
Again p3-p2=2 (p2-p1)=2 (p4-p3).The avg no of all four number is not a prime no. one of this prime number is ?

a.23 b.89 c.71 d. cant be determined.

solution please..