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the answer is absolutely correct

There are 100 tickets numbered from 1 to 100 .3 tickets are drawn at a
random. Find the probability that the numbers on the tickets are in G.P
having a integral common ratio?

x^3 - x = x(x-1)(x+1)

x + x^1998 + x^1999 + x^2000 +x^2001 = x( 1+ x^1997 + x^1998 + x^1999

+x^2000 )

now using remainder theorem (x-1)(x+1) for the values x =1 and x= -1

x=1 gives remainder as 5

x=-1 gives remainder as 1

hence the overall remaider is 5 for the expression

answer to 2nd question c)2ab/?(a²+b²)

due to reflection there is a additional phase difference of pie introduced { 2(pie) +(pie)=3(pie) }

since the frequency of reflected and incident light be the same

let the angular speed of reflected light w1

2(pie) /w = 3(pie)/ w1

w1 = (3/2)*w

namaste sir,

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