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What is the remainder when 100! is divided by 97^2?

S' is a region enclosing all such points (x, y) in the X-Y plane, whose distance from the origin is less than or equal to 3√2 units. The number of points, in the region 'S', with integer co-ordinates is

Q.67 Let p, q, r and s be distinct real numbers. Max(a,b) = larger number between a and b, and Min(a,b) = smaller number between a and b. If N = Max[Min(p,q), Min(r,s)] and S = Min[Max(p,r), Max(q,s)], which of the following is definitely true? a N ≤ S, for all values of p, q, r and s b N ≥ S, for all values of p, q, r and s c N ≠ S, for all values of p, q, r and s d No specific relation exists between N and S

how to solve cubic equations?

For real numbers x and y, such that xy ≠ 0, the following functions are defined. f(x, y) = root(x + y) if x+y > 0 and f(x, y) = (x + y)^2 otherwise. g(x, y) = (x + y)^2 if x + y ≮ 0 and g(x, y) = –( x + y) otherwise. Find the number of ordered pairs of the form (x, y), such that x, y belongs to Z; – 4 ≤ x ≤ 4; –3 ≤ y ≤ 3 and f(x, y) = g(x, y).

an ant climbing up a vertical pole ascends 12 metres and slips down 5 metre in every alternate hour. If the pole is 63metres high how long will it take it to reach the top

an ant climbing up a vertical pole ascends 12 metres and slips down 5 metre in every alternate hour. If the pole is 63metres high how long will it take it to reach the top

I made an error while attempting the mocks. My answers were being cleared after moving on to the next question. Hence my final scores were not being registered properly. How do i attempt the paper again? So as to know my correct marks?

if f(mn)=f(m)*f(n) &f;(2)=1/4 find f(1/2)

if f(mn)=f(m)*f(n)