Statement 1: Let `E=[1/3+1/(50)]+[1/3+2/(50)]+` upto 50 terms, then `E` is divisible by exactly two primes. Statement 2: `[x+n]=[x]+n ,n in I` and `[x+y]=[x]+[y]` if `x ,y in I`

Let E=[(1)/(3)+(1)/(50)]+[(1)/(3)+(2)/(50)]+... upto 50 terms,then exponent of 2 in (E)! is

x^(2n-1)+y^(2n-1) is divisible by x+y

Let E = [(1)/(3) + (1)/(50)]+[(1)/(3)+(2)/(50)]+[(1)/(3)+(3)/(50)]+…….. upto 50 terms where [.] denotes the greatest integer terms then

If n in N,x^(2n-1)+y^(2n-1) is divisible by x+y if n is

Statement-1: 2^(33)-1 is divisible by 7. Statement-2: x^(n)-a^(n) is divisibel by x-a, for all n in N and x ne a .

Statement 1:3^(2n+2)-8n-9 is divisible by 64,AA n in N. Statement 2:(1+x)^(n)-nx-1 is divisible by x^(2),AA n in N

Using mathematical induction, prove that for x^(2n-1)+y^(2n-1) is divisible by x+y for all n in N

Statement-1: The middle term of (x+(1)/(x))^(2n) can exceed ((2n)^(n))/(n!) for some value of x. Statement-2: The coefficient of x^(n) in the expansion of (1-2x+3x^(2)-4x^(3)+ . . .)^(-n) is (1*3*5 . . .(2n-1))/(n!)*2^(n) . Statement-3: The coefficient of x^(5) in (1+2x+3x^(2)+ . . .)^(-3//2) is 2.1.