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

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

Statement 1: 3^(2n+2)-8n-9 is divisible by 64 ,AAn in Ndot Statement 2: (1+x)^n-n x-1 is divisible by x^2,AAn in Ndot

Statement -1 for all natural numbers n , 2.7^(n)+3.5^(n)-5 is divisible by 24. Statement -2 if f(x) is divisible by x, then f(x+1)-f(x) is divisible by x+1,forall x in N .

If y=tan^(-1)1/(1+x+x^2)+tan^(-1)1/(x^2+3x+3)+tan^(-1)1/(x^2+5x+7)++ upto n terms, then find the value of y^(prime)(0)dot

Statement -I: X={8n+1:n inN},then XnnY=Y, Y={(2n+1)^2:n in N} because statement -II:x is a subset of y

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.

Statement-1: If x, y are positive real number satisfying x+y=1 , then x^(1//3)+y^(1//3)gt2^(2//3) Statement-2: (x^(n)+y^(n))/(2)lt((x+y)/(2))^(n) , if 0ltnlt1 and x,ygt0.

If y=tan^(-1)(1/(1+x+x^2))+tan^(-1)(1/(x^2+3x+3))+tan^(-1)(1/(x^2+5x+7))++ upto n terms, then find the value of y^(prime)(0)dot

Statement-1 The number of terms in the expansion of (x + (1)/(x) + 1)^(n) " is " (2n +1) Statement-2 The number of terms in the expansion of (x_(1) + x_(2) + x_(3) + …+ x_(m))^(n) "is " ^(n + m -1)C_(m-1) .