[" If "[x]" is the greatest integer function and "],[K=Lt],[K=2^(+)(([x^(3))/(3)-[(x)/(3)]^(3))" then the value "3k]

If [x] is the greatest integer function, then underset (x to 2^+)lim ([x]^3/3-[x/3]^3)=

If x^(2)+3x+5 is the greatest common divisor of (x^(3)+ax^(2)+bx+1) and (2x^(3)+7x^(2)+13x+5) then find the value of [a+b]. [Note : [k] denotes greatest integer less than or equal to k.]

f(x)=[2x]sin3pixa n df^(prime)(k^(prime))=lambdakpi(-1)^k (where [.] denotes the greatest integer function and k in N), then find the value of lambda .

If (2x+3)/((x-3)(x+k))=9/(4(x-3))-1/(4(x+k)) " then "k=

If the term independent of x in the expansion of ((k)/(3)x^(2)-(3)/(2x))^(9) be 2268 , find the value of k .

If the sum of all solutions of the equation [x]-{x}= (x)/(3) ,(where and {.} are greatest integer function and fractional part function respectively) is k ,then the value of 10k/3 is