If `[x]` denotes the integral part of `x` and `n` is a natural number such that `1<=n<100` then the number of solutions of the equation `[(n)/(2)]+[(n)/(3)]+[(n)/(5)]=(n)/(2)+(n)/(3)+(n)/(5)` is

If [x] denotes the integral part of x , find int_0^x[t+1]^3dt .

If [x] denotes the integral part of x and m= [|x|/(1+x^2)],n= integral values of 1/(2-sin3x) then (A) m!=n (B) mgtn (C) m+n=0 (D) n^m=0

If [x] and {x} denote the integral part and the fractional part of a real number x ,then the number of negative real number (s) x for which 2[x]-2{x}=x, is

Let f(x)=[x] +sqrt({x}) , where [.] denotes the integral part of x and {x} denotes the fractional part of x. Then f^(-1)(x) is

If [x] denotes the integral part of x and f(x)=min(x-[x],-x-[-x]) show that: int_-2^2f(x)dx=1

If int_-1^1(sin^-1[x^2+1/2]+cos^-1[x^2-1/2])dx=kpi where [x] denotes the integral part of x , then the value of k is …

If [x] denotes the integral part of x and a_(n)=sum_(r=0)^(n-1)[x+(r)/(n)] then find Lt_(n)rarr oo(a_(1)+a_(2)+...a_(n))/(n^(2))

If [x] denotes the integral part of x ,then the domain of the function f(x)=sin^(-1)[2x^(2)-3]+log_(2)log_((1)/(2))(x^(2)-5x+5)

If [x] denotes the integral part of x and k=sin^-1 ((1+t^2)/(2t))gt0 then integral valueof alpha for which the equation (x-[k])(x+alpha)-1=0 has integral roots is (A) 1 (B) 2 (C) 4 (D) none of these