`a=1+1/2^2+1/3^2+1/4^2+....+1/(2015)^2`Evaluate [a] where [a] denotes integral part of a

The roots of equation x^2+2(a-3)x+9=0 lie between -6 and 1 and 2 , h_1,h_2,.....h_20 [a] are in HP where [a] denotes the integral part of a and 2, a_1,a_2,......a_20 ,[a] are in AP, then ((a_3h_18)/3) is equal to

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 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 …

Let f(n) = [(1)/(2) + (n)/(100)] where [n] denotes the integral part of n. Then the value of sum_(n=1)^(100) f(n) is

If both roots of x^(2)-2ax+a^(2)-1=0 lies in (-2, 1) then [a] , where [.] denotes greatest integral function is

Statement-1: int_-3^3 x^8{x^9}dx=2xx3^7 , where {x} denotes the fractional part of x .Statement-2: [x]+[-x]=-1 , if x is not an integer, where [x] denotes the integral part of x . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

Statement-1: int_-3^3 x^8{x^9}dx=2xx3^7 , where {x} denotes the fractional part of x .Statement-2: [x]+[-x]=-1 , if x is not an integer, where [x] denotes the integral part of x . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

If both roots of the equation x^2-2ax+a^2-1=0 lie between -3 and 4 and [a] denotes the integral part of a, then [a] cannot be

Let f(x)=(sin^(101)x)/([(x)/(pi)]+(1)/(2)) , where [x] denotes the integral part of x is

Let f(n) = [1/2 + n/100] where [x] denote the integral part of x. Then the value of sum_(n=1)^100 f(n) is