If `[dot]` represents the greatest integer function, then `int_4^(10)([x^2])/([x^2-28 x+196]+[x^2])dxi se q u a lto` 0 (b) 1 (b) 3 (d) none of these

If [dot] denotes the greatest integer function, then find the value of int_1^2[3x]dx

Let [.] represent the greatest integer function and f (x)=[tan^2 x] then :

int_0^oo(dx)/([x+sqrt(x^2+1)]^3)i se q u a lto 3/8 (b) 1/8 (c) -3/8 (d) none of these

Let f:(4,6)vec(6,8) be a function defined by f(x)=x+[x/2]dotw h e r e[dot] denotes the greatest integer function, then f^(-1)(x) is equal to (A) x-2 (B) x-[x//2] (C) -x-2 (D) none of these

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2))i se q u a lto 1 (b) 0 (c) 2 (d) none of these

If [x] stands for the greatest integer function, the value of overset(10)underset(4)int([x^(2)])/([x^(2)-28x+196]+[x^(2)])dx , is

If [dot] denotes the greatest integer function, then (lim)_(xvec0)x/a[b/x] a. b/a b. 0 c. a/b d. does not exist

Let f : R->R be given by f(x) = {|x-[x]| , when [x] is odd and |x-[x]-1| , when [x] is even ,where [.] denotes the greatest integer function , then int_-2^4 f(x) dx is equal to (a) (5)/(2) (b) (3)/(2) (c) 5 (d) 3

("lim")_(xvecoo){1/(1-n^2)+2/(1-n^2)+......n/(1-n^2)}i se q u a lto 0 (b) -1/2 (c) 1/2 (d) none of these

Let [x] denote the greatest integer less than or equal to x , then int_0^(pi/4) sinx d(x-[x])= (A) 1/2 (B) 1-1/sqrt(2) (C) 1 (D) none of these