If 1 lies between the roots of equation `y^? - my +1 = 0` and [x] denotes the integral part of x, then `[((4|x|)/(x^2+16))]`where `x in R` is equal to

If {x} denotes the fractional part of x, then int_(0)^(x)({x}-(1)/(2)) dx is equal to

The difference between the roots of the equation x^2-6x- 16 = 0 is:

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

If 2 lies between the roots of the equation t ^(2) - mt +2 =0,(m in R) then the value of [((2 |x|)/(9+x ^(2)))^(m)] is: (where [.] denotes greatest integer function)

Show that: int_0^[x] (x-[x])dx=[x]/2 , where [x] denotes the integral part of x .

If a=sin\ pi/18 sin\ (5pi)/18 sin\ (7pi)/18, and x is the solution of the equation y=2[x]+2 and y=3[x-2], where [x] denotes the integral part of x then a= (A) [x] (B) 1/[x] (C) 2[x] (D) [x]^2

int_0^1 [x^2-x+1]dx , where [x] denotes the integral part of x , is (A) 1 (B) 0 (C) 2 (D) none of these

Show that: int_0^x[x]dx=[x]([x]-1)/2+[x](x-[x]) , where [x] denotes the integral part of x .