The period of `f(x)=[x]+[2x]+[3x]+[4x]+[n x]-(n(n+1))/2x ,` where `n in N ,` is (where `[dot]` represents greatest integer function). (a) `n` (b) 1 (c) `1/n` (d) none of these

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

The area made by curve f(x)=[x]+sqrt(x-[x]) and x-axis when 0le xle n (n in N) is equal to { where [x] is greatest integer function}

The range of f(x)=[1+sinx]+[2+sin(x/2)]+[3+sin (x/3)]+....+[n+sin (x/n)]AAx in [0,pi] , where [.] denotes the greatest integer function, is,

The integral int_(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (where [.] represents the greatest integer function) -1/2 (b) 0 (c) 1 (c) 21n(1/2)

The value of int_0^x[cost]dt ,x in [(4n+1)pi/2,(4n+3)pi/2]a n dn in N , is equal to where [.] represents greatest integer function. pi/2(2n-1)-2x pi/2(2n-1)+x pi/2(2n+1)-x (d) pi/2(2n+1)+x

int_0^x[sint]dt ,w h e r ex in (2npi,(2n+1)pi),n in N ,a n d[dot] denotes the greatest integer function is equal to -npi (b) -(n+1)pi 2npi (d) -(2n+1)pi

If |[x^n, x^(n+2),x^(2n)],[1,x^a, a],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R ,where n in N , then value of a is (a) n (b) n-1 (c) n+1 (d) none of these

Suppose that f is an even, periodic function with period 2,a n dt h a tf(x)=x for all x in the interval [0,1] . The values of [10f(3. 14)] is(where [.] represents the greatest integer function) ______

Suppose that f is an even, periodic function with period 2,a n dt h a tf(x)=x for all x in the interval [0,1] . The values of [10f(3. 14)] is(where [.] represents the greatest integer function) ______

lim_(xto0^(+)) (sum_(r=1)^(2n+1)[x^(r)]+(n+1))/(1+[x]+|x|+2x), where ninN and [.] denotes the greatest integer function, equals