The domain of the function `f(x)=1/(sqrt({sinx}+{sin(pi+x)}))` where `{dot}` denotes the fractional part, is (a)`[0,pi]` (b) `(2n+1)pi/2, n in Z` (c)`(0,pi)` (d) none of these

The domain of the function f(x)=x/(sqrt(sin(lnx)-cos(lnx))),(n in Z) is (a) (e^(2npi),e^((3n+1/2)pi)) (b) (e^((2n+1/4)pi),e^((2n+5/4)pi)) (e^((2n+1/4)pi),e^((2n-3/4)pi)) (d) none of these

The total number of solution of sin{x}=cos{x} (where {} denotes the fractional part) in [0,2pi] is equal to 5 (b) 6 (c) 8 (d) none of these

The period of the function f(x)=(6x+7)+cospix-6x , where [dot] denotes the greatest integer function is: 3 (b) 2 pi (c) 2 (d) none of these

The domain of the function f(x)=(log)_e{(log)_(|sinx|)(x^2-8x+23)-{3/((log)_2|sinx|)}} contains which of the following interval(s)? (a) (3,pi) (b) (pi,(3pi)/2) (c) ((3pi)/2,5) (d) none of these

The function f(x)=(tan |pi[x-pi]|)/(1+[x]^(2)) , where [x] denotes the greatest integer less than or equal to x, is

Let x in (0,pi/2)dot Then find the domain of the function f(x)=1/sqrt((-(log)_(sinx)tanx))

The domain of the function f(x)=sqrt(log(1/(|sinx|))) (a) R-{-pi,pi} (b) R-{npi|npiZ} (c) R-{2npi|n in z} (d) (-oo,oo)

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

On which of the following intervals is the function x^(100)+sinx-1 decreasing? (a) (0,pi/2) (b) (0,1) (c) (pi/2,pi) (d) none of these

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these