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 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 (0,pi) (d) none of these

Function f(x)=sin(lnx)-"cos"(lnx) is (a)M.I. in [e^(2npipi/4),e^(2npi+(3pi)/4)] (b)M.D. In [e^(2npi+(3pi)/4),e^(2npi+(7pi)/4)] (c)M.D. in [e^(2npi(5pi)/4),e^(2npipi/4)] (d)M.I. in [e^(2npi+(3pi)/4),e^(2npi+(7pi)/4)]

The domain of definition of the function f(x)=sqrt(-cosx)+sqrt(sinx) is: [2npi,2npi+pi/2],n in I b. [2npi,(2n+1)pi],n in I c. [2n+1/2pi(2n+1)pi],n in I d. [(2n+1)pi,(2n+3/2)pi],n in I

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

Find the point of inflection of the function: f(x)=sin x (a) 0 (b) n pi,n in Z (c) (2n+1)(pi)/(2),n in Z (d) None of these

The value of lim_(x rarr 1)(2-x)^(tan((pix)/2)) is (a) e^(-2/pi) (b) e^(1/pi) (c) e^(2/pi) (d) e^(-1/pi)

Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a) e^(5pi//18) (b) e^(13pi//18) (c) e^(-2pi//18) (d) none of these

The value of x satisfying the equation cos(lnx)=0, is (A) e^(pi//2) (B) e^(-(2009)pi//2) (C) e^(1000pi) (D) e^(-3pi//2)

Let f(x)=e^cos^((-1)){sin(x+pi/3)}dot Then, f((8pi)/9)= e^(5pi//18) (b) e^(13pi//18) (c) e^(-2pi//18) (d) none of these

The function f (x)={((x ^(2n)))/((x ^(2n) sgn x)^(2n+1))((e ^(1/x)-e ^(-1/x))/(e ^(1/x)+e ^(-(1)/(x))))x ne0 n in N is: