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

The length of the longest interval in which the function 3sinx-4sin^3x is increasing is pi/3 (b) pi/2 (c) (3pi)/2 (d) pi

Which of the following functions are decreasing on 0,(pi)/(2) ?

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 x^x decreases in the interval (0,e) (b) (0,1) (0,1/e) (d) none of these

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

Separate the intervals of monotonocity for the function f(x)=sinx+cosx ,x in (0,2pi)

One of the root equation cosx-x+1/2=0 lies in the interval (a) (0,pi/2) (b) (-pi/(2,0)) (c) (pi/2,pi) (d) (pi,(3pi)/2)

The value of c in Lagranges theorem for the function f(x)=logsinx in the interval [pi/6,(5pi)/6] is (a) pi/4 (b) pi/2 (c) (2pi)/3 (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

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (pi)/3 (d) (5pi)/3 (e) none of these