If `f(x)=sin^(-1)cosx ,` then the value of `f(10)+f^(prime)(10)` is (a)`11-(7pi)/2` (b) `(7pi)/2-11` (c)`(5pi)/2-11` (d) none of these

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dxdot

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (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

If f(x)=|sinx|+|cosx|, then the value f(x)^'a tx=(7pi)/6 is (a)positive (b) (1-sqrt(3))/2 (c)0 (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

The value of cos""(pi)/(11)+cos""(3pi)/(11)+cos""(5pi)/(11)+cos""(7pi)/(11)+cos""(9pi)/(11), is

The value of is sum_(k=1)^(10)(sin"" (2k pi)/(11)+ icos ""(2k pi)/(11)) is

The least and the greatest values of (sin^(-1)x)^3+(cos^(-1)x)^3 are (a) (-pi)/2,pi/2 (b) (-pi^3)/8,(pi^3)/8 (c) (pi^3)/(32),(7pi^3)/8 (d) none of these

If z=sec^(-1)(x+1/x)+sec^(-1)(y+1/y), where x y<0, then the possible values of z is (a) (8pi)/(10) (b) (7pi)/(10) (c) (9pi)/(10) (d) (21pi)/(20)

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a) -1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these