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

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

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

If f^(prime)(x)=f(x)+int_0^1f(x)dx ,gi v e nf(0)=1, then the value of f((log)_2 2) is (a) 1/(3+e) (b) (5-e)/(3-e) (c) (2+e)/(e-2) (d) none of these

The range of f(x)=[|sin x|+|cosx"|""]"dot Where [.] denotes the greatest integer function, is {0} (b) {0,1} (c) {1} (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 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

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

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