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 f(x)=|sinx-|cosx||, then the value of f^(')(x) at x=(7pi)/6 is

If f(x)=sin^(-1)cos x, then the value of f(10)+f'(10) is (a)11-(7 pi)/(2) (b) (7 pi)/(2)-11 (c) (5 pi)/(2)-11( 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

The value of c in Lagranges theorem for the function f(x)=log sin x in the interval [(pi)/(6),(5 pi)/(6)] is (pi)/(4) (b) (pi)/(2)(2 pi)/(3) (d) none of these

f:Nto[-sqrt2,sqrt2]:f(x)=sinx+cosx , then f(x) is

If f(x)=sqrt(x^(2)-10x+25), then the derivative of f(x) in the interval [0,7] is (a) 1 (b) -1( c) 0 (d) none of these

If A=f(x)=[(cosx, sinx, 0),(-sinx, cosx,0),(0,0,1)], then the value of A^-1= (A) f(x) (B) -f(x) (C) f(-x) (D) -f(-x)

The value of int_0^(pi//2)(sqrt(cosx))/(sqrt(cos x)+sqrt(s in x))dx is pi//2 b. pi//4 c. 0 d. none of these

Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3) (b) sqrt(x)+3 (c) x+sqrt(3) (d) none of these