If `y=cos^(-1)((5cosx-12sinx)/(13)),w h e r ex in (0,pi/2),` then `(dy)/(dx)` is. (a)1 (b) `-1` (c) `0` (d) none of these

Find (dy)/(dx) for y=sin^(-1)(cosx), where x in (0,2pi)dot

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

Which of the following is/are true? (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,pi),i s-1 (dy)/(dx)fory=sin^(-1)(cosx),w h e r ex in (0,2pi),i s1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (-pi/2,pi/2),i s-1 (dy)/(dx)fory=cos^(-1)(sinx),w h e r ex in (pi/2,(3pi)/2),i s-1

Evaluate: int_0^(npi+t)(|cosx|+|sinx"|"")"dx ,w h e r et in [0,f[pi/2]

The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w h e r e n >0,m<=0, is 3 (b) 1 (c) 2 (d) None of these

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to (a) pi/2 (b) -pi (c) pi (d) -pi/2

If (lim)_(xvec0)(f(x))/(x^2)-aa n d(lim)_(xvec0)(f(1-cosx))/(g(x)sin^2x)=b(w h e r eb!=0)dot then (lim)_(xvec0)(g(1-cos2x))/(x^4) is (4a)/b b. a/(4b) c. a/b d. none of these

int_(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e+1 (b) 1-e (c) e-1 (d) none of these