`f(x)=(x-1)|(x-2)(x-3)|dot` Then `f` decreases in (a)`(2-1/(sqrt(3)),2)` (b) `(2,2+1/(sqrt(3)))` (c)`(2+1/(sqrt(3)),4)` (d) `(3,oo)`

If 4\ cos^(-1)x+sin^(-1)x=pi , then the value of x is (a) 3/2 (b) 1/(sqrt(2)) (c) (sqrt(3))/2 (d) 2/(sqrt(3))

The value of ("lim")_(xvec2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3 , then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

Differentiate tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)),\ -1/(sqrt(3))

Differentiate tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)),\ -1/(sqrt(3))

The function f(x)=x(x+4)e^(-x//2) has its local maxima at x=adot Then (a) a=2sqrt(2) (b) a=1-sqrt(3) (c) a=-1+sqrt(3) (d) a=-4

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If I=int(sinx+sin^3x)/(cos2x)dx=Pcosx+Qlog|f(x)|+R , then (a) P=1/2,Q=-3/(4sqrt(2)) (b) P=1/4, Q=1/(sqrt(2)) (c) f(x)=(sqrt(2)cosx+1)/(sqrt(2)cosx-1) (d) f(x)=(sqrt(2)cosx-1)/(sqrt(2)cosx+1)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-2)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4

If 3\ sin^(-1)((2x)/(1+x^2))-4\ cos^(-1)((1-x^2)/(1+x^2))+2\ tan^(-1)((2x)/(1-x^2))=pi/3 , then x is equal to 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4