Let `f(x)=int(dx)/((x^(2)+1)(x^(2)+9))` and `f(0)=0` if `f(sqrt(3))=(5)/(36)k`,then `k` is
(a)`(pi)/(6)`(b) `(pi)/(3)`(c)`(pi)/(2)`(d) `(pi)/(4)`

Range of function f(x)=arccot(2x-x^(2)) is [(pi)/(4),(3 pi)/(3)](b)[0,(pi)/(4)][0,(pi)/(2)] (d) [(pi)/(4),pi]

If f(x)=sqrt(1+cos^(2)(x^(2))), then f'((sqrt(pi))/(2)) is (sqrt(pi))/(6)(b)-sqrt(pi/6)1/sqrt(6)(d)pi/sqrt(6)

The range of f(x)=sin^(-1)(sqrt(x^(2)+x+1)) is (0,(pi)/(2))(b)(0,(pi)/(3))(c)((pi)/(3),(pi)/(2)) (d) [(pi)/(6),(pi)/(3)]

The domain of the function f given by f(x)=sqrt(log_(0.3)((e^(x)-1)/(e^(x)-tan x))) contains (A) (0,(pi)/(4)](B)[(pi)/(4),(pi)/(2))(C)[-(3 pi)/(4),-(pi)/(2)) (D) ((pi)/(2),(5 pi)/(4)]

If f(x)=A sin((pi x)/(2))+b,f'((1)/(2))=sqrt(2) and int_(0)^(1)f(x)dx=(2A)/(pi), then constants A and B are (pi)/(2)and(pi)/(2) (b) (2)/(pi) and (3)/(pi)0 and -(4)/(pi) (d) (4)/(pi) and 0

Let f(x)=(k cos x)/(pi-2x) if x!=(pi)/(2) and f(x=(pi)/(2)) if x=(pi)/(2) then find the value of k if lim_(x rarr(pi)/(2))f(x)=f((pi)/(2))

f:R rarr R , f(x)=tan^(-1)(2^x) + k is an odd function, then k= (A) -pi/4 (B) (pi)/(4) (C) -(pi)/(2) (D) (pi)/(2)

If P = int_(0)^(3pi) f(cos^(2)x)dx and Q=int_(0)^(pi) f(cos^(2)x)dx , then

The range of f(x)=cot^(-1)(log_(1/2)(x^(4)-2x^(2)+3)) is ( (pi)/(2) (3 pi)/(4) 0 (3 pi)/(4) pi) (0 (3 pi)/(4)

Let F(x)=int e^(sin^(-1)x)(1-(x)/(sqrt(1-x^(2))))dx and F(0)=1, If F((1)/(2))=(k sqrt(3)e^((pi)/(6)))/(pi), then the value of k is