`sin^(-1)(0)` is equal to :
(a) `0`
(b) `pi/6`
(c) `pi/2`
(d) `pi/3`

int_0^1d/(dx){sin^(-1)((2x)/(1+x^2))}dx is equal to 0 (b) pi (c) pi//2 (d) pi//4

If int_0^oo(sinx)/xdx=pi/2,t h e nint_0^oo(sin^3x)/x dx is equal to (a)pi/2 (b) pi/4 (c) pi/6 (d) (3pi)/2

int_0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 (d) pi

If AandB are acute positive angles satisfying the equations 3sin^(2)A+2sin^(2)B=1 and 3sin2A-2sin2B=0, then A+2B is equal to (a) pi (b) (pi)/(2) (c) (pi)/(4) (d) (pi)/(6)

If (1-tantheta)/(1+tantheta) = 1/sqrt3 , where theta in (0, pi/2) , then theta = (a) pi/6 (b) pi/4 (c) pi/12 (d) pi/3

cos^(-1)((cos(7 pi))/(6)) is equal to ( a ) (7 pi)/(6) (B) (5 pi)/(6) (C) (pi)/(3)(D)(pi)/(6)

(lim)_(x rarr0)((sin(pi cos^(2)x))/(x^(2))) is equal to (a) -pi( b) pi(c)(pi)/(2)(d)1

sin^(-1)sqrt((2-sqrt(3))/4)+cos^(-1)(sqrt(12)/4)+sec^(-1)(sqrt(2))= (a) 0 (b) pi/4 (c) pi/6 (d) pi/2

If f(x)=0 is a quadratic equation such that f(-pi)=f(pi)=0 and f((pi)/(2))=-(3 pi^(2))/(4) then lim_(x rarr-pi)(f(x))/(sin(sin x)) is equal to (a)0( b) pi (c) 2 pi (d) none of these

Let Z_(0) is the root of equation x^(2)+x+1=0 and Z=3+6i(Z_(0))^(81)-3i(Z_(0))^(93) Then arg (Z) is equal to (a) (pi)/(4) (b) (pi)/(3)(c)pi(d)(pi)/(6)