If `z` is a complex number lying in the fourth quadrant of Argand plane and `|[(kz)/(k+1)]+2i|>sqrt(2)` for all real value of`k(k!=-1),` then range of `"a r g"(z)` is a.`(pi/8,0)` b. `(pi/6,0)` c.`(pi/4,0)` d. none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

The range of the function tan^(-1)((x^2+1)/(x^2+sqrt(3))),x in R is a. [pi/6,pi/2) b. [pi/6,pi/3) c. [pi/6,pi/4] d. none of these

The value of the integral int_(-(3pi)/4)^((5pi)/4)((sinx+cosx)/(e^(x-pi/4)+1))dx (A) 0 (B) 1 (C) 2 (D) none of these

If a r g(z)<0, then a r g(-z)-"a r g"(z) equals pi (b) -pi (d) -pi/2 (d) pi/2

If cos3x+sin(2x-(7pi)/6)=-2 , then x is equal to (k in Z) pi/3(6k+1) (b) pi/3(6k-1) pi/3(2k+1) (d) none of these

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( barz )_2dot

If a complex number z satisfies |2z+10+10 i|lt=3sqrt(3)-5, then the least principal argument of z is a. -(5pi)/6 b. -(11pi)/(12) c. -(3pi)/4 d. -(2pi)/3

If z is a complex number such that -pi//2lt=a r g zlt=pi//2, then which of the following inequality is true? (a) |z- z |lt=|z|(a r g z-a r g z ) b. |z- z |geq|z|(a r g z-a r g z ) c. |z- z |<(a r g z-a r g z ) d. none of these

If 3tan(theta-15^0)=tan(theta+15^0), then theta is equal to n in Z) n pi+pi/4 (b) npi+pi/8 npi+pi/3 (d) none of these

If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be pi/4 b. pi/4 c. (3pi)/4 d. -(3pi)/4