If power factor is `(1)/(2)` in a series RL circuit, `R=100Omega` ,then `L` is
1) `(sqrt(3))/(pi)H`
2) `pi H`
3) `(pi)/(sqrt(3))H`
4) None of these

If the power factor is 1//2 in a series RL circuit with R = 100 Omega . If AC mains, 50 Hz is used then L is

sin^-1 (-1/2)+tan^-1 (sqrt(3))= (A) -pi/6 (B) pi/3 (C) pi/6 (D) none of these

sin^-1 (cos(sin^-1(sqrt(3)/2))= (A) pi/3 (B) pi/6 (C) - pi/6 (D) none of these

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If |cos^(-1)((1-x^2)/(1+x^2))| < pi/3,t h e n (a) x in [-1/3,1/(sqrt(3))] (b) x in [-1/(sqrt(3)),1/(sqrt(3))] x in [0,1/(sqrt(3))] (d) none of these

In Fig. 15.109, the area of segment A C B is (FIGURE) (a) (pi/3-(sqrt(3))/2)\ r^2 (b) (pi/3+(sqrt(3))/2)\ r^2 (c) (pi/3-2/(sqrt(3)))\ r^2 (d) None of these

Area bounded by the curve y=sqrt(sin[x]+[sinx]),(w h e r e[dot] is greatest integer function), lines x=1a d nx=pi/2a d bt h exa xi si s : (A) (sin1) pi/2-1 (B) sqrt(sin2.)(pi/2-1) (C) sqrt(cos1.)(pi/2-1) (D) none of these

Area bounded by the curve y=sqrt(sin[x]+[sinx]),(w h e r e[dot] is greatest integer function), lines x=1a d nx=pi/2a d bt h exa xi si s : pi/2-1 (B) sqrt(sin2.)(pi/2-1) (C) sqrt(cos1.)(pi/2-1) (D) none of these

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (4pi)/3 (d) (5pi)/3 (e) none of these