Two beams of light having intensities I and 4I interfere to produce a fringe pattern on the screen. Phase difference between the beams is $\pi/2$ at point A and  $\pi$ at B. Difference of intensities at A and B is

4I

The correct answer is option 2: 4I

$ I_A = I_1 + I_2 + 2\sqrt{I_1 I_2}cos\phi = I + 4I + 2\sqrt{I.4I} cos\frac{\pi}{2} = 5I$

$ I_B = I_1 + I_2 + 2\sqrt{I_1 I_2}cos\phi = I + 4I + 2\sqrt{I.4I} cos\pi = 5I - 4I = I$

$ I_A - I_B = 5I - I = 4I$