Objective questions on Gauss's Law for JEE Main and Advanced

Question 1
A point charge (Q) is located at the centre of a cube of edge length a, find the final electric flux over one face of the cube
a. Q/ε0
b. Q/6ε0
c. 6Q/ε0
d. none of the above

Question 2
Three point charges q + Q, q, q - Q are enclosed by the surface S. What the net flux crosses S
a. 3q/ε0
b. 2q//ε0
c. (3q – Q) /ε0
d. can not be determine based on the data given in question

Question 3
Find the electric field inside the sphere which carries a charge density proportional to the distance from the origin
ρ = kr
a. ρ/ε0
b. ρr/ε0
c. ρr20
d. none of the above

Question 4
A point charge Q(C) is placed at the origin. Find the electric flux of which an area 4π m2 on a concentric spherical shell of radius R
a. Q/R2ε0
b. Q/ε0
c. Q/4R2ε0
d. none of the above

Question 5
As per Gauss law
$\int E.dS$ =qin0