What can be said for electric charge if electric flux assocaited with closed loop is zero ?

A sphere encloses an electric dipole with charge $\pm 3 \times 10^{-6} \;\mathrm{C} .$ What is the total electric flux across the sphere?......${Nm}^{2} / {C}$

What is the direction of electric field intensity ?

An infinitely long thin non-conducting wire is parallel to the $z$-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\epsilon_0$. Which of the following statements is (are) true?

$(A)$ The electric flux through the shell is $\sqrt{3} R \lambda / \epsilon_0$

$(B)$ The z-component of the electric field is zero at all the points on the surface of the shell

$(C)$ The electric flux through the shell is $\sqrt{2} R \lambda / \epsilon_0$

$(D)$ The electric field is normal to the surface of the shell at all points

An electric charge $q$ is placed at the centre of a cube of side $\alpha $. The electric flux on one of its faces will be

Gauss’s law should be invalid if