List of top Mathematics Questions on Vector Calculus asked in CPET

Consider the following assertions:
(I) \(\displaystyle\iint_S(x\hat i+y\hat j+z\hat k)\cdot\hat n\,dS=2V\), where \(\hat n\) is the unit outward surface normal and S is a closed surface enclosing a volume V.
(II) \(\displaystyle\int_C(yz\hat i+xz\hat j+xy\hat k)\cdot d\vec r=3\), where C is the boundary of a surface S.
Choose the correct option:

Which of the following statements is/are true?
(I) The vector field \(\vec{F}(x,y,z)=(yz,\,zx,\,xy)\) is solenoidal.
(II) The vector field \(\vec{F}(x,y,z)=(x^2-y^2,\,2xy,\,z^3)\) is conservative.