\[
\textbf{MCQs on Vector and Tensor Analysis with Answers}
\]
\[
\textbf{Q1: The divergence of the vector field } \vec{F} = \nabla \cdot \vec{F} \text{ is:}
\]
\[
\text{(A) } \text{A scalar quantity} \quad
\text{(B) } \text{A vector quantity} \quad
\text{(C) } \text{A tensor quantity} \quad
\text{(D) } \text{None of these}
\]
\[
\textbf{Answer: (A) } \text{A scalar quantity}
\]
\[
\textbf{Q2: The curl of a vector field } \vec{F} \text{ is given by:}
\]
\[
\text{(A) } \nabla \cdot \vec{F} \quad
\text{(B) } \nabla \times \vec{F} \quad
\text{(C) } |\nabla| \vec{F} \quad
\text{(D) } \vec{F} \cdot \nabla
\]
\[
\textbf{Answer: (B) } \nabla \times \vec{F}
\]
\[
\textbf{Q3: A tensor of rank 2 in three-dimensional space has how many components?}
\]
\[
\text{(A) } 6 \quad
\text{(B) } 9 \quad
\text{(C) } 3 \quad
\text{(D) } 12
\]
\[
\textbf{Answer: (B) } 9
\]
\[
\textbf{Q4: The gradient of a scalar field is:}
\]
\[
\text{(A) } A scalar field \quad
\text{(B) } A vector field \quad
\text{(C) } A tensor field \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } A vector field
\]
\[
\textbf{Q5: Which of the following is true for a symmetric tensor?}
\]
\[
\text{(A) } T_{ij} = -T_{ji} \quad
\text{(B) } T_{ij} = T_{ji} \quad
\text{(C) } T_{ij} \neq T_{ji} \quad
\text{(D) } T_{ij} = 0
\]
\[
\textbf{Answer: (B) } T_{ij} = T_{ji}
\]
\[
\textbf{Q6: The determinant of the metric tensor in Cartesian coordinates is:}
\]
\[
\text{(A) } 0 \quad
\text{(B) } 1 \quad
\text{(C) } -1 \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } 1
\]
\[
\textbf{Q7: The dot product of two vectors results in:}
\]
\[
\text{(A) } A scalar quantity \quad
\text{(B) } A vector quantity \quad
\text{(C) } A tensor quantity \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (A) } A scalar quantity
\]
\[
\textbf{Q8: A tensor that remains invariant under coordinate transformations is called:}
\]
\[
\text{(A) } A vector \quad
\text{(B) } A scalar \quad
\text{(C) } An isotropic tensor \quad
\text{(D) } A covariant tensor
\]
\[
\textbf{Answer: (C) } An isotropic tensor
\]
\[
\textbf{Q9: The rank of the Kronecker delta } \delta_{ij} \text{ is:}
\]
\[
\text{(A) } 0 \quad
\text{(B) } 1 \quad
\text{(C) } 2 \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (C) } 2
\]
\[
\textbf{Q10: The divergence theorem relates the surface integral of a vector field to:}
\]
\[
\text{(A) } Its curl \quad
\text{(B) } Its gradient \quad
\text{(C) } Its divergence \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (C) } Its divergence
\]
