List of top Mathematics Questions on Vector Calculus asked in TS PGECET

Curl of \[ \vec{V}=e^{xyz}(\hat{i}+\hat{j}+\hat{k}) \] at the point \((1,1,1)\) is

The divergence of \[ \left(2x^{2}z\,\hat{i}+xy^{2}z\,\hat{j}+3yz^{2}\,\hat{k}\right) \] at the point \((1,1,1)\) is

If \[ I=\int_C x^2y\,dx-xy^2\,dy, \] where \(C\) is the circle \[ x^2+y^2=16, \] then \(2I=\)

Curl of \[ \vec{V}=e^{xyz}(\hat{i}+\hat{j}+\hat{k}) \] at the point \((1,1,1)\) is

The divergence of \[ \left(2x^{2}z\,\hat{i}+xy^{2}z\,\hat{j}+3yz^{2}\,\hat{k}\right) \] at the point \((1,1,1)\) is

If \[ I=\int_C x^2y\,dx-xy^2\,dy, \] where \(C\) is the circle \[ x^2+y^2=16, \] then \(2I=\)

The value of $\oint_C x \, dy - y \, dx$, where $C$ is the boundary of the rectangular region formed by $x = 5$, $x = 12$, $y = 0$, and $y = 8$ is:

The value of $\oint_C x \, dy - y \, dx$, where $C$ is the boundary of the rectangular region formed by $x = 5$, $x = 12$, $y = 0$, and $y = 8$ is:

Evaluate \[ \iint_D x^2y\,dx\,dy, \] where \[ D:\;x^2+y^2\le16. \]

If \[ \overline{V}=x^{2}y\,\overline{i}-yz^{2}\,\overline{j}+xyz\,\overline{k} \] is the linear velocity of a particle in circular motion at the point \((1,1,1)\), then its angular velocity is