Q1. The magnitude of the gradient of the function \(F = xyz^3\) at \((1,0,2)\) is

Q2. Determine the constant 'C' such that the vector \(\vec F=(x+5y)\hat a_x+(y-3x)\hat a_y+(x+cz)\hat a_z\) will be Solenoidal.

Q3. In a Cartesian coordinate system, axes x, y and z are at __________to each other.

Q4. The cross product of the same vector to itself is _                      .

Q5. Cylindrical coordinate 'z' is related to the Cartesian coordinate as                     .

Q6. In a Spherical coordinate system, Φ is                         .

Q7. As per coulomb's law, electric field intensity (E) for a simple point charge is: (Consider R as radius of sphere)


Assuming the conductor carries charge \(\pm q\) per unit length, with the inner conductor being positively charged. Applying Gauss' theorem to cylindrical Gaussian surface of radius \(r\), the radial component of electric field intensity \(D_r\) is given by :

Q9. As per Gauss' Law, charge density inside a perfect conductor is zero if E is ________.

Q10. Divergence of the vector field, \(V(x,y,z) = - (x\cos(xy) + y)i + (ycos(xy))j + (sinz^2 + x^2 + y^2)k \) is