List of top Questions asked in GATE CH- 2023

The vector \(\vec{v}\) is defined as \[ \vec{v} = zx\,\hat{i} + 2xy\,\hat{j} + 3yz\,\hat{k}. \] Which one of the following is the CORRECT value of divergence of \(\vec{v}\), evaluated at the point \((x,y,z) = (3,2,1)\)?

Given that \( F=\dfrac{|z_1+z_2|}{|z_1|+|z_2|} \), where \(z_1=2+3i\) and \(z_2=-2+3i\) with \(i=\sqrt{-1}\), which one of the following options is CORRECT?

For a two-dimensional plane, the unit vectors \((\hat{e}_r,\hat{e}_\theta)\) of the polar coordinate system and \((\hat{i},\hat{j})\) of the cartesian coordinate system are related by \[ \hat{e}_r=\cos\theta\,\hat{i}+\sin\theta\,\hat{j}, \qquad \hat{e}_\theta=-\sin\theta\,\hat{i}+\cos\theta\,\hat{j}. \] Which one of the following is the CORRECT value of \(\dfrac{\partial(\hat{e}_r+\hat{e}_\theta){\partial\theta}\)?}

Which one of the following statements related to octane number is NOT correct?

Which one of the following options represents the major components of oleum?