If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

$A$ conductor of resistance $3 \Omega$ is stretched uniformly until its length is doubled. The wire is now bent in the form of an equilateral triangle. The effective resistance between the ends of any side of the triangle in ohms is

Which of the following is a disaccharide?

$A$ solid cylinder of mass $M$ and radius $R$ rolls without slipping down an inclined plane of length $L$ and height $h$. What is the velocity of its center of mass when the cylinder reaches the bottom of the incline?

If $\vec{u}, \vec{v},$ and $\vec{w}$ are three non-coplanar vectors,then $(\vec{u} + \vec{v} - \vec{w}) \cdot ((\vec{u} - \vec{v}) \times (\vec{v} - \vec{w})) = \dots$

If $n(A) = 3$ and $n(B) = 6$ and $A \subseteq B$,then the number of elements in $A \cap B$ is equal to