From which part of the plant is cocoa obtained from $Theobroma$ $cacao$?

$A$ plane passing through $(-1, 2, 3)$ and whose normal makes equal angles with the coordinate axes is

Three blocks,$A, B$ and $C,$ of masses $4\,kg, 2\,kg$ and $1\,kg$ respectively,are in contact on a frictionless surface,as shown. If a force of $14\,N$ is applied on the $4\,kg$ block,then the contact force between $A$ and $B$ is ....... $N$.

The longest distance of the point $(a, 0)$ from the curve $2 x^2+y^2=2 x$ is

The number of structural isomers for $C_6H_{14}$ is

$A$ block of mass $2 \ kg$ is tied to one end of a $2 \ m$ long metal wire of $1.0 \ mm^2$ area of cross-section and rotated in a vertical circle such that the tension in the wire is zero at the highest point. If the maximum elongation in the wire is $2 \ mm$, the Young's modulus of the metal is (Acceleration due to gravity $= 10 \ ms^{-2}$)