If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to

If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$ $(H^2>A B)$ forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)$ is equal to :

When the size of a spherical nanoparticle decreases from $30 \, nm$ to $10 \, nm$,the ratio of surface area to volume becomes:

Assertion $(A)$: The boiling points of noble gases increase from $He$ to $Xe$.
Reason $(R)$: The interatomic van der Waals' attractive forces increase from $He$ to $Xe$.
The correct answer is:

$A$ uniform chain has a mass $m$ and length $l$. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is

Two wires $A$ and $B$ of the same material have radii in the ratio $2:1$ and lengths in the ratio $4:1$. The ratio of the normal forces required to produce the same change in the lengths of these two wires is