In the following circuit,the equivalent resistance between $A$ and $B$ is ...... $\Omega$.

Among the second period elements,the actual ionization enthalpies are in the order $Li < B < Be < C < O < N < F < Ne$. Explain why:
$(i)$ $Be$ has higher $\Delta_{i}H$ than $B$.
$(ii)$ $O$ has lower $\Delta_{i}H$ than $N$ and $F$.

The volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is $3$. Then the volume of the parallelepiped formed by the coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$. If $p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1$,then which one of the following statements is not true?

The $K.E.$ and $P.E.$ of a particle executing $SHM$ with amplitude $A$ will be equal when its displacement is

$A$ fish looking up through the water sees the outside world,contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \ cm$ below the water surface,the radius of this circle in $cm$ is