The number of geometrical isomers for octahedral $[Co(NH_3)_2Cl_4]^-$,square planar $[AuCl_2Br_2]^-$ and $[Pt(en)Cl_2]$ are

$A$ polygon has $54$ diagonals. Then,the number of its sides is

In the Davisson-Germer experiment, an electron beam of energy $75 \ eV$ falls normally on the surface of a crystal. If the maximum intensity is obtained at an angle of $45^{\circ}$ to the direction of the incident beam, then the inter-atomic distance in the lattice plane of the crystal will be :-............... $\mathring{A}$

The resistance across $M$ and $N$ in the given figure is

$\int_{-1}^1 \frac{\cosh x}{1+e^{2 x}} d x$ is equal to :

Given $\lambda \in [0, 20]$,find the number of integral values of $\lambda$ for which the function $f(x) = x^3 - 12x + \lambda$ has a point of local maxima.