The 'spin only' magnetic moment value of $$\mathrm{MO}_4{ }^{2-}$$ is ________ BM. (Where M is a metal having least metallic radii. among $$\mathrm{Sc}, \mathrm{Ti}, \mathrm{V}, \mathrm{Cr}, \mathrm{Mn}$$ and $$\mathrm{Zn}$$ ).

(Given atomic number: $$\mathrm{Sc}=21, \mathrm{Ti}=22, \mathrm{~V}=23, \mathrm{Cr}=24, \mathrm{Mn}=25$$ and $$\mathrm{Zn}=30$$)

Number of amine compounds from the following giving solids which are soluble in $$\mathrm{NaOH}$$ upon reaction with Hinsberg's reagent is _________.

Let $$A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]$$. If $$A^3=4 A^2-A-21 I$$, where $$I$$ is the identity matrix of order $$3 \times 3$$, then $$2 a+3 b$$ is equal to

The value of $$k \in \mathbb{N}$$ for which the integral $$I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}$$, satisfies $$147 I_{20}=148 I_{21}$$ is