The major product of the following reaction is :

Consider the hydrated ions of Ti²⁺, V²⁺, Ti³⁺, and Sc³⁺. The correct order of their spin-only magnetic moments is :

If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + $$\lambda $$z = $$\mu $$, ($$\lambda $$, $$\mu $$ $$ \in $$ R), has infinitely many solutions, then the value of $$\lambda $$ + $$\mu $$ is :

If $$\alpha $$ and $$\beta $$ are the roots of the quadratic equation,
x² + x sin $$\theta $$ - 2 sin $$\theta $$ = 0, $$\theta \in \left( {0,{\pi \over 2}} \right)$$, then
$${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - 12}} + {\beta ^{ - 12}}} \right).{{\left( {\alpha - \beta } \right)}^{24}}}}$$ is equal to :