In the qualitative analysis of phosphorus, the following reaction occurs:
\[ \text{PO}_4^{3-} \text{ or } \text{HPO}_4^{2-} + (\text{NH}_4)_2\text{MoO}_4 \xrightarrow{\text{H}^+} (\text{NH}_4)_3\text{PO}_4 \cdot 12\text{MoO}_3 \downarrow \]
The product, $(\text{NH}_4)_3\text{PO}_4 \cdot 12\text{MoO}_3$, is a canary yellow precipitate known as ammonium phosphomolybdate.
Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with
\(K_4\)[Fe(CN)\(_6\)] is : \[ {Cu}^{2+}, \, {Fe}^{3+}, \, {Ba}^{2+}, \, {Ca}^{2+}, \, {NH}_4^+, \, {Mg}^{2+}, \, {Zn}^{2+} \]
If \[ \frac{dy}{dx} + 2y \sec^2 x = 2 \sec^2 x + 3 \tan x \cdot \sec^2 x \] and
and \( f(0) = \frac{5}{4} \), then the value of \[ 12 \left( y \left( \frac{\pi}{4} \right) - \frac{1}{e^2} \right) \] equals to: