Which of the following metals releases hydrogen gas upon reaction with cold dilute $HNO_3$?

If $A = \begin{bmatrix} 1 & 2 \\ 4 & 2 \end{bmatrix}$,then show that $|2A| = 4|A|$.

If the equilibrium constant for the reaction,$H_{2(g)} + I_{2(g)} \rightleftharpoons 2 HI_{(g)}$ is $K$,what is the equilibrium constant of $HI_{(g)} \rightleftharpoons \frac{1}{2} H_{2(g)} + \frac{1}{2} I_{2(g)}$?

If the roots of the equations $px^2 + 2qx + r = 0$ and $qx^2 - 2\sqrt{pr}x + q = 0$ are real,then

For the reaction sequence given below, the correct statement$(s)$ is$(are)$
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$(A) \ P$ is optically active.
$(B) \ S$ gives Bayer's test.
$(C) \ Q$ gives effervescence with aq. $NaHCO _3$.
$(D) \ R$ is an alkyne.

If $\int \sqrt{\frac{x}{a^3-x^3}} \, dx = g(x) + c$,then $g(x)$ is equal to: