$A$ metal which does not react with nitrogen is

$A$ gaseous mixture consists of $16\,g$ of helium and $16\,g$ of oxygen. The ratio $(C_p/C_v)$ of the mixture is

Identify the mixture that shows positive deviation from Raoult's law.

If $x y \neq 0, x+y \neq 0$ and $x^m y^n=(x+y)^{m+n}$,where $m, n \notin N$,then $\frac{d y}{d x}$ is equal to

Let $\alpha$ and $\beta$ be the roots of the equation $x^2 - x - 1 = 0$. If $p_k = (\alpha)^k + (\beta)^k$ for $k \geq 1$,then which one of the following statements is not true?

The function $f: R \rightarrow R$ is defined by $f(x)=3^{-x}$. Observe the following statements about it:
$I$. $f$ is one-one
$II$. $f$ is onto
$III$. $f$ is a decreasing function
Which of these statements are true?