If $x + \sqrt{x^2 + 1} = a$,then $x =$

If $\int \frac{dx}{x^2+2x+2} = f(x) + c$,then $f(x)$ is equal to :

The compound which does not show paramagnetism is :-

$10 \ g$ of hydrogen and $64 \ g$ of oxygen were filled in a steel vessel and exploded. The amount of water produced in this reaction will be ........... $mol$.

If $y = \sin(m \sin^{-1} x)$,then $(1 - x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

If $\left[\begin{array}{rrr}1 & 2 & x \\ 4 & -1 & 7 \\ 2 & 4 & -6\end{array}\right]$ is a singular matrix,then $x$ is equal to