The value of \( x \) that satisfies the equation:
\[ \begin{vmatrix} x & 1 & 1 \\ 2 & 2 & 0 \\ 1 & 0 & -2 \end{vmatrix} = 6 \]
If \( 2 \) is a solution of the inequality \( \frac{x-a}{a-2x}<-3 \), then \( a \) must lie in the interval:
Which of the following changes alone would cause increase in the value of the equilibrium constant of the reaction? \(PCl_5(g) \rightarrow PCl_3(g) + Cl_2(g); \Delta H>0\)
For the reaction:
$3Fe_{(s)} + 2O_2{(g)} \rightarrow Fe_3O_4{(s)}$
$\Delta H = -1650\,\text{kJ mol}^{-1}$, $\Delta S = -600\,\text{J K}^{-1} \text{mol}^{-1}$ at $300\,\text{K}$. What is the value of free energy change for the reaction at $300\,\text{K}$?
In Young’s double slit experiment, to change the bandwidth from $\beta$ to $\frac{\beta}{4}$ without changing the experimental setup, the wavelength of light $\lambda$ used must be changed to
The instantaneous displacement of a particle executing simple harmonic motion is given by \(x = 2(\cos(\pi t) + \sin(\pi t))\). The amplitude of oscillation is