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The locus of the centre of the circle touching the $X$-axis and passing through the point $(-1,1)$ is
The ratio of times taken by a freely falling body to travel first 5 m , second 5 m , third 5 m distances is
Identify the incorrect statement from the following?
If $n, K \in N$ such that $n \neq 3 K$, then $(\sqrt{3}+i)^{2 n}+(\sqrt{3}-i)^{2 n}=$
At 1000 K , the equilibrium constant for the reaction, $\mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ is 0.53 . In a one litre vessel, at equilibrium the mixture contains 0.25 mole of $\mathrm{CO}, 0.5$ mole of $\mathrm{CO}_2, 0.6$ mole of $\mathrm{H}_2$ and $x$ moles of $\mathrm{H}_2 \mathrm{O}$. The value of $x$ is