The equation of the parabola with focus $(0, 0)$ and directrix $x + y = 4$ is

One hundred identical coins,each with probability $p$ of showing heads,are tossed once. If $0 < p < 1$ and the probability of heads showing on $50$ coins is equal to that of heads showing on $51$ coins,then the value of $p$ is

Persistent nucellus in the seed is known as

$AB_{3(g)}$ dissociates as $AB_{3(g)} \rightleftharpoons AB_{2(g)} + \frac{1}{2}B_{2(g)}$. When the initial pressure of $AB_3$ is $800 \ torr$ and the total pressure at equilibrium is $900 \ torr$,what fraction of $AB_{3(g)}$ is dissociated (in $\%$)?

The only cations present in a slightly acidic solution are $Fe^{3+}$,$Zn^{2+}$,and $Cu^{2+}$. The reagent that,when added in excess to this solution,would identify and separate $Fe^{3+}$ in one step is

An object takes $n$ times as much time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by: