"Exobiology" refers to the study of

If $x = \frac{1}{2} \left( \sqrt{3} + \frac{1}{\sqrt{3}} \right)$,then the value of $\frac{\sqrt{x^2 - 1}}{x - \sqrt{x^2 - 1}}$ is equal to

Two steel wires of same length $L$ but radii $r$ and $2r$ are connected together end to end and tied to a wall as shown. $A$ force $F$ stretches the combination by $10 \ mm$. How far does the midpoint $A$ move in $mm$?

If the position vectors of the vertices of a triangle are $2 \hat{i}-\hat{j}+\hat{k}$,$\hat{i}-3 \hat{j}-5 \hat{k}$,and $3 \hat{i}-4 \hat{j}-4 \hat{k}$,then the triangle is

Standard entropy of $X_2, Y_2$ and $XY_3$ are $60, 40$ and $50 \, J \, K^{-1} \, mol^{-1}$,respectively. For the reaction,$\frac{1}{2} X_2 + \frac{3}{2} Y_2 \to XY_3, \Delta H = -30 \, kJ$,to be at equilibrium,the temperature will be .....$K$.

Identify the logic operation carried out by the following circuit.