One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5)$. What is the value of $\gamma$ for the mixture? Here,$\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

Which of the following reagents is known as Fenton's reagent?

The centroid of the triangle formed by the pair of straight lines $12x^2 - 20xy + 7y^2 = 0$ and the line $2x - 3y + 4 = 0$ is:

In a bicycle,the radius of the rear wheel is twice the radius of the front wheel. If $r_F$ and $r_r$ are the radii,and $v_F$ and $v_r$ are the speeds of the topmost points of the wheels respectively,then:

Considering only the principal values of inverse functions,the set $A = \{x \geq 0 : \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\}$

$A$ finite ladder is constructed by connecting several sections of $2\,\mu F$ and $4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between? (Answer in $\mu F$)