Let $PS$ be the median of the triangle with vertices $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is:

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.

In a playground,there is a merry-go-round of mass $120 \ kg$ and radius $4 \ m$. The radius of gyration is $3 \ m$. $A$ child of mass $30 \ kg$ runs at a speed of $5 \ m/s$ tangent to the rim of the merry-go-round when it is at rest and then jumps on it. Neglecting friction,find the angular velocity of the merry-go-round and child in $rad/s$.

If the equation whose roots are $p$ times the roots of $x^4 - 2ax^3 + 4bx^2 + 8ax + 16 = 0$ is a reciprocal equation,then $|p| = $

Into how many subclasses is the class $Dicotyledonae$ divided?

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$ is: