$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to a volume $\frac{V_i}{32}$,where $V_i$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$. The value of $x$ is:

If $ad-bc \neq 0$,then the area (in sq. units) of the parallelogram formed by the lines $ax+by+2=0$,$ax+by+5=0$,$cx+dy+3=0$ and $cx+dy+7=0$ is

In which of the following is lead sulfate $(PbSO_4)$ soluble?

The centroid of the triangle formed by the lines $6x^2 + xy - y^2 = 0$ and $x + 3y - 10 = 0$ is

Two particles of masses $m_1$ and $m_2$ in projectile motion have velocities $\vec{v}_1$ and $\vec{v}_2$ respectively at time $t = 0$. They collide at time $t_0$. Their velocities become $\vec{v}_1'$ and $\vec{v}_2'$ at time $2t_0$ while still moving in air. The value of $|(m_1 \vec{v}_1' + m_2 \vec{v}_2') - (m_1 \vec{v}_1 + m_2 \vec{v}_2)|$ is

Jelly is a colloidal solution of