The osmotic pressure of a $5\% \, w/v$ solution of cane sugar at $150 \, ^\circ C$ is ......... $atm$.

The phase difference between two waves,represented by $y_1 = 10^{-6} \sin \{100t + (x/50) + 0.5\} \ m$ and $y_2 = 10^{-6} \cos \{100t + (x/50)\} \ m$,where $x$ is in meters and $t$ is in seconds,is approximately .... $radians$.

The set of solutions of the system of equations
$
\begin{aligned}
x+y & =\frac{2 \pi}{3} \\
\text{and} \quad \cos x+\cos y & =\frac{3}{2},
\end{aligned}
$
where $x, y$ are real,is

$A$ pair of substances which gives the same products on reaction with water is

Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ are $m_A$ and $m_B$,respectively. The gases are allowed to expand isothermally to the same final volume $2V$. The changes in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$,respectively. Then:

Four charges are placed at the circumference of a dial clock as shown in the figure. If the clock has only an hour hand, then the resultant force on a charge $q_0$ placed at the center points in the direction which shows the time as: (in $.30$)