The number of $p\pi-d\pi$ 'pi' bonds present in $XeO_3$ and $XeO_4$ molecules,respectively,are:

If $f(0)=0, f(1)=1, f(2)=2$ and $f(x)=f(x-2)+f(x-3)$ for $x=3, 4, 5, \ldots$, then $f(9)$ is equal to

The circuit shown contains a $12 \, V$ battery,a $4 \, \Omega$ resistor,and two branches in parallel,each containing an ideal diode and a resistor. Branch $1$ has diode $D_1$ and a $3 \, \Omega$ resistor,while branch $2$ has diode $D_2$ and a $2 \, \Omega$ resistor. Determine the total current flowing in the circuit. (in $, A$)

$A$ block of metal is heated to a temperature much higher than the room temperature and allowed to cool in a room free from air currents. Which of the following curves correctly represents the rate of cooling?

For one mole of a van der Waals gas,when $b = 0$ and $T = 300 \ K$,the plot of $PV$ versus $1/V$ is shown below. The value of the van der Waals constant $a \ (atm \ L^2 \ mol^{-2})$ is:

Out of $30$ points in a plane,$8$ of them are collinear. The number of straight lines that can be formed by joining these points is: