If temperature and volume are same, the pressure of gas obeying van der Waal's equation is smaller than that of an ideal gas"
Your statement is false. There are cases where the pressure from the Van der Waals pressure is higher than the pressure from the Ideal Gas Law.

The Van der Waals equation introduces two corrections to the Ideal Gas Law:


It accounts for attractive forces between gas particles. This means that the Van der Waals pressure can be lower than the Ideal Gas pressure.
It accounts for the small but nonzero volume of the particles. This means that the Van der Waals pressure can be higher than the Ideal Gas pressure.


Depending on the amount and nature of your gas, the volume and the temperature, either one of these effects can dominate.

Qualitatively:

In a situation where gas molecules are squished together very closely, the Van der Waals equation yields:


Higher pressures for molecules that are big but not sticky, like isobutane, and
Lower pressures for molecules that are small but sticky, like hydrogen chloride.


Quantitatively:

I'm attaching a spreadsheet with a bunch of examples; pardon the German. For a number of situations described by:


substance, column A
volume (liters), column B
amount (moles), column C
temperature (°C), column D


the pressure is given according to the Ideal Gas Law (column I) and the Van der Waals equation (column J).

There are examples that follow your 'rule', and the Van der Waals pressure is lower than the Ideal Gas Law pressure; e.g., row 6.

There are examples that do not follow your 'rule', and the Van der Waals pressure is lower than the Ideal Gas Law pressure; e.g., row 11 or 22.

Keep in mind that both equations only apply to gases; look up phase diagrams and make sure the gases in question don't condense under the conditions given. Rows 12, 13, 23 are supercritical fluids.

You'll find that the Ideal Gas Law is quite precise in most cases, and the cases where it's not, are those where the gas is close to not being a gas anymore.