Each E-coli bacterium measures 0.5 μm in width by 2 μm in length i.e, 2000 nm.
So option (b) is correct,

The van der Waals diameter of a $C _{60}$ molecule is about 1.1 nanometer (nm).

Because of its very small size, the nano-material has tensile strength greater than that of steel. 

Quantum mechanics is required to understand the behavior of nanoscale systems because Newtonian theories collapse and fail at this scale. If Newtonian laws governed the working of atoms, then negatively charged electrons would be attracted to the positively charged nucleus of the atoms and the two would collide, but this does not happen.

Nano-materials have the dimensions of about 1-100 nanometers, their material properties change significantly. This is the size scale where quantum effects rule the behavior and properties of particles. Properties of materials depend on size and structure of the material. Even if size is same but the structure of the material is different,  physical properties like melting point, electrical conductivity, etc changes.

Nano-particles have a relatively larger surface area when compared to the same volume of the material.
For example: Consider a sphere of radius r. 

Carbon nanobud is a material that combines carbon nanotubes and spheroid fullerenes, both allotropes of carbon, in the same structure, forming "buds" attached to tubes. Consequently, nanobuds exhibit the properties of both carbon nanotubes and fullerenes.

Greater the surface area, greater are the reaction rates.
This is because reaction occurs when particles in gas/liquid collide with the particles in solid. Increasing the surface area of solid increases the chances of collision taking place. So, reaction rate increases as the surface area is increased.

Different physical, chemical, biological methods such as ball milling, inert gas condensation, wet chemical methods are used for obtaining nano-sized materials. So answer is (d) All of the above. 

Conventional sources of energy include coal, petroleum, natural gas, wood etc. Carbon is their main constituent.

The bulk modulus of single walled phase nanotubes is 462 to 546 GPa, even higher than that of diamond (420 GPa for single diamond crystal). This is because chemical bonding of nanotubes involves entirely $sp^{2}$ hybrid carbon atoms. These bonds, which are similar to those of graphite and are stronger than diamond (which employ $sp^{3}$ hybrid carbon atoms), this provides nanotubes with their unique strength.

Nanotechnology uses:

1. Medicine: for chemotherapy and anti-ageing drugs
2. Used in 3D printing
3. Super fluidity at high temperature.

STM: Scanning Tunneling Microscope.
It is an instrument for imaging surfaces at the atomic level. It is based on the concept of Quantum tunneling. When a conducting tip is brought very near to surface to be examined, a potential difference applied between two can allow electrons to tunnel through the vacuum between them.

A paper battery is a battery made using a paper-thin sheet of cellulose infused with aligned carbon nano-tubes. It acts as a high energy battery. It provides long term, steady power production and burst of energy. These batteries are non-toxic, flexible and used in electronic, medical devices and new technologies.

Cylindrical fullerenes are also called carbon nanotubes or buckytubes. These are a form of carbon similar to graphite found in pencils. They are hollow cylindrical tubes and are 10,000 times smaller than a human hair.

1. Fullerene is another form of carbon allotropes.
   2. It can be identified as $C-60$ since, it is made of $60$atoms, arranged in the shape of a football.
   3. Since, this look like the geodesic dome designed by the US archited Buckminster Fuller, the molecule was named Fullerence.

Ultrahard Fullerites are made under high pressure 13 GPa and require high temperature for heating up to 1100 K (more than 820°C).

Size of Red Blood Cells is around 6 to 8 microns. 
i.e. $6-8\times10^{-6}$ m.
So, out of options available, 5000 nm or 5 μm lies near this range. So answer is 5000 nm.

Size of Nanoparticles lies in the range of 1 to 100 nm