A  NMR spectrum produces one signal for each unique carbon and one signal for each group of similar carbons in a given molecule. There are 15 carbon atoms in this molecule. However, many of them can be grouped because they are similar to each other. Additionally, the molecule is perfectly symmetric, meaning that corresponding carbon atoms on each side of the line of symmetry are similar. The pictured molecule shows the carbon atoms that would show up as distinct signals on the  NMR spectrum:

The correct answer is "two of these."

The molecular formula was given. Therefore, we simply needed to use the following formula to find out how many DBE's (Double Bond Equivalents) that are present in the compound: 

A double bond equivalent is a ring or a pi bond (i.e. a double bond would count as one DBE while a triple bond would count as two DBEs). We know that the compound must have a ring or a double bond. However, without more information, we cannot tell if the compound is a cyclohexane or a hexene.

Count for the longest carbon chain starting at the end closest to the double bond. Seven carbons make up this chain, so use hept- and there is a double bond, so end with -ene. The methyl group is located at the 3rd carbon and the double bond starts at the 2nd carbon. The molecule has a trans configuration, so it should have E in its name.

Single bonds undergo free rotation, and so this molecule had an internal plane of symmetry giving it only 9 signals. Total number of carbons were 16. If you cannot see the symmetry, rotate the bonds to match alkyl chains.

The best procedure to use when determining conjugation of a compound is ultraviolet spectroscopy. Conjugation is present in compounds of connected p-orbitals with delocalized electrons, this is often seen in alternating double bonds and single bonds. UV spectroscopy is used because these conjugated systems are able to absorb light in the ultraviolet and visible spectrum making them visible for observation.

Thin layer chromatography (TLC) is used to find the identity of a compound in a mixture. A TLC plate is a sheet of plastic or glass which is coated with a solid adsorbent, such as silica. A small portion of the mixture is spotted near the bottom of the TLC plate, which is placed in a liquid solvent so that the bottom of the plate is in the solvent. This liquid (solvent) slowly rises up the TLC plate by capillary action. As it moves past the spot that was applied to the plate, an equilibrium is formed for each portion of the mixture between the molecules of that portion which are adsorbed on the solid and the molecules which are still in solution. The components should differ in solubility and in the degree of their adsorption, and some components will travel further up the plate than others will. When the solvent reaches the top of the plate, the plate is removed from the liquid and the separated components of the mixture are seen, either with the naked eye or under UV light if components are not colored. Then, we can determine the identity of a component of the mixture using R_f value.

To find the R_f value, we divide the distance traveled by the unknown component by the distance traveled by the solvent front. This equation has nothing to do with the temperature, thickness of the adsorbent, or the amount of material spotted. 

Each proton (hydrogen) in a different environment gives a unique NMR signal. If we analyze this compound we see there are eight different protons, each noted by a different letter in the image.

To appear as a triplet, a carbon would have to have a signal that is split by two attached hydrogens. In the given compound there are two carbons that have two hydrogens attached to them.

One of the predominate diagnostic bands in IR spectroscopy is the strong absorption between  for a carbonyl group. The other groups have absorptions in the IR spectrum, but at differing frequencies:

 (stretch) at 

 at 

 at 

The correct answer is "Bombardment by free radical electrons which causes the formation of a radical cation and spontaneous bond cleavage throughout the molecule, depending on instability of the bond and stability of the fragments." First the parent molecule (the compound being identified) is bombarded by free radicals, resulting in a molecular radical cation, and then the molecular ion spontaneously fragments at the weak bonds and where the resulting fragments will be thermodynamically stable. These fragments then reach the detector plate at different places depending on the mass of each fragment.

Incorrect answers:

"Bombardment by free radical electrons which radicalizes the molecule at different atoms, resulting in distinct fragments" is incorrect because it indicates that the desired fragmentation of the molecule is through direct abstraction of a radical by the free radical, rather than a spontaneous self-cleaving process. If this occurs, it is not a desirable result, because the molecular ion will no longer be structurally in tact for the next chamber of the mass spectrometry in which it is meant to fragment and be separated based on mass/charge ratio. It is also somewhat sterically unlikely for a free radical electron to directly cause the splitting of carbon-carbon bonds in a sterically bulky organic molecule -- the free radical electron is more likely to abstract a proton and leave a positive radical charge on the molecule.

"Spontaneous homolytic cleavage of unstable bonds with good leaving groups, unmediated by electron bombardment" is incorrect because mass spectrometry methods use electrons to induce radical cation formation.

"Ionization through proton bombardment, depending on instability of the bond and stability of the fragments" is false because electrons, rather than protons, are used to ionize the molecule. 

"Putting the molecule through a strong magnetic field, resulting in various electron spins of the hydrogens in the molecule" is incorrect because it does not reflect the spectra produced by mass spectrometry, nor the method by which molecular fragments are produced.