Okay, let's try to figure out the correct answer to this question. The problem is about identifying the chemical formula of an unknown compound based on its FTIR, 1H NMR, and Mass Spectrometry (MS) data. The options given are C6H12O, C6H10O, C6H10O2, and C6H12O2. Let's break down each piece of information step by step.

First, let's look at the FTIR spectrum. The FTIR shows a very broad absorption peak at 3000 cm⁻¹. Broad peaks around this region usually indicate the presence of an -OH group. So, the compound likely contains an alcohol or a carboxylic acid. But wait, carboxylic acids have a strong absorption around 1700 cm⁻¹ as well. The IR also shows peaks at 1700 and 1650 cm⁻¹. The 1700 peak could be a carbonyl group (C=O), which is common in esters, ketones, aldehydes, or carboxylic acids. The 1650 peak might be an ether or an ester. Hmm, if there's an -OH group, maybe it's an ester. Esters have a carbonyl around 1700 and an -OH (from the alcohol part) which would show that broad peak. Alternatively, if it's a carboxylic acid, there would be a broad peak from the -OH as well, but carboxylic acids usually have a stronger peak around 2500-3300 for the O-H stretch, which is not mentioned here. So maybe it's an ester. Let's tentatively note that the compound has an ester group (COOR) and an -OH group (from the broad peak). Wait, but in esters, the carbonyl is around 1700, and the O-H from the alcohol part would show a broad peak around 3000. That fits with the FTIR data. So the structure might have an ester group and an alcohol group. But wait, if it's an ester, the formula would have an O in the ester (like R-O-CO-R'), so the molecular formula would include O from the ester group and another O from the alcohol. Alternatively, maybe it's a ketone, but ketones don't have O-H. Wait, but the FTIR shows a broad peak at 3000, which is characteristic of an -OH group. So the compound must have at least one -OH group. So either an alcohol or a carboxylic acid. But carboxylic acids have two O-H groups (the -COOH has two O's), but the IR would have a strong peak around 2500-3300 for the O-H stretch. If that's not mentioned, maybe it's an alcohol. Let's keep that in mind.

Next, the 1H NMR spectrum shows peaks corresponding to vinyl hydrogens. Vinyl hydrogens are protons on a double bond, like in CH2=CH-. So the compound has a double bond, meaning it's an alkene. The presence of vinyl hydrogens suggests the structure has a double bond. So the molecule likely has a structure like RCH2CH2, but with a double bond. Wait, but vinyl groups are CH2=CH-, so maybe the structure has a CH2=CH group. Alternatively, the molecule could be a diene, but the presence of a double bond is a key point here.

The mass spectrum has a fragment peak at m/z = 45. Let's think about possible fragments. The molecular ion would be the molecular weight, but the fragment at 45 is likely a common fragment. The fragment at 45 could correspond to an [M - H]+ ion. Let's check the molecular formula. Let's assume the molecular formula has a molecular weight. For example, if the formula is C6H12O2, the molecular weight would be (6*12) + (12*1) + (2*16) = 72 +12 +32 = 116. Then, if we lose H, the fragment would be 115. But 45 is much lower. Alternatively, maybe the fragment is a smaller part of the molecule. 45 is a common fragment for something like CH2CH2O (but that's not right). Wait, 45 could be the fragment of a carbonyl group losing the rest. For example, if the molecular ion is an ester, say RCOOR', then the fragment [M - HCOOR'] would be (M - (44)), but that's not matching. Alternatively, maybe the fragment is a fragment from the molecule. Let's think of the molecular formula and possible molecular weights. The options are:

A. C6H10O: molecular weight = (6*12) + (10*1) + (16) = 72 +10 +16 = 98.

B. C6H12O2: molecular weight = 72 +12 +32 = 116.

C. C6H10O2: 72 +10 +32 = 114.

D. C6H12O: 72 +12 +16 = 100.

If the fragment is at 45, maybe it's a neutral loss of a fragment. For example, if the molecular formula is C6H10O2 (option C), molecular weight 114. If it loses (CH2O2) which is 34 (12 + 2*16?), wait, that's not. Alternatively, maybe it's losing a fragment like CH3CH2O (46), but 45 is one less. Hmm. Alternatively, if the molecular formula is C6H10O2, and the fragment is at 45, perhaps it's losing a (CH2O) group. Wait, CH2O is 30 (12 + 16). But 45 -30=15, which doesn't make sense. Alternatively, maybe the fragment is a carbonyl group. For example, if the molecule is an ester RCOOR', then the fragment would be RCOO^- plus a fragment. Wait, but the mass fragment is 45. Let's think of possible neutral losses. For example, if the molecule is C6H10O2, and it loses (CH2O), which is 30, then the remaining would be 114-30=84. But 45 is half of that. Alternatively, maybe the fragment is (CH3CH2O), which is 46. But 45 is one less. Alternatively, maybe the fragment is (CH2O) which is 30, but 45 is not matching. Wait, maybe the fragment is a ketone group losing the rest. For example, if the molecule is C6H10O2, and it loses (CH2O) twice. Wait, maybe not. Let's think differently. The molecular formula must have a molecular weight that when subtracted by 45 gives a possible fragment. Let's check each option:

Option A: C6H10O (98). If the fragment is 45, then the remaining would be 98 -45 =53. But 53 doesn't correspond to any common fragment. 

Option B: C6H12O2 (116). 116 -45=71. 71 is possible as a fragment, but not sure.

Option C: C6H10O2 (114). 114 -45=69. Not sure.

Option D: C6H12O (100). 100 -45=55. Not a common fragment.

Alternatively, maybe the fragment is a part of the molecule. For example, if the molecule is an ester, like RCOOR', then the fragment could be RCOO^- which would have a mass of (12n + (16*2) + (1*m)), but I'm not sure. Alternatively, maybe the fragment is a group like CH2=CH2 (28), but 45 is higher. Alternatively, maybe it's a fragment from the vinyl group. For example, the vinyl group (CH2=CH-) has a molecular weight of 28 (12*2 + 1*4), but 45 is higher. Alternatively, maybe the fragment is a smaller part, like a methyl group (15), but 45 is three times that. Hmm. Alternatively, maybe the fragment is a result of a cleavage. For example, if the molecule has a ketone group (which would have a peak around 1700 in IR), and the fragment is the ketone group. But the IR shows a carbonyl at 1700, so maybe it's a ketone. Wait, but the FTIR also shows a peak at 1650, which could be an ether or ester. Wait, esters typically have two carbonyl-related peaks? No, esters have one carbonyl peak around 1700, and the O-H from the alcohol (if it's an ester) would be around 3000. But in this case, the FTIR shows a broad peak at 3000, which is the O-H, so the compound is likely an ester with an -OH group. Wait, but an ester is RCOOR', which doesn't have an -OH. Unless it's an ethyl ester, but then there's no O-H. Wait, maybe it's a carboxylic acid. Wait, but carboxylic acids have a broad O-H peak around 2500-3300. The IR here shows a broad peak at 3000, which could be from a carboxylic acid. But then the 1700 peak would be the carbonyl, and 1650 might be from an ester or ether. Hmm. This is getting a bit confusing. Let's recap.

FTIR: broad peak at 3000 (O-H), 1700 (C=O), 1650 (maybe ether or ester).

1H NMR: vinyl hydrogens (so double bond).

Mass spec: fragment at 45.

Possible molecular formulas: C6H12O (D), C6H10O (A), C6H10O2 (C), C6H12O2 (B).

Let's think about each option.

Option A: C6H10O. Molecular weight 98. If it's a carboxylic acid, the formula would be C6H10O2 (since a carboxylic acid has two O's: COOH). But option A is C6H10O, which has only one O. So if it's a carboxylic acid, the formula would be C6H10O2. So option A is not a carboxylic acid. Alternatively, if it's an alcohol, then C6H10O would have one O. But an alcohol would have a broad O-H peak in IR. However, the IR shows a broad peak at 3000, which could be from an -OH group. But if the compound is an alcohol, then the molecular formula should have one O. But then, the presence of a double bond (from NMR) would mean it's an alcohol with a double bond. So possible structure: CH2=CHCH2CH2CH2CH2OH. Wait, but that would have a molecular formula of C6H12O. Wait, but in that case, the molecular formula is C6H12O, which is option D. But the NMR would show the vinyl protons (CH2=CH), so that would fit. The IR would show O-H (3000) and C=O (1700 if it's an ester, but this is an alcohol. Wait, alcohol doesn't have a carbonyl. So the IR would show O-H (3000) and maybe an O-O stretch? No, that's not right. Wait, the IR shows 1700 and 1650. If the compound is an alcohol, there's no carbonyl, so the 1700 peak must be from something else. Maybe an ether or ester. Wait, but the compound can't be an ether if it's an alcohol. This is getting a bit tangled.

Alternatively, maybe the compound is an ester with an -OH group. Wait, but esters are RCOOR', which don't have an -OH. Unless it's an ethyl ester, but then the structure would be RCOOEt, which would have an ester group (carbonyl) and an ethyl group. But that doesn't add an -OH. Wait, maybe the compound is a phenol with an ester group. For example, a benzene ring with an ester substituent and a hydroxyl group. But the molecular formula would then include more carbons. The options don't have a benzene ring (C6 would be possible if it's a benzene ring with substituents). For example, if the molecule is a benzene ring with an ester group (COOCH2CH3) and a hydroxyl group (OH) attached. But that would be more than 6 carbons. Wait, the molecular formulas given are all C6, so maybe it's a cyclic ester or something else. Hmm.

Alternatively, maybe the compound is a cyclic ether with a carbonyl group. But cyclic ethers like epoxides don't have carbonyl groups. Wait, maybe it's a diketone? No, that would have multiple carbonyl peaks. Alternatively, maybe the compound is a conjugated diene with an ester group. But the molecular formula would need to account for that.

Let me try to approach this differently. Let's think about the molecular weight. The mass spectrum has a fragment at 45. Let's think about possible fragments. 45 could be the molecular weight of (CH2)3O (46), but 45 is one less. Alternatively, maybe it's a fragment like (CH2O) which is 30, but that's not 45. Wait, 45 is 12*3 + 1*3 + 16*0 = 36 +3 =39. No. Wait, 45 = 12*3 + 3*1 + 16*0 = 36 +3 =39. No. Alternatively, 45 is 12*1 + 1*10 + 16*1 = 12 +10 +16=38. No. Wait, maybe 45 is the molecular weight of something else. Let's think of possible functional groups. For example, if the molecule has a fragment with a ketone group (like CH3CO-), which is 58. But 45 is less than that. Alternatively, maybe it's a fragment like CH2=CH2 (28), but that's not 45. Alternatively, maybe it's a fragment from the ester group. For example, if the ester is RCOOR', then the fragment could be RCOO^- with a mass of (12n + 16*2 + ...) but I'm not sure. Alternatively, maybe the fragment is a part of the alkene. For example, if the molecule has a CH2=CH group, then the fragment could be CH2=CH- (28), but 45 is higher. Alternatively, maybe the fragment is a result of a cleavage between oxygen and carbon. For example, if the molecule is an ester RCOOR', and it loses R'OH, then the fragment would be RCOO^- which would have a molecular weight of (12n + 16*2 + ...). Let's check for each option:

Option C: C6H10O2 (114). If the molecular weight is 114, and the fragment is 45, then the remaining would be 69. 69 could be the molecular weight of a fragment like C3H6O (58) but that's not matching. Alternatively, maybe the fragment is a smaller part. For example, if the molecule is an ester RCOOR', and it loses the R' group (like an alcohol), then the fragment would be RCOO^- which would be 114 - (molecular weight of R'OH). Let's see. For option C, molecular weight is 114. If R' is C2H5 (ethyl, molecular weight 46), then R'OH is 46 +17=63. 114 -63=51. Not 45. If R' is C3H7 (isopropyl, molecular weight 57), then R'OH is 57 +17=74. 114-74=40. Not 45. Alternatively, maybe the fragment is from the ester group. For example, if the ester is RCOOR', the fragment could be RCOO^- which would have a molecular weight of (12n + 16*2) + ... Not sure. Alternatively, maybe the fragment is a result of a carbonyl group losing some parts. For example, if the molecule has a ketone group, which would have a peak around 1700, but the IR here has 1700 and 1650. So maybe it's an ester. Let's try to think of possible structures.

Suppose the compound is an ester with a double bond. For example, CH2=CHCOOCH2CH2CH3. Wait, that would be C6H10O2. Let's check the molecular formula: the ester group is COO, and the rest is CH2=CHCH2CH2CH2CH3. Wait, that's 6 carbons in the ester part (COOCH2CH2CH3) plus the CH2=CH group. Wait, no, the ester group is RCOOR', so if R is CH2=CH- and R' is CH2CH2CH3 (isopropyl?), then the molecular formula would be CH2=CHCOOCH2CH2CH3. Let's count the carbons: CH2=CH (2) + COO (2) + CH2CH2CH3 (3) = 7 carbons. Wait, but the options are all C6. So maybe the structure is different. Alternatively, maybe the ester is part of a cyclic structure. For example, a six-membered ring with an ester substituent. But that might complicate things.

Alternatively, let's consider the molecular formula of each option and see which one fits the data.

Option A: C6H10O. Molecular weight 98. If it's an ester, the formula should be C6H10O2. So not this option.

Option B: C6H12O2. Molecular weight 116.

Option C: C6H10O2. Molecular weight 114.

Option D: C6H12O. Molecular weight 100.

Now, considering the IR data: broad peak at 3000 (O-H), 1700 (C=O), 1650 (maybe ether or ester). If the compound is an ester, it would have a carbonyl (1700) and an O-H (if it's an alcohol ester, but esters don't have O-H). Wait, no. Esters have O in the ester group (COO), but they don't have an -OH. So if the IR shows a broad peak at 3000, that suggests an -OH group. Therefore, the compound must have an -OH group. So if it's an ester, the ester would be RCOOR', and the -OH must be from another part. Wait, but then the formula would have an additional O. For example, if the compound is an ethyl ester of a carboxylic acid, then the formula would be C6H12O2 (since the acid is C6H12O3, but ester would lose an H2O, making it C6H12O2). Wait, but the molecular formula here is C6H12O2 (option B). Let's check that.

If the compound is an ester with a formula C6H12O2, then the structure could be something like CH2CH2COOCH2CH2CH3. Wait, but that would have 6 carbons in the ester part. Let me see: the ester group is O, so the structure would be RCOOR', where R is CH2CH2 and R' is CH2CH2CH3. Wait, but that would be 2 + 3 =5 carbons, plus the COO. Hmm, maybe not. Alternatively, the molecule could be a cyclic ester, like a lactone. For example, a six-membered ring with an ester group. But that might not fit the molecular formula.

Alternatively, let's think of the compound as a diol ester or something else. Wait, but the NMR shows vinyl hydrogens, so a double bond is present. So the structure must have a double bond and an ester group and an -OH group. Wait, but an ester doesn't have an -OH. So maybe the -OH is part of the ester? No, esters are RCOOR', which don't have an -OH. Unless it's a hemiacetal or something else, but that's unlikely. Alternatively, maybe the compound is a phenol with an ester substituent. For example, a benzene ring with an ester group and a hydroxyl group. But then the molecular formula would have more carbons, but the options are all C6. So maybe it's a cyclic ester with a hydroxyl group. For example, a six-membered ring with an ester group and a hydroxyl group. But I'm not sure. Let's think of the possible structures.

Alternatively, maybe the compound is a propionyl alcohol ester. For example, if the compound is CH2=CHCH2COOCH2CH3. Let's count the carbons: CH2=CH (2) + CH2 (1) + COO (2) + CH2CH3 (2) = total of 7 carbons. But the options are all C6. So that's not matching.

Alternatively, maybe the compound is a diester. For example, two ester groups. But then the molecular formula would have more oxygens. Let's check the options. Option B is C6H12O2, which has two oxygens. So if it's a diester, that would need two ester groups, which would require four oxygens. But that's not the case here. So maybe not.

Alternatively, maybe the compound is a methyl vinyl ester with an -OH group. For example, CH2=CHCOOCH2CH2CH3. Wait, that's 6 carbons: CH2=CH (2) + COO (2) + CH2CH2CH3 (3) = 7 carbons. No. Hmm. This is getting complicated. Let's try a different approach.

Let's consider the molecular formula and the possible structures that fit the spectral data.

First, the IR shows a broad peak at 3000 cm⁻¹, indicating an -OH group. The 1700 cm⁻¹ peak suggests a carbonyl group (C=O). The 1650 cm⁻¹ could be an ether or ester. The NMR shows vinyl hydrogens, so a double bond is present. The mass spectrum has a fragment at 45. Let's see which molecular formulas are possible.

Option A: C6H10O. Molecular weight 98. If it's an alcohol, then it has an -OH. But the presence of a double bond would require a certain structure. For example, CH2=CHCH2CH2CH2CH2OH. Molecular formula C6H12O. Wait, but that's option D. So that's not option A. Alternatively, maybe the structure is CH2=CHCH(OH)CH2CH2CH3. Molecular formula would be C6H12O. Again, not option A. So option A is C6H10O, which would have less hydrogen. Maybe a cyclic structure? For example, cyclohexene with an -OH. Molecular formula would be C6H10O. Let's check: cyclohexene is C6H10, adding an -OH would make it C6H10O. That fits option A. The IR would show a broad peak from the -OH. The NMR would show the vinyl protons from the double bond. The mass spectrum fragment at 45: cyclohexene with an -OH would have a molecular weight of 98. If it loses a fragment of 45, the remaining would be 53. But how? The fragment could be part of the molecule. For example, if the molecule is cyclohexene with an -OH, like cyclohexene-1-ol. The molecular formula is C6H10O. The mass of the molecule is 98. If the fragment is 45, maybe it's losing a part of the molecule. For example, if the fragment is a substituent. But this is speculative. Alternatively, if the fragment is the cyclopropane ring or something, but that's not matching. Alternatively, if the fragment is a methyl group, but 45 is more than that. Not sure.

Option B: C6H12O2. Molecular weight 116. If it's an ester, but where's the -OH? Wait, maybe it's a hemiacetal or something else. Alternatively, if it's an ester with an -OH elsewhere. For example, a diol ester? Not sure. Alternatively, maybe it's a cyclic ester (lactone) with an -OH. For example, a six-membered lactone (like gamma-butyrolactone) with an additional -OH. But gamma-butyrolactone is C4H6O2. Adding an -OH would make it C4H7O3, which is not matching. Alternatively, maybe it's a different cyclic structure. Alternatively, the compound could be a methyl acrylate with an -OH. For example, CH2=CHCOOCH2CH2CH2OH. Molecular formula would be C6H12O3. But that's not matching any options. So maybe not.

Option C: C6H10O2. Molecular weight 114. If it's an ester, then it should have two O's. The presence of a -OH would require an additional O, making it three O's. But the molecular formula is C6H10O2, so it can't have an -OH. Therefore, the -OH must be part of the structure without adding an O. Wait, that's not possible. If the compound has an -OH group, the molecular formula would have an additional O. So if the molecular formula is C6H10O2, the compound can't have a -OH group. But the IR shows a broad peak at 3000 cm⁻¹, which suggests an -OH. Therefore, option C is unlikely because it doesn't have enough O's. Wait, unless the -OH is part of the ester. But esters don't have -OH. Therefore, option C can be eliminated because it can't have an -OH group with two O's. Wait, but the molecular formula is C6H10O2, which is two O's. If the compound has an -OH, then it would need three O's (one from the -OH and two from the ester groups). Therefore, option C is impossible because it can't have an -OH group. So we can eliminate option C.

Option D: C6H12O. Molecular weight 100. If it's an alcohol, then the formula would be C6H12O. The IR shows a broad O-H peak, which fits. The NMR shows vinyl hydrogens, which would require a double bond. So the structure would have both a double bond and an -OH. For example, a cyclohexene ring with an -OH attached. The molecular formula would be C6H10O, but option D is C6H12O. So the structure would need to have more hydrogens. For example, maybe a vinyl group (CH2=CH-) attached to an -OH group and a ring. For example, cyclopentene with an -OH substituent. The formula would be C6H10O. But option D is C6H12O. So that's two more hydrogens. Maybe the structure is something like CH2=CHCH2CH2CH2CH2OH. But that's seven carbons. Wait, no. Let me think again. If the structure is a vinyl group (CH2=CH-) attached to an -OH and a ring. For example, cyclohexene with a substituent. Wait, cyclohexene is C6H10. If there's an -OH substituent, then the formula becomes C6H10O. But option D is C6H12O. So that's two more hydrogens. That could be if there's a CH2 group somewhere. For example, if the structure is CH2=CHCH2CH2CH2CH2OH. Wait, that's seven carbons. No. Alternatively, maybe the structure is CH2=CHCH(OH)CH2CH2CH3. Molecular formula would be C6H12O. Yes! That fits option D. So the structure would be CH2=CHCH(OH)CH2CH2CH3. Let's check: CH2=CH (2 carbons), CH(OH) (1 carbon with OH), CH2CH2CH3 (3 carbons). Total 6 carbons. Hydrogens: CH2=CH has 3 H (CH2=CH-), CH(OH) has 2 H, CH2CH2CH3 has 6 H. Wait, but the formula is C6H12O. Let's count the hydrogens:

CH2=CH-CH(OH)-CH2-CH2-CH3

Each part:

CH2=CH-: 3 H (since CH2=CH has two H's, but one is part of the double bond. Wait, CH2=CH- has two H's on the CH2 and one on the CH. Wait, the structure is CH2=CH-CH(OH)-CH2-CH2-CH3.

Breaking it down:

CH2=CH-: 2 H (since CH2 has two H's, but the double bond is between the two CH2's. Wait, actually, CH2=CH- would have two H's on the CH2 and one on the CH (since it's CH2=CH-). So total of 3 H's in the first group.

Then CH(OH)-: 1 H (the CH part) plus the OH (which is not a hydrogen). So 1 H.

Then CH2-CH2-CH3: Each CH2 has 2 H's, so 2+2+3 =7 H's? Wait, CH2-CH2-CH3: first CH2 has 2 H's, second CH2 has 2 H's, and CH3 has 3 H's. So total 2+2+3=7 H's.

Adding up: 3 (first group) +1 (CH(OH)) +7 (last part) =11 H's. But the molecular formula is C6H12O. So that's 12 H's. Hmm, discrepancy here. Maybe my structure is wrong. Alternatively, perhaps the structure is CH2=CH-CH2-CH(OH)-CH2-CH3. Let's count the hydrogens:

CH2=CH-: 3 H's (2 on CH2, 1 on CH).

CH2-: 2 H's.

CH(OH)-: 1 H (the CH part).

CH2-CH3: 2 H's on the first CH2 and 3 on CH3. Total: 2+3=5.

Total H's: 3 +2 +1 +5=11. Still 11 H's. But the molecular formula is C6H12O. So need one more H. Maybe the structure is different. Alternatively, maybe there's a branch. For example, CH2=CH-CH(OH)-CH2-CH2-CH2. Wait, but that's only 5 carbons. Hmm. Alternatively, maybe the structure is CH2=CH-CH2-CH2-CH(OH)-CH3. Let's count:

CH2=CH-:3 H.

CH2-:2 H.

CH2-:2 H.

CH(OH)-:1 H.

CH3:3 H.

Total:3+2+2+1+3=11. Still 11 H's. So maybe this structure isn't correct. Alternatively, maybe the structure is CH2=CH-CH2-CH2-CH2-CH2-OH. But that's seven carbons. No. Alternatively, maybe the structure is CH2=CH-CH2-CH2-CH(OH)-CH3. Let's count:

CH2=CH-:3 H.

CH2-:2 H.

CH2-:2 H.

CH(OH)-:1 H.

CH3:3 H.

Total:3+2+2+1+3=11. Still 11 H's. Hmm. Maybe I'm missing something. Alternatively, maybe the formula is C6H12O. Let's calculate the degrees of unsaturation. Degrees of unsaturation = (2C +2 - H - X + N)/2. For C6H12O: (2*6 +2 -12 -0 +0)/2 = (14 -12)/2=1. So one degree of unsaturation. That could be a double bond. Which fits with the vinyl hydrogens. So the structure must have a double bond and an -OH group. So maybe the structure is something like CH2=CH-CH(OH)-CH2-CH2-CH3. That has a double bond and an -OH. The molecular formula would be C6H12O. Let's check:

CH2=CH-CH(OH)-CH2-CH2-CH3:

Carbon count:6.

Hydrogen count: Let's see:

CH2=CH-: 3 H.

CH(OH)-: 1 H (the CH) +1 H (the OH) but OH is not a hydrogen. Wait, the CH(OH) group has only one H (the CH part). Then CH2-CH2-CH3: each CH2 has 2 H's. So total:

3 (from CH2=CH) +1 (from CH(OH)) +2 (from CH2) +2 (from CH2) +3 (from CH3) =3+1+2+2+3=11 H's. But the formula is C6H12O. So missing one H. Maybe the structure has a branch with an extra H. Alternatively, maybe the OH is part of a different group. Alternatively, maybe the structure is CH2=CH-CH2-CH(OH)-CH2-CH3. Let's count:

CH2=CH-:3 H.

CH2-:2 H.

CH(OH)-:1 H.

CH2-CH3:2 H (from CH2) +3 H (from CH3) =5 H.

Total:3+2+1+5=11. Still 11. Hmm. Maybe there's a mistake in the structure. Alternatively, maybe the structure is CH2=CH-CH2-CH2-CH2-CH2-OH. But that's seven carbons. No. Alternatively, maybe the structure is CH2=CH-CH(OH)-CH2-CH2-CH2. But again, seven carbons. Hmm. This is tricky. Let's step back.

The mass spectrum fragment at 45. If the molecular formula is C6H12O, then the fragment could be losing a CH2 group. 45 is 12*3 +1*3 +16*0 =36 +3=39. Not 45. Alternatively, maybe a fragment like CH2=CH-CH2-CH2-CH(OH)-CH3. Wait, not sure. Alternatively, the fragment could be a carbonyl group. For example, if the molecule has a carbonyl group, losing part of it. But the molecular formula doesn't include a carbonyl. Alternatively, maybe the fragment is a result of hydrogen bonding. Not sure. Alternatively, maybe the fragment is a methyl group attached to something else. For example, losing a CH3 group would leave 98-15=83. Not 45. Alternatively, maybe the fragment is a fragment from the ester group. For example, if the ester is RCOOR', losing RCOO would leave R'OH. But R'OH would have molecular weight of (molecular weight of R' +17). Let's check for each option:

Option D: C6H12O. If it's RCOOR', then RCOO would be 45. Let's see. R'OH would be 45. But R'OH is the fragment. R'OH would have molecular weight M = (mass of R') +17. So if M=45, then R' would be 45-17=28. 28 is C2H6 (ethane) but with an OH group would be C2H5OH=30. No. Alternatively, maybe R' is C3H5 (45-17=28? Wait, 45-17=28? No. 45-17=28. 28 is C2H6. So R' would be C2H5. But R'OH would be C2H5OH=30. Which doesn't match. Alternatively, maybe the fragment is part of the ester. For example, if the ester is RCOOR', and the fragment is RCOO^-, then the molecular weight of RCOO^- would be (mass of RCOO^-). Let's see. RCOO^- would be (mass of R) + (mass of COO^-). Let's assume R is C3H5 (45-17=28. Wait, 28 is C2H6, which is 28. So RCOO^- would be C3H5COO^-=C4H5O2. The molecular weight is (4*12)+(5*1)+(2*16)=48+5+32=85. Not 45. Hmm. Alternatively, maybe the fragment is the alcohol group. If the alcohol is R-OH, then R-OH would have a molecular weight of (mass of R)+17. For example, if R is C3H7, then R-OH would be 45. Wait, C3H7 is 30 (3*12 +7*1=43). 43+17=60. Not 45. If R is C2H5, then 29 +17=46. Close, but not 45. If R is C1H3, which is 15, then 15+17=32. Not 45. Hmm. Alternatively, maybe the fragment is something else. Alternatively, maybe the fragment is a smaller part of the molecule. For example, if the molecule is CH2=CHCH(OH)CH2CH2CH3, then losing part of it. But not sure. Alternatively, maybe the fragment is a result of the hydrogen bonding. For example, losing a proton. But that would be a different fragment. Not sure.

This is getting quite complicated. Let's try another approach. Let's consider the possible options and see which one fits all the data.

Option A: C6H10O. Molecular weight 98. If it's an alcohol, then -OH group. But the molecular formula is C6H10O. If it's a cyclohexene with an -OH group, like cyclohexene-1-ol, the formula would be C6H10O. The NMR would show the vinyl protons (CH2=CH). The IR would show a broad O-H peak. The mass spectrum fragment at 45: if the molecule is C6H10O, and it loses a fragment of 45, which would be C3H6O. Let's check: 3*12 +6*1 +16=36 +6 +16=58. Not 45. Alternatively, maybe losing a part of the structure. For example, if the molecule is cyclohexene-1-ol, which is C6H10O. The molecular weight is 98. If it loses a fragment of 45, then the remaining would be 53, which doesn't correspond to any common fragment. Alternatively, maybe the fragment is the cyclohexene part. For example, cyclohexene is C6H10, molecular weight 82. Losing a fragment of 82 would leave 16, which is O. But O is not a fragment. Alternatively, the fragment could be a part of the molecule. Not sure. But this is getting too speculative.

Option B: C6H12O2. Molecular weight 116. If it's an ester, then the formula would have two O's. The presence of a -OH group would require three O's, which is not possible. Therefore, option B is unlikely.

Option C: C6H10O2. Molecular weight 114. If it's an ester, then two O's. But no -OH group. The IR would not show a broad peak at 3000 cm⁻¹. Therefore, option C is eliminated.

Option D: C6H12O. Molecular weight 100. If it's an alcohol with a double bond. The IR shows a broad peak at 3000 (OH), 1700 (C=O), 1650 (ether or ester). The NMR shows vinyl protons. The mass spectrum fragment at 45. Let's think: if the molecule is CH2=CH-CH2-CH(OH)-CH2-CH3. Molecular formula C6H12O. The fragment at 45 could be a part of the molecule. For example, the fragment might be CH2=CH-CH(OH)-CH2-CH2-CH3 losing something. Not sure. Alternatively, maybe the fragment is the -OH group. If the -OH group is lost, then the fragment would be CH2=CH-CH2-CH2-CH2CH3, which is C5H10. Molecular weight is 5*12 +10=70. Not 45. Alternatively, maybe the fragment is the CH2=CH- group. Molecular weight 28 + 2*1=30. Not 45. Alternatively, maybe the fragment is the CH2=CH-CH2- part. Molecular weight 30 + something. Not matching. Alternatively, maybe the fragment is a result of the ester group. For example, if the ester is RCOOR', then losing RCOO^- would leave R'OH. But the molecular formula is C6H12O. If the ester is RCOOR', then RCOOR' would have two O's. So R' would be CH2CH2CH3. Then RCOO would be something like C3H6O2. Molecular weight of RCOO would be 3*12 +6*1 +32=36+6+32=74. Then R'OH would be 74-17=57. Not 45. Hmm.

Alternatively, maybe the fragment is a methyl group. For example, losing a CH2 group. But 45-12=33. Not matching. Alternatively, maybe losing a fragment like CH2=CH-CH2-CH2-CH2-CH2-OH. No, that's longer.

This is getting too tangled. Let's try to summarize:

The IR shows a broad peak (OH), 1700 (C=O), and 1650 (probably ester or ether). The NMR shows vinyl protons. Mass spectrum fragment at 45. The options are:

A: C6H10O (98)
B: C6H12O2 (116)
C: C6H10O2 (114) → likely eliminated because no OH
D: C6H12O (100)

The correct answer is likely D: C6H12O. Because the molecular formula fits an alcohol with a double bond. The ester group would require an O, but the formula here has only one O, so it's an alcohol. The fragment at 45 might be the result of losing a part of the molecule. For example, if the structure is CH2=CHCH2CH2CH2CH2OH, but that's C6H12O. Wait, that structure has 6 carbons, 12 hydrogens, and 1 O. The NMR would show the vinyl protons. The IR would show the OH peak. The mass spectrum fragment at 45: maybe the fragment is the CH2=CHCH2CH2CH2- part. Molecular weight of that would be 45? Let's see: CH2=CHCH2CH2CH2- has molecular weight 12*5 (5 carbons) + 10 (5 double bonds? Wait, no. Let's calculate: CH2=CHCH2CH2CH2- is CH2=CH-CH2-CH2-CH2-, which is 5 carbons. Molecular formula C5H9. Molecular weight 5*12 +9=69. Not 45. Alternatively, maybe the fragment is part of the structure. For example, if the molecule is CH2=CHCH(OH)CH2CH2CH3, the molecular formula is C6H12O. The fragment at 45 could be the CH2=CH group (28) plus something else. Not sure. Alternatively, maybe the fragment is the -OH group, but that's 17. Hmm. Alternatively, maybe the fragment is a part of the molecule. For example, losing a smaller fragment. Not sure, but given that option D has all the necessary features (vinyl group, OH group, and the ester/acid groups from IR), and the molecular formula fits, I think the correct answer is D.
</think>