Identify the structure of the compound (C3H5NO) given its NMR chemical shifts
Dhruba Charan Dash published the problem in his analytical chemistry textbook (ISBN 9788120353008). This is the picture that goes with the question:

Notice that the scale of the chemical shift increases with the strength of the magnetic field $B$. This means they are using the $\tau$ scale instead of the $\delta$ scale. The modern description of the signals would be $\delta = 10 - \tau$, where $\tau$ is the value given in the figure.
So we have a singlet at 4.30 ppm (B = broad?) and triplets at 3.83 ppm (typo in the figure, should be 6.17 instead of 5.17) and 2.63 ppm.
$$\delta\ 2.63 \text{ (triplet, 2 H)}$$
$$\delta\ 3.83 \text{ (triplet, 2 H)}$$
$$\delta\ 4.30 \text{ (broad, 1 H)}$$
For completeness, I will post the answer given by the author Dhruba Charan Dash:

PROBLEM 13.17 PMR spectrum of the compound $\ce{C3H5ON}$ in an acidic medium is shown below. Suggest its structure. Given that the peak 1 disappears in the presence of $\ce{D2O}$.
Solution Analysis of the spectrum:
(i) Since the peak 1 disappears in the presence of $\ce{D2O}$, it may represent a group containing active hydrogen. This group may be a hydroxyl group.
(ii) The peaks 2 and 3 must represent the hydrogen atoms attached to the methylene group.
(iii) The analysis of integral trace indicates the presence of 1, 2, and 2 protons within the peaks 1, 2 and 3 respectively.
The point (iii) suggests the presence of two methylene groups. These must be attached each other (point (ii)). The only structure consistent with the above facts is $$\ce{HOCH2CH2CN}$$

It is clear why the question posed by the OP (and by the teacher of the OP, as I learned in chat) was hard to solve. A single problem transcribing the question (replacing $\tau$ with $\delta$) obfuscated the intended chemical shift values.
For reference, here is the problem as presented to the OP: