A mixture of four peptides, PKKRK, RGERV, RYRGV and LVVYP, is loaded onto an ion-exchange column at pH = 7.2. If carboxymethyl (CM) cellulose is used as the stationary phase of this column, then which peptide elutes first? 
Step 1: Nature of the stationary phase
Carboxymethyl (CM) cellulose is a cation-exchange resin.
- It contains negatively charged carboxyl groups at pH 7.2.
- Therefore, it binds to positively charged peptides (cationic residues).
- Neutral or negatively charged peptides will bind weakly or not at all, and thus elute first.
Step 2: Analyze the peptides at pH 7.2
We must consider the approximate charges of side chains at pH 7.2: - Lysine (K), Arginine (R): positively charged (+1 each).
- Glutamic acid (E): negatively charged (–1 each).
- Tyrosine (Y), Proline (P), Valine (V), Glycine (G), Leucine (L): neutral.
Step 3: Calculate net charges
PKKRK: Contains 3 Lys (+3), 1 Arg (+1), 1 Pro (0). Net charge $\approx +4$. Strongly cationic $⇒$ binds strongly to CM-cellulose.
RGERV: Contains Arg (+1), Glu (–1), Arg (+1), Val (0). Net charge $\approx +1$. Moderately positive $⇒$ binds moderately.
RYRGV: Contains Arg (+1), Tyr (0), Arg (+1), Gly (0), Val (0). Net charge $\approx +2$. Positive $⇒$ binds.
LVVYP: Contains Leu (0), Val (0), Val (0), Tyr (0), Pro (0). Net charge $\approx 0$. Neutral $⇒$ weak/no binding.
Step 4: Elution order
- Peptides with higher positive charge bind more strongly to the negatively charged CM-cellulose.
- Therefore, the order of elution will be from least positive to most positive.
- Neutral peptide LVVYP (charge 0) will elute first.
Therefore, the peptide that elutes first is (D) LVVYP.
Which one of the given figures P, Q, R, and S represents the graph of the following function? \[ f(x) = |x + 2| - |x - 1| \] 
An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of the light beam. The cylinder can be reoriented in any direction within the light beam. Under these conditions, which one of the shadows P, Q, R, and S is NOT possible?
What is the major product formed in the given reaction? 

