Problem 60 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of tripeptides formed by 3 different amino acids are? (a) 3 (b) 4 (c) 5 (d) 6

Step-by-Step Solution

Answer

(d) 6 tripeptides.

Step 1: Understanding the Problem

We need to determine how many different tripeptides can be formed using 3 different amino acids. A tripeptide consists of three amino acids linked together in a specific sequence.

Step 2: Identifying the Components

We are given 3 different amino acids to work with. These can be labeled as A, B, and C for simplicity.

Step 3: Arranging the Amino Acids

The sequence in which the three amino acids are arranged matters in forming different tripeptides. Each unique sequence represents a different tripeptide.

Step 4: Calculating Permutations

Since we are arranging 3 different amino acids, we calculate the number of permutations. The formula for permutations of n distinct items is given by n!, where n is the number of items.

Step 5: Applying the Formula

For our problem, n = 3. Therefore, the number of permutations is: \[ 3! = 3 \times 2 \times 1 = 6 \] Different sequences can be formed from 3 different amino acids.

Step 6: Concluding the Solution

With all permutations calculated, there are 6 different tripeptides that can be formed from 3 distinct amino acids.

Key Concepts

Tripeptides

Tripeptides are fascinating molecules essential for numerous biological processes. They are composed of three amino acids linked together. These links are known as peptide bonds, which form during a process called condensation.
Tripeptides play vital roles in various functions within the body, such as serving as building blocks for proteins, acting in signal transduction, or even having specific activities themselves, like some bioactive peptides.
Understanding tripeptides begins with grasping the sequence's importance. This sequence dictates the molecule's properties and its biological activity. Changing even a single amino acid in this chain can radically transform the tripeptide's function. This illustrates why the study of permutation in permutations is crucial when determining possible tripeptide formations.

Amino Acids

Amino acids are organic compounds that combine to form proteins and are fundamental to biological functions. In any given organism, a set of 20 amino acids is encoded by the genetic code. Each amino acid has a unique side chain, giving proteins their incredible diversity.
When discussing forming tripeptides from three different amino acids, it's important to recognize that each distinct amino acid brings different chemical properties. The variation in these properties affects the tripeptide's overall characteristics.
Furthermore, the arrangement of amino acids in a tripeptide sequence contributes directly to the molecule's chemical behavior. This is why the order matters so much when calculating permutations of amino acids and why every distinct order is counted as a separate tripeptide.

Factorial Calculation

Factorial calculation is a fundamental principle in mathematics, particularly useful in permutations and combinations. When calculating how many ways to arrange a set of distinct items, factorials provide the answer. For any number of items, n, the factorial is denoted as n! and is the product of all positive integers up to n.
For example, if you want to find the possible arrangements of 3 amino acids, you would compute 3!. This would equal 3 × 2 × 1, resulting in 6. This means there are six different ways to sequence the three amino acids in forming tripeptides.
In permutations, the calculation of factorials ensures all distinct sequences are included. It underscores the concept that order matters, as each unique arrangement is considered a different permutation. Employing factorial calculations makes it efficient to determine the total number of possible arrangements in various scenarios, including the formation of tripeptides from amino acids.