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

Step 1: Understanding the Problem

We need to determine how many different tripeptides can be formed using 3 different amino acids. A tripeptide is a chain of 3 amino acids linked together, and the order in which they are linked matters.

Step 2: Identify the Formula to Use

Since the order of amino acids is important, we will use permutations to solve this problem. For 3 different items, the number of permutations is given by 3! (3 factorial).

Step 3: Calculate the Number of Permutations

To find the number of ways to arrange 3 different amino acids in a sequence, calculate 3! as follows: \[ 3! = 3 \times 2 \times 1 = 6 \]

Step 4: Determine the Answer

From the calculation, 3 different amino acids can form a total of 6 different tripeptides.

Key Concepts

Tripeptides

In chemistry, a tripeptide is a protein subunit composed of three amino acids linked together by peptide bonds. Tripeptides are the simplest form of proteins, and they play crucial roles in biological processes. Each amino acid in a tripeptide can be present in a different sequence, forming various combinations. For example, if we have amino acids A, B, and C, possible tripeptides include ABC, ACB, BAC, BCA, CAB, and CBA. Notice how the order matters? This is because the function and properties of a tripeptide can change with different arrangements of amino acids. It is through the sequence of amino acids that tripeptides and larger proteins become functionally diverse. Understanding tripeptides helps comprehend how proteins are assembled and how they function in biochemical reactions.

Amino Acids

Amino acids are organic compounds that serve as the building blocks for proteins. They are composed of an amino group, a carboxyl group, a hydrogen atom, and a distinct side chain known as an R group, all attached to the same carbon atom, called the alpha carbon. This arrangement gives amino acids their versatility and defines their unique characteristics. Without these distinct side chains, amino acids would have very little functional diversity. Amino acids join together through peptide bonds in a specific sequence to form polypeptides and proteins. Since amino acids determine the structure and function of proteins, they are essential for diverse biological activities, ranging from catalysis by enzymes to signaling as hormones. The 20 different amino acids in nature can combine in countless variations to create the proteins that perform most of the work in cells.

Factorial Calculation

Factorial calculation is a mathematical concept used to find out how many ways 'n' items can be arranged. It is especially useful in permutations, where the order of arrangement is important. In the context of our example, calculating the factorial helps us find how many different tripeptides we can make from given amino acids. The notation for a factorial is an exclamation mark (!) after a number. For example, 3! means 3 factorial, which is calculated as:

• 3! = 3 × 2 × 1 = 6

This calculation tells us that there are 6 possible ways to arrange 3 distinct amino acids in a sequence, leading to the formation of 6 different tripeptides. Factorials grow very quickly with larger quantities, demonstrating the complexity and vast possibilities in biological systems and arrangements.