Assertion (A) : For DNA sequencing, the total DNA from a cell is isolated and converted into random fragments of relatively smaller sizes.

Reason (R) : Human genome is said to have approximately 3 x 10⁹ bp and the total estimated cost for sequencing is very high.

The correct option is: Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

Step-by-step Explanation:

1. Analysis of Assertion (A):
Assertion (A) states: "For DNA sequencing, the total DNA from a cell is isolated and converted into random fragments of relatively smaller sizes."
During DNA sequencing projects, such as the Human Genome Project, the complete DNA of a cell is isolated. Since DNA molecules are extremely long polymers, it is technically impossible to sequence a whole chromosome or a very long DNA molecule in one single, continuous stretch with existing sequencing technologies. Therefore, the DNA is randomly sheared or cut into smaller, manageable fragments. These smaller fragments are then sequenced, and the overlapping sequences are aligned using specialized computer algorithms to reconstruct the continuous genome. Thus, Assertion (A) is true.

2. Analysis of Reason (R):
Reason (R) states: "Human genome is said to have approximately 3 × 10⁹ bp and the total estimated cost for sequencing is very high."
The human haploid genome indeed contains approximately
$$3\times {10}^9$$
base pairs (bp). At the beginning of the Human Genome Project, the estimated cost of sequencing was about US $3 per base pair, making the total estimated cost of the project extremely high (around 9 billion USD). Therefore, the statement in Reason (R) is factually correct, making Reason (R) true.

3. Evaluating the Link Between Assertion and Reason:
Now we must determine if Reason (R) explains why Assertion (A) is true.
The fragmentation of DNA (Assertion A) is done because of the technological limitation that long DNA sequences cannot be read in a single run. The high cost and the massive size of the human genome (Reason R) represent the scale and economic challenges of the project, but they do not dictate the physical/technical requirement of breaking DNA into smaller fragments for sequencing.
Since the technological limitation is the actual reason for fragmentation, and not the cost, Reason (R) is not the correct explanation for Assertion (A).

Conclusion:
Both Assertion (A) and Reason (R) are individually true statements, but Reason (R) is not the correct explanation of Assertion (A).