Careless handling can lead to gross errors in a scientific experiment or measurement. Let's understand each type of error first.

Systematic error: This type of error occurs due to a fault in the experimental setup or measuring instrument, leading to consistent deviation from the true value. For example, if a weighing balance is faulty and consistently shows a weight higher than the actual weight, then all measurements taken using that balance will have a systematic error.

Random error: This type of error occurs due to unpredictable and inconsistent factors such as human error, environmental fluctuations, or instrument instability. It leads to random deviation of measurements from the true value. Random errors can be reduced by taking multiple measurements and calculating the average.

Gross error: This type of error occurs due to a mistake in the experiment or measurement that leads to a significant deviation from the true value. It can be caused by human error, faulty equipment, or improper experimental design. Gross errors can invalidate the entire experiment and lead to incorrect conclusions.

Now, let's come back to the question. Careless handling refers to a lack of attention or negligence while performing an experiment or measurement. This can lead to significant mistakes such as using the wrong reagent, misreading the instrument, or contaminating the sample. Such mistakes can result in a gross error that can lead to incorrect conclusions and wasted resources.

Therefore, the correct answer to the question is option 'B' - Gross error.