Free Errors and Significant Figures MCQs with Answers

1. The length of a strip is measured by a metre scale as 3.4 cm. The reading measured on the Vernier callipers for the length of the strip will be

• A. 0.34 cm.
• B. 3.4 cm.
• C. 3.40 cm.
• D. 3.400 cm.

Explanation: The correct answer is 3.400 cm. Vernier calipers provide more precise measurements than a standard metre scale, typically offering precision to the thousandths of a centimeter. While a metre scale measures to one decimal place (3.4 cm), a Vernier caliper extends this precision, recording the measurement as 3.400 cm to reflect the additional accuracy. The other options either reduce the precision or fail to extend it to the level provided by Vernier calipers.

2. Random errors can be reduced byI. taking zero correctionII. taking mean of several measurementsIII. comparing the instrument with a more accurate one

• A. II only.
• B. III only.
• C. I and II.
• D. I and III.

Explanation: Option II is correct because taking the mean of several measurements helps to minimize the effect of random errors by averaging out the variations that occur in repeated measurements.Option I is incorrect because zero correction is used to address systematic errors, which are consistent and predictable, rather than random errors.Option III is incorrect because comparing the instrument with a more accurate one helps identify and correct systematic errors, not random errors.Therefore, only taking the mean of several measurements (Option II) is effective in reducing random errors.

3. The number of significant figures in the sum of 1.21 x 10^5 and 3.26 x 10^3 is

• A. 3
• B. 5
• C. 6
• D. 8

Explanation: To find the number of significant figures in the sum of 1.21 × 105 and 3.26 × 103, first, convert both numbers to the same power of ten: 1.21 × 105 = 121000 and 3.26 × 103 = 3260. Add them to get 124260. When written in scientific notation, this becomes 1.24260 × 105, which has 8 significant figures. Thus, Option D is correct, while the other options underestimate the number of significant figures due to incorrect alignment or rounding.

4. A systematic error can be removed by

• A. Taking mean reading.
• B. Repeating the reading.
• C. Changing the surrounding.
• D. Recalibrating the instrument.

Explanation: Systematic errors are consistent biases in measurement that arise from flaws in the measurement system, such as miscalibrated instruments. To remove systematic errors, recalibration of the instrument is necessary, ensuring that it provides accurate readings. Taking mean readings or repeating measurements do not correct systematic errors because these methods only address random errors. Changing the surroundings may impact measurements but doesn't target the root cause of systematic errors.

5. Uncertainty in measurement can occur due to theI. limitation of instrumentsII. natural variationsIII. frequent errors

• A. I only.
• B. III only.
• C. I and II.
• D. II and III.

Explanation: Uncertainty in measurement can arise from multiple sources. Natural variations (II) refer to the inherent variability in the system being measured, which can lead to different results even if the procedure is repeated exactly. Frequent errors (III) refer to mistakes that occur during the measurement process, which can be due to human error or instrument calibration issues. Although the limitation of instruments (I) can also cause uncertainty, the correct combination of factors listed in the options that lead to uncertainty are II and III. Therefore, the correct answer is Option D.

6. Random errors can be reduced byI. taking zero correctionII. taking mean of several measurementsIII. comparing the instrument with another more accurate one

• A. II only.
• B. III only.
• C. I and II.
• D. I and III.

Explanation: The correct answer is Option A:II only.Random errors can be reduced by taking the mean of several measurements, as this averages out the unpredictable variations inherent in each measurement. Option III addresses systematic errors, as comparing with a more accurate instrument helps identify consistent deviations. Option I, zero correction, is also a method to correct systematic errors, not random errors.

7. The CORRECT scientific notation for 100.00 is

• A. 1.00 x 10^-3
• B. 1.00 x 10^-2
• C. 1.00 x 10^2
• D. 1.00 x 10^3

Explanation: The correct scientific notation for 100.00 is1.00 × 103because scientific notation requires expressing a number as a product of a coefficient (between 1 and 10) and a power of ten. Here, 1.00 is the coefficient, and the power of ten indicates how many places the decimal must move to recreate the original number. Moving the decimal three places to the right from 1.00 results in 100.00. Option A and B represent much smaller numbers (0.001 and 0.01, respectively), and Option C represents 100, not 100.00, thus not accurately reflecting the decimal precision.

8. The type of error, which is produced by a faulty measuring instrument is called

• A. Logical error
• B. Random error
• C. Personal error
• D. Systematic error

Explanation: The correct answer is systematic error. Systematic errors are errors that consistently occur in the same direction whenever a particular measurement is made. This type of error can be caused by a faulty measuring instrument, such as a scale that is not calibrated correctly. In contrast, logical errors are related to incorrect reasoning, random errors are unpredictable fluctuations, and personal errors are due to human mistakes. Understanding the source of error is crucial in scientific measurement and experimentation.

9. The multiplication product of 20.21 with 20.22 upto four significant figures is

• A. 408.6
• B. 408.64
• C. 408.6462
• D. 409.0

Explanation: To solve this problem, multiply 20.21 by 20.22 to get approximately 408.6442. To express this result with four significant figures, round it to 408.6. Option A is correct because it uses four significant figures. Option C is incorrect because it does not round the result and exceeds four significant figures. Option D rounds the result to a whole number, which doesn't meet the requirement for four significant figures.

10. In a champions' trophy of dart match, a player was given three chances to hit the centre target with darts. He managed to hit all the darts close to each other but away from the centre.The given case depicts that the player's shots were

• A. Precise
• B. Accurate
• C. Uncertain
• D. Unreliable

Explanation: The correct answer is precise. Precision in measurements or actions means the results are consistent or close to each other, regardless of whether they are close to the target. In this scenario, the player's shots were consistently grouped together, which demonstrates precision. Accuracy, on the other hand, is about how close those shots are to the intended target. Since the shots were away from the center, they were not accurate. The terms 'uncertain' and 'unreliable' do not apply here because the shots were consistent, indicating reliability and certainty in the result.