NEETAceToday's NEET Daily

Least count, significant figures and errors in measurements: NEET MCQs with answers

84 questions on this topic of Physics and Measurement (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

Practise Physics and Measurement freeAll Physics and Measurement questions

Free with a Google sign-in; NEET Daily needs no sign-in at all.

easy

1. A student measures the period of oscillation of a simple pendulum. In successive measurements, the readings turn out to be 2.56 s, 2.62 s, 2.70 s, 2.58 s and 2.54 s. The absolute error in the third measurement is:

  1. 0.10 s
  2. 0.05 s
  3. 0.02 s
  4. 0.08 s
Show answer and explanation

Answer: (A) 0.10 s

The mean value of the period is (2.56 + 2.62 + 2.70 + 2.58 + 2.54) / 5 = 13.00 / 5 = 2.60 s. The absolute error in the third measurement is |2.70 - 2.60| = 0.10 s.

medium

2. A physical quantity is calculated as Z = A²B³/C. The percentage errors in measuring A, B and C are 3.5%, 2% and 2% respectively. The maximum percentage error in Z is:

  1. 11 %
  2. 7.5 %
  3. 15 %
  4. 42 %
Show answer and explanation

Answer: (C) 15 %

Relative errors add, each multiplied by its power, even for a quantity in the denominator: ΔZ/Z = 2(ΔA/A) + 3(ΔB/B) + ΔC/C = 2×3.5 + 3×2 + 2 = 15%.

Quick tip: Multiply each percentage error by its power and always add, never subtract.

NCERT Class 11

hard

3. When the number 3.745 and 3.735 are rounded off to three significant figures following the standard scientific rounding conventions, the resulting values are respectively:

  1. 3.75 and 3.73
  2. 3.75 and 3.74
  3. 3.74 and 3.73
  4. 3.74 and 3.74
Show answer and explanation

Answer: (D) 3.74 and 3.74

According to rounding rules: if the digit to be dropped is 5 followed by zeros, the preceding digit is left unchanged if it is even, and increased by 1 if it is odd. In 3.745, the preceding digit 4 is even, so it remains 3.74. In 3.735, the preceding digit 3 is odd, so it is rounded up to 3.74.

medium

4. A physical quantity is calculated as Q = A³/B. The percentage errors in measuring A and B are 2% and 1%. The maximum percentage error in Q is:

  1. 5 %
  2. 3 %
  3. 14 %
  4. 7 %
Show answer and explanation

Answer: (D) 7 %

Maximum relative errors add for products and quotients, weighted by powers: 3×2% + 1×1% = 7%.

easy

5. Which of the following pairs of measured values have the same number of significant figures?

  1. 0.02040 kg and 2.040 × 10² kg
  2. 0.0050 m and 5.00 × 10⁻³ m
  3. 0.070 s and 700 s
  4. 0.00305 A and 3.050 × 10⁻² A
Show answer and explanation

Answer: (A) 0.02040 kg and 2.040 × 10² kg

In 0.02040 kg, leading zeros are not significant, giving 4 significant figures (2, 0, 4, 0). In 2.040 × 10² kg, all digits in the mantissa are significant, giving 4 significant figures. For the other options: 0.0050 m has 2 while 5.00 × 10⁻³ m has 3; 0.070 s has 2 while 700 s has 1 (without decimal); 0.00305 A has 3 while 3.050 × 10⁻² A has 4.

hard

6. Two resistors of resistances R₁ = (100 ± 3) Ω and R₂ = (200 ± 4) Ω are connected in parallel. The equivalent resistance with its maximum absolute error is:

  1. (66.7 ± 3.5) Ω
  2. (66.7 ± 7.0) Ω
  3. (66.7 ± 2.3) Ω
  4. (66.7 ± 1.8) Ω
Show answer and explanation

Answer: (D) (66.7 ± 1.8) Ω

For parallel combination, 1/R = 1/R₁ + 1/R₂, so R = (100 × 200)/(100 + 200) = 200/3 ≈ 66.7 Ω. Differentiating gives ΔR/R² = ΔR₁/R₁² + ΔR₂/R₂². Thus, ΔR = R² [ΔR₁/R₁² + ΔR₂/R₂²] = (200/3)² [3/10000 + 4/40000] = (40000/9) [4/10000] = 16/9 ≈ 1.8 Ω. So, R = (66.7 ± 1.8) Ω.

medium

7. Z = A²B³/C, where A, B and C are measured with percentage errors of 1.5%, 3% and 1%. The maximum possible percentage error in Z is:

  1. 13 %
  2. 11 %
  3. 5.5 %
  4. 27 %
Show answer and explanation

Answer: (A) 13 %

Relative errors add, each multiplied by its power, even for a quantity in the denominator: ΔZ/Z = 2(ΔA/A) + 3(ΔB/B) + ΔC/C = 2×1.5 + 3×3 + 1 = 13%.

Quick tip: Multiply each percentage error by its power and always add, never subtract.

NCERT Class 11

medium

8. A physical quantity is calculated as Q = A/B². The percentage errors in measuring A and B are 1.5% and 3%. The maximum percentage error in Q is:

  1. 15 %
  2. 3.75 %
  3. 7.5 %
  4. 4.5 %
Show answer and explanation

Answer: (C) 7.5 %

Maximum relative errors add for products and quotients, weighted by powers: 1×1.5% + 2×3% = 7.5%.

medium

9. A physical quantity is calculated as Q = A³/B. The percentage errors in measuring A and B are 2% and 3%. The maximum percentage error in Q is:

  1. 18 %
  2. 3 %
  3. 5 %
  4. 9 %
Show answer and explanation

Answer: (D) 9 %

Maximum relative errors add for products and quotients, weighted by powers: 3×2% + 1×3% = 9%.

medium

10. A student determines the density of a cube by measuring its mass as m = (20.0 ± 0.2) g and its edge length as L = (2.00 ± 0.01) cm. The maximum percentage error in the measurement of the density of the cube is:

  1. 1.5%
  2. 2.5%
  3. 2.0%
  4. 3.5%
Show answer and explanation

Answer: (B) 2.5%

Density is given by ρ = m / L³. The maximum fractional error is (Δρ/ρ) = (Δm/m) + 3(ΔL/L). Here, (Δm/m) × 100% = (0.2 / 20.0) × 100% = 1.0%, and (ΔL/L) × 100% = (0.01 / 2.00) × 100% = 0.5%. Thus, the maximum percentage error is 1.0% + 3(0.5%) = 2.5%.

medium

11. A physical quantity is calculated as Q = A³/B². The percentage errors in measuring A and B are 1% and 2%. The maximum percentage error in Q is:

  1. 1 %
  2. 7 %
  3. 3 %
  4. 5 %
Show answer and explanation

Answer: (B) 7 %

Maximum relative errors add for products and quotients, weighted by powers: 3×1% + 2×2% = 7%.

medium

12. A physical quantity is calculated as Z = A²B³/C. The percentage errors in measuring A, B and C are 2%, 1.5% and 3% respectively. The maximum percentage error in Z is:

  1. 11.5 %
  2. 18 %
  3. 5.5 %
  4. 6.5 %
Show answer and explanation

Answer: (A) 11.5 %

Relative errors add, each multiplied by its power, even for a quantity in the denominator: ΔZ/Z = 2(ΔA/A) + 3(ΔB/B) + ΔC/C = 2×2 + 3×1.5 + 3 = 11.5%.

Quick tip: Multiply each percentage error by its power and always add, never subtract.

NCERT Class 11

Keep going with Physics and Measurement. All 194 questions with instant answers, your mistakes saved for revision and your accuracy by topic.
Start practising

Other topics in Physics and Measurement