JEE Main - Errors in measurements and dimensional analysis Online Test (MCQ Quiz)

1. What is the absolute error in a measurement?

A) The ratio of the true value to the measured value B) The difference between the true value and the measured value C) The ratio of the error to the measured value D) The square of the measured value

2. Which of the following represents the relative error?

A) Absolute Error / True Value B) Measured Value / Absolute Error C) True Value / Absolute Error D) Measured Value / True Value

3. Percentage error is defined as:

A) Relative Error * 100% B) Absolute Error / 100% C) True Value * Relative Error D) Measured Value * 100%

4. If a measurement is 5.0 cm and the true value is 5.1 cm, what is the absolute error?

A) 0.1 cm B) -0.1 cm C) 5.0 cm D) 5.1 cm

5. If the measured value is 10 units and the true value is 12 units, what is the relative error?

A) 1/6 B) 1/5 C) 5/6 D) 6/5

6. If the absolute error is 0.02 m and the true value is 2.5 m, what is the percentage error?

A) 0.8% B) 0.08% C) 8% D) 2%

7. When adding two quantities with their absolute errors, the absolute error in the sum is:

A) The difference of the absolute errors B) The sum of the absolute errors C) The product of the absolute errors D) The ratio of the absolute errors

8. When subtracting two quantities with their absolute errors, the absolute error in the difference is:

A) The sum of the absolute errors B) The difference of the absolute errors C) The product of the absolute errors D) The ratio of the absolute errors

9. When multiplying two quantities with their relative errors, the relative error in the product is:

A) The difference of the relative errors B) The product of the relative errors C) The sum of the relative errors D) The ratio of the relative errors

10. When dividing two quantities with their relative errors, the relative error in the quotient is:

A) The difference of the relative errors B) The product of the relative errors C) The sum of the relative errors D) The ratio of the relative errors

11. If a quantity is raised to a power 'n', the relative error in the result is:

A) n times the relative error of the quantity B) 1/n times the relative error of the quantity C) n squared times the relative error of the quantity D) The square root of n times the relative error of the quantity

12. In the measurement of length 'l' = 10.0 ± 0.1 cm, what is the percentage error?

A) 1% B) 0.1% C) 10% D) 0.01%

13. If x = a + b, and the errors in a and b are Δa and Δb, the error in x is:

A) Δx = Δa - Δb B) Δx = Δa + Δb C) Δx = Δa * Δb D) Δx = Δa / Δb

14. If y = a - b, and the errors in a and b are Δa and Δb, the error in y is:

A) Δy = Δa + Δb B) Δy = Δa - Δb C) Δy = Δa * Δb D) Δy = Δa / Δb

15. If z = a * b, and the relative errors in a and b are Δa/a and Δb/b, the relative error in z is:

A) Δz/z = Δa/a - Δb/b B) Δz/z = Δa/a + Δb/b C) Δz/z = (Δa/a) * (Δb/b) D) Δz/z = (Δa/a) / (Δb/b)

16. If P = a / b, and the relative errors in a and b are Δa/a and Δb/b, the relative error in P is:

A) ΔP/P = Δa/a - Δb/b B) ΔP/P = Δa/a + Δb/b C) ΔP/P = (Δa/a) * (Δb/b) D) ΔP/P = (Δa/a) / (Δb/b)

17. If V = a^n, the relative error in V is:

A) ΔV/V = n * (Δa/a) B) ΔV/V = (1/n) * (Δa/a) C) ΔV/V = n^2 * (Δa/a) D) ΔV/V = sqrt(n) * (Δa/a)

18. What is dimensional analysis primarily used for?

A) Calculating precise numerical values B) Checking the consistency of physical equations C) Determining the nature of matter D) Measuring very small distances

19. Which of the following is a fundamental dimension in the SI system?

A) Force B) Velocity C) Mass D) Energy

20. The dimensions of velocity are:

A) [M L T^-1] B) [L T^-1] C) [M L^-1 T] D) [L^2 T^-1]

21. The dimensions of acceleration are:

A) [L T^-2] B) [L T^-1] C) [M L T^-2] D) [L^2 T^-2]

22. The dimensions of force are:

A) [M L T^-2] B) [M L^-1 T^-2] C) [M L^2 T^-2] D) [M L T]

23. The dimensions of energy are:

A) [M L^2 T^-2] B) [M L T^-2] C) [M L^2 T^-1] D) [M L^-1 T^-2]

24. The dimensions of pressure are:

A) [M L^-1 T^-2] B) [M L T^-2] C) [M L^2 T^-2] D) [L T^-2]

25. The dimensions of density are:

A) [M L^-3] B) [M L^3] C) [M^-1 L^3] D) [M L^-1]

26. Which of the following is a dimensionless quantity?

A) Strain B) Force C) Velocity D) Acceleration

27. The dimensions of angular velocity are:

A) [T^-1] B) [M T^-1] C) [L T^-1] D) [M L T^-1]

28. The dimensions of impulse are:

A) [M L T^-1] B) [M L T^-2] C) [M L^2 T^-1] D) [M L^-1 T^-1]

29. The dimensions of surface tension are:

A) [M T^-2] B) [M L T^-2] C) [M L^2 T^-2] D) [L T^-2]

30. If a quantity 'Q' is measured as x ± Δx, then Δx represents:

A) The true value of Q B) The relative error in Q C) The absolute error in Q D) The percentage error in Q

31. The principle of homogeneity of dimensions states that:

A) Dimensions of each term in an equation must be different B) Dimensions of each term in an equation must be the same C) Dimensions of only the first term must be checked D) Dimensions are irrelevant in physical equations

32. Dimensional analysis cannot be used to:

A) Derive relations between physical quantities B) Check the dimensional correctness of an equation C) Convert units from one system to another D) Determine the value of dimensionless constants

33. If the error in measuring the radius of a circle is 1%, what is the error in measuring its area?

A) 1% B) 2% C) 0.5% D) 4%

34. The error in measuring the side of a cube is 2%. What is the maximum percentage error in its volume?

A) 2% B) 4% C) 6% D) 8%

35. If the error in measuring the velocity of a particle is 3%, what is the error in measuring its kinetic energy?

A) 3% B) 6% C) 9% D) 1.5%

36. The dimensions of Planck's constant (h) are:

A) [M L^2 T^-1] B) [M L T^-1] C) [M L^2 T^-2] D) [M L^-1 T^-1]

37. The dimensions of angular momentum are:

A) [M L^2 T^-1] B) [M L T^-1] C) [M L^2 T^-2] D) [M L^-1 T^-1]

38. The dimensions of the gravitational constant (G) are:

A) [M^-1 L^3 T^-2] B) [M L^3 T^-2] C) [M^-1 L^-3 T^-2] D) [M L T^-2]

39. Which of the following is a unit of energy?

A) Watt B) Joule C) Newton D) Pascal

40. The dimensions of work done are the same as:

A) Power B) Momentum C) Energy D) Force

41. If measurements of length and time are made with an accuracy of ±1% and ±2% respectively, what is the accuracy in the calculation of velocity (v = l/t)?

A) ±1% B) ±2% C) ±3% D) ±4%

42. Which of the following is NOT a fundamental unit in the SI system?

A) Meter B) Kilogram C) Second D) Newton

43. The dimensions of coefficient of viscosity are:

A) [M L^-1 T^-1] B) [M L T^-1] C) [M L^-1 T^-2] D) [M L^2 T^-1]

44. If the period of oscillation of a simple pendulum is given by T = 2π√(l/g), where l is length and g is acceleration due to gravity, then the dimensions of g are:

A) [L T^-2] B) [L T^-1] C) [L^2 T^-2] D) [M L T^-2]

45. A measurement has an error of ±0.5 units. If the measured value is 10.0 units, what is the percentage error?

A) 0.5% B) 5% C) 10% D) 2%

46. The dimensions of the universal gas constant (R) are:

A) [M L^2 T^-2 K^-1] B) [M L^2 T^-2] C) [M L T^-2 K^-1] D) [M L^2 T^-1 K]

47. If the percentage errors in the measurement of mass and velocity are 2% and 3% respectively, the maximum percentage error in the kinetic energy (KE = 1/2 mv^2) is:

A) 5% B) 8% C) 11% D) 12%

48. Which of the following is a derived unit?

A) Ampere B) Kelvin C) Mole D) Watt

49. The dimensions of angular acceleration are:

A) [T^-2] B) [L T^-2] C) [M T^-2] D) [M L T^-2]

50. If the error in measuring the diameter of a wire is 1%, what is the error in measuring its radius?

A) 0.5% B) 1% C) 2% D) 0.25%

Errors in measurements and dimensional analysis - Online Test

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