Units and Measurements NEET PYQReal NEET & AIPMT 2005–2021 questions, year-tagged, with solutions
By the RankUp team, founded by Dr. Deepak Sahu (MBBS Gold Medalist, NEET PG AIR 1731) · Updated
Every Units and Measurements question from the NEET & AIPMT papers on this site (2005–2021), newest first. Each is tagged with its paper. Tap an option to check your answer and read the explanation.
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Units and Measurements previous year questions
24 questions. Tap an option to check your answer.
Q1NEET 2021
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities. Find the dimensions of energy.
Not quite — the answer is B.
Energy = force × displacement, and displacement has the dimensions of acceleration × time². Hence [E] = [F][A][T²]. Writing [F][A][T] forgets that distance needs time squared.
Q2NEET 2021
A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions on the circular scale. The diameter of the wire from the above data is :
Not quite — the answer is D.
Least count = 1 mm/100 = 0.01 mm. Diameter = 0 + 52 × 0.01 mm = 0.52 mm = 0.052 cm. The trap 0.52 cm forgets the mm-to-cm conversion.
Q3NEET 2021
If E and G respectively denote energy and gravitational constant, then E/G has the dimensions of :
Not quite — the answer is A.
[E] = ML²T⁻² and [G] = M⁻¹L³T⁻². So E/G = M²L⁻¹T⁰. Forgetting that G carries M⁻¹ would give a single power of mass.
Q4NEET 2020 · Q146
A screw gauge has least count of 0.01 mm and there are 50 divisions in its circular scale. The pitch of the screw gauge is :
Not quite — the answer is C.
Least count = pitch / number of circular scale divisions, so pitch = 0.01 mm × 50 = 0.5 mm. The least count itself is not the pitch.
Q5NEET 2020 · Q167
Dimensions of stress are :
Not quite — the answer is D.
Stress is force per area: [MLT⁻²]/[L²] = [ML⁻¹T⁻²], the same as pressure. [MLT⁻²] is force itself and [ML²T⁻²] is energy.
Q6NEET 2020 · Q176
Taking into account of the significant figures, what is the value of 9.99 m − 0.0099 m ?
Not quite — the answer is B.
9.99 − 0.0099 = 9.9801 m, but in subtraction the result keeps as many decimal places as the least precise term; 9.99 has two decimal places, so the answer is 9.98 m. 9.9801 m reports more precision than the data justify.
Q7NEET 2019 · Q44
In an experiment, the percentage of error occurred in the measurement of physical quantities A, B, C and D are 1%, 2%, 3% and 4% respectively. Then the maximum percentage of error in the measurement X, where X = A²B^(1/2) / (C^(1/3) D³), will be:
Not quite — the answer is B.
Maximum relative errors add regardless of whether the quantity is in the numerator or denominator: 2 × 1% + ½ × 2% + ⅓ × 3% + 3 × 4% = 2 + 1 + 1 + 12 = 16%. Subtracting the denominator errors gives the wrong −10%.
Q8NEET 2018 · Q37
A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of −0.004 cm, the correct diameter of the ball is
Not quite — the answer is D.
Observed reading = 0.5 cm + 25 × 0.001 cm = 0.525 cm. Correct reading = observed − zero error = 0.525 − (−0.004) = 0.529 cm. Adding the negative zero error with the wrong sign gives 0.521 cm.
Q9NEET 2017 · Q163
A physical quantity of the dimensions of length can be formed out of c, G and e²/4πε₀ is [c is velocity of light, G is universal constant of gravitation, e is charge]:
Not quite — the answer is A.
e²/4πε₀ = F r² has dimensions [M L³ T⁻²] and G has [M⁻¹ L³ T⁻²], so G e²/4πε₀ has [L⁶ T⁻⁴]; its square root is [L³ T⁻²]. Dividing by c² [L² T⁻²] leaves [L]. Multiplying by c² instead gives L⁵T⁻⁴.
Q10NEET 2017 (Gujarati paper) · Q180
A student performs an experiment of measuring the thickness of a slab with a vernier calliper whose 50 divisions of the vernier scale are equal to 49 divisions of the main scale. He noted that zero of the vernier scale is between 7.00 cm and 7.05 cm mark of the main scale and 23rd division of the vernier scale exactly coincides with the main scale. The measured value of the thickness of the given slab using the calliper will be:
Not quite — the answer is B.
One main scale division is 0.05 cm (the marks are at 7.00 and 7.05 cm), so the least count = 1 MSD − 1 VSD = 0.05/50 = 0.001 cm. Reading = 7.00 + 23 × 0.001 = 7.023 cm. 7.23 cm would wrongly take the least count as 0.01 cm.
Q11NEET 2016 Phase 2 · Q1
Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
Not quite — the answer is A.
Using [h] = ML²T⁻¹, [G] = M⁻¹L³T⁻², [c] = LT⁻¹: hG has dimensions L⁵T⁻³ and c³ has L³T⁻³, so hG/c³ = L² and √(hG)/c^(3/2) = L (the Planck length). With c^(5/2) in the denominator the result would be T, not L.
Q12AIPMT 2015
If energy (E), velocity (V) and time (T) are chosen as the fundamental quantities, the dimensional formula of surface tension will be:
Not quite — the answer is D.
Surface tension has dimensions [MT⁻²]. With E = [ML²T⁻²] and V = [LT⁻¹], M = E V⁻², so [MT⁻²] = [E V⁻² T⁻²].
Q13AIPMT 2014
If force (F), velocity (V) and time (T) are taken as fundamental units, then the dimensions of mass are:
Not quite — the answer is C.
F = ma = m(V/T), so m = FT/V, i.e. [F V⁻¹ T].
Q14NEET 2013
In an experiment four quantities a, b, c and d are measured with percentage error 1%, 2%, 3% and 4% respectively. Quantity P is calculated as follows: P = a³b²/(cd). % error in P is
Not quite — the answer is A.
Maximum fractional errors add with powers as weights: ΔP/P = 3(1%) + 2(2%) + 3% + 4% = 3 + 4 + 3 + 4 = 14%. Getting 10% comes from ignoring the powers and just adding the four errors.
Q15AIPMT 2012 Prelims
The damping force on an oscillator is directly proportional to the velocity. The units of the constant of proportionality are
Not quite — the answer is D.
F = bv, so b = F/v with units (kg m s⁻²)/(m s⁻¹) = kg s⁻¹. kg m s⁻² is the unit of force itself, not of the constant.
Q16AIPMT 2011 Mains
The density of a material in CGS system of units is 4 g/cm³. In a system of units in which unit of length is 10 cm and unit of mass is 100 g, the value of density of material will be
Not quite — the answer is D.
New unit of density = 100 g/(10 cm)³ = 0.1 g/cm³. So 4 g/cm³ = 4/0.1 = 40 new units. Dividing the wrong way gives 0.4.
Q17AIPMT 2010 Mains · Q65
A student measures the distance traversed in free fall of a body, initially at rest in a given time. He uses this data to estimate g, the acceleration due to gravity. If the maximum percentage errors in measurement of the distance and the time are e1 and e2 respectively, the percentage error in the estimation of g is
Not quite — the answer is B.
For free fall from rest h = ½gt², so g = 2h/t². Maximum relative errors add with their powers: Δg/g = Δh/h + 2Δt/t, giving e₁ + 2e₂. Subtracting errors (e₁ − 2e₂) is wrong because maximum errors always add.
Q18AIPMT 2010 Prelims · Q1
The dimension of (1/2)ε₀E², where ε₀ is permittivity of free space and E is electric field, is
Not quite — the answer is C.
(1/2)ε₀E² is the energy density of the electric field, i.e. energy per unit volume. Its dimensions are ML²T⁻²/L³ = ML⁻¹T⁻². ML²T⁻² is the dimension of energy itself, which forgets the division by volume.
Q19AIPMT 2009 Prelims · Q12
If the dimensions of a physical quantity are given by Mᵃ Lᵇ Tᶜ, then the physical quantity will be:
Not quite — the answer is D.
Pressure = force/area = MLT⁻²/L² = ML⁻¹T⁻², so a = 1, b = −1, c = −2. Velocity has no mass dimension (a = 0), acceleration has no mass dimension, and force is MLT⁻², so the other pairings are wrong.
Q20AIPMT 2008 Prelims · Q1
Which two of the following five physical parameters have the same dimensions? (a) energy density (b) refractive index (c) dielectric constant (d) Young's modulus (e) magnetic field
Not quite — the answer is D.
Energy density is energy per unit volume, [ML²T⁻²]/[L³] = [ML⁻¹T⁻²], and Young's modulus is stress/strain, also [ML⁻¹T⁻²]. Refractive index and dielectric constant are both dimensionless, but the magnetic field [MT⁻²A⁻¹] matches neither of them.
Q21AIPMT 2008 Prelims · Q2
If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
Not quite — the answer is C.
V = (4/3)πr³, so ΔV/V = 3(Δr/r) = 3 × 2% = 6%. Taking 8% would wrongly cube the error itself instead of multiplying it by the power 3.
Q22AIPMT 2007 Prelims · Q24
Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be
Not quite — the answer is C.
R = V/I and V = W/q has dimensions ML²T⁻²/(IT) = ML²T⁻³I⁻¹, so R = ML²T⁻³I⁻². ML²T⁻³I⁻¹ is the dimension of potential difference, not resistance.
Q23AIPMT 2006 Prelims · Q17
The velocity v of a particle at time t is given by v = at + b/(t + c), where a, b and c are constants. The dimensions of a, b and c are respectively :
Not quite — the answer is A.
Every term must have the dimensions of velocity [LT⁻¹]. From at, a = [LT⁻²]. In b/(t + c), c is added to time so c = [T]; then b/[T] = [LT⁻¹] gives b = [L]. The other choices fail the rule that only like quantities can be added.
Q24AIPMT 2005 Prelims · Q19
The ratio of the dimensions of Planck's constant and that of the moment of inertia is the dimension of :
Not quite — the answer is A.
[h] = ML²T⁻¹ and [I] = ML², so [h/I] = T⁻¹, the dimension of frequency. Angular momentum has the dimensions of h itself, not h/I.
How often Units and Measurements came up
Questions from this chapter in each paper on this site.
- NEET 2021: 3
- NEET 2020: 3
- NEET 2019: 1
- NEET 2018: 1
- NEET 2017: 1
- NEET 2017 (Gujarati paper): 1
- NEET 2016 Phase 2: 1
- AIPMT 2015: 1
- AIPMT 2014: 1
- NEET 2013: 1
- AIPMT 2012 Prelims: 1
- AIPMT 2011 Mains: 1
- AIPMT 2010 Mains: 1
- AIPMT 2010 Prelims: 1
- AIPMT 2009 Prelims: 1
- AIPMT 2008 Prelims: 2
- AIPMT 2007 Prelims: 1
- AIPMT 2006 Prelims: 1
- AIPMT 2005 Prelims: 1
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