JEE Main Units and Measurement PYQs [2020-2024]

A vernier caliper has 10 main scale divisions coinciding with 11 vernier scale divisions. 1 main scale division equals 5 mm. The least count of the device is

(A) 1/2 mm
(B) 5/2 mm
(C) 5/11 mm
(D) 0.3 mm

Statement-I : Positive zero error is added in measurement. 
Statement-II : Defect may occurs during manufacturing of measuring instruments. 

(A) Statement-I is correct while statement-II is wrong 
(B) Statement-I is wrong while statement-II is correct 
(C) Both statements are wrong 
(D) Both statements are correct

In a vernier caliper 49 main scale divisions are equal to 50 vernier scale divisions. If one main scale division is 0.5 mm, then the vernier constant is

(A) 0.01 mm
(B) 0.1 mm
(C) 0.1 cm
(D) 0.01 cm

Match List I with List II [JEE Main 2023]

Choose the correct answer from the options given below.

(A) A-I, B-III, C-IV, D-II
(B) A-I, B-II, C-III, D-IV
(C) A-II, B-III, C-IV, D-I
(D) A-III, B-I, C-II, D-IV

Match List I with List II [JEE Main 2023]

Choose the correct answer from the options given below:

(A) A – IV, B – II, C – I, D – III
(B) A – II, B – III, C – IV, D – I
(C) A – III, B – I, C – IV, D – II
(D) A – I, B – IV, C – III, D – II

Match column I with column II and choose the correct option.

(A) I → a, II → c, III → b, IV → d
(B) I → d, II → b, III → c, IV → a
(C) I → d, II → c, III → b, IV → a
(D) I → a, II → c, III → d, IV → b

Match the physical quantity in column-I with the respective dimension in column-II and choose the correct option.

(A) I(P), II(Q), III(R), IV(S)
(B) I(R), II(P), III(Q), IV(S)
(C) I(R), II(S), III(Q), IV(P)
(C) I(R), II(P), III(S), IV(Q)

Match List I with List II: 

Choose the correct answer from the options given below: 

(A) A-IV, B-I, C-III, D-II
(B) A-I, B-IV, C-III, D-II
(C) A-IV, B-III, C-I, D-II
(D) A-IV, B-I, C-II, D-III

$(P + \frac a{V^2}) (V – b) = RT$ represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^2}a$ , will be

(A) Bulk modulus
(B) Modulus of rigidity
(C) Compressibility
(D) Energy density

The frequency (v) of an oscillating liquid drop may depend upon radius (r) of the drop, density (p) of liquid and the surface tension (s) The values of a, b and c respectively are of the liquid as: v = r^ap^bs^c

(A) $\left(-\frac 32, -\frac 12, \frac 12\right)$
(B) $\left(\frac 32, -\frac 12, \frac 12\right)$
(C) $\left(\frac 32, \frac 12, -\frac 12\right)$
(D) $\left(-\frac 32, \frac 12, \frac 12\right)$

Density (p) of a body depends on the force applied (F), its speed (v) and time of motion (t) by the relation p = KF^av^bt^c , where K is a dimensionless constant. Then

(A) a=1, b=-4 and c=-2
(B) a=2, b=-4 and c=-1
(C) a=-1, b=-4 and c=2
(D) a=1, b=4 and c=-2

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

(A) [PA⁻¹T⁰]
(B) [PAT⁻¹]
(C) [PA⁻¹T]
(D) [PA⁻¹T⁻¹]

The equation of a circle is given by 𝑥²+𝑦²=𝑎², where 𝑎 is the radius. If the equation is modified to change the origin other than (0,0) then. find out the correct dimensions of A and B in a new equation : (𝑥−𝐴𝑡)²+(𝑦−𝑡𝐵)²=𝑎². The dimensions of 𝑡 is given as [T⁻¹].

(A) A=[LT], B=[L⁻¹T⁻¹]
(B) A=[L⁻¹T⁻¹], B=[LT]
(C) A=[L⁻¹T], B=[LT⁻¹]
(D) A=[L⁻¹T⁻¹], B=[LT⁻¹]

If frequency can be represented as f = (radius)a (density)b (surface tension)c. Find a, b, c?

(A) $\left(\frac 32, \frac 12, -\frac 12\right)$
(B) $\left(-\frac 32, -\frac 12, \frac 12\right)$
(C) $\left(-\frac 32, \frac 12, -\frac 12\right)$
(D) $\left(\frac 12, \frac 32, -\frac 12\right)$

Which of the following physical quantities have the same dimensions?

(A) Electric displacement ($\vec D$) and surface charge density
(B) Displacement current and electric field
(C) Current density and surface charge density
(D) Electric potential and energy

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

(A) F²V^–2T⁶
(B) FV⁴T^–6
(C) FV^–2T²
(D) FV^–4T^–2

R₁ = (15 ± 0.5) Ω
R₂ = (10 ± 0.5) Ω
Find % error in equivalent resistance if resistors R₁ and R₂ are connected in parallel ? 

(A) 5%
(B) 4.33%
(C) 3%
(D) 3.33%

What is the maximum percentage error in the measurement of quantity l, if it is given by l = a²b² ⁄ c√d . Given the percentage error in the calculation of a, b, c and d are 1%, 2%, 3% and 4% respectively

(A) 11%
(B) 12%
(C) 9%
(D) 13%

Two resistances are given as R1 = (10±0.5)Ω and R2 = (15±0.5)Ω. The percentage error in the measurement of equivalent resistance when they are connected in parallel is

(A) 6.33 
(B) 2.33 
(C) 4.33
(D) 5.33

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Range is maximum at θ = 45º.
Reason (R): Range is maximum when sin (2θ) = 1.
In the light of the above statements, choose the correct answer from the options given below:

(A) Both (A) and (R) are true & (R) is the correct explanation of assertion.
(B) Both (A) and (R) are true but (R) is not correct explanation of assertion.
(C) (A) is true and (R) is false.
(D) (A) is false and (R) is false.

If mass, radius of cross-section and height of a cylinder are (0.4+0.01) g, (6+0.03) m and height (8+0.04) m. The maximum percentage error in the measurement of density of cylinder is?

(A) 1%
(B) 4%
(C) 8%
(D) 7%

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%,2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be

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

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab at 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is x/10 x 10^-3 , where x is ______

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by 0.5 mm on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while 46th division the circular scale coincide with the reference line. The diameter of the wire is ______ × 10^-2 mm