JEE Main Units and Measurements Previous year Question

1.(JEE Main 2023 (Online) 11th April Morning Shift )

Given below are two statements :

Statements I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances.

Statements II : $Au < Parsec (Pc) < ly$

In the light of the above statements, choose the most appropriate answer from the options given below:

(A) Both Statements I and Statements II are incorrect.

(B) Both Statements I and Statements II are correct,

(C) Statements I is incorrect but Statements II is correct.

(D) Statements I is correct but Statements II is incorrect.

Correct answer is (D)

Statement I is correct. Astronomical unit (AU), parsec (pc), and light year (ly) are indeed units for measuring astronomical distances.

However, Statement II is incorrect. The correct order of these units is:

$AU < ly < Parsec (Pc)$

1 AU is the average distance from the Earth to the Sun, which is about 93 million miles or 150 million kilometers.

1 light year is the distance that light travels in one year in a vacuum, which is approximately 9.461 trillion kilometers (5.878 trillion miles).

1 parsec is equal to about 3.26 light years, or approximately 30.9 trillion kilometers (19.2 trillion miles).

So, the correct answer is Statement I is correct but Statement II is incorrect.

2.(JEE Main 2023 (Online) 30th January Evening Shift )

Match List I with List II:

List I		List II
A.	Torque	I.	$kg m^{- 1} s^{- 2}$
B.	Energy density	II.	$kg {ms}^{- 1}$
C.	Pressure gradient	III.	$kg m^{- 2} s^{- 2}$
D.	Impulse	IV.	$kg m^{2} s^{- 2}$

Choose the correct answer from the options given below:

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

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

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

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

Correct answer is (A)

Torque $\to$ kg m $^{2}$ s $^{- 2}$ (IV)

Energy density $\to$ kg m $^{- 1}$ s $^{- 2}$ (I)

Pressure gradient $\to$ kg m $^{- 2}$ s $^{- 2}$ (III)

Impulse $\to$ kg m s $^{- 1}$ (II)

3.(JEE Main 2022 (Online) 29th July Evening Shift )

Match List I with List II.

	List I		List II
A.	Torque	I.	Nms $^{- 1}$
B.	Stress	II.	J kg $^{- 1}$
C.	Latent Heat	III.	Nm
D.	Power	IV.	Nm $^{- 2}$

Choose the correct answer from the options given below :

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

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

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

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

Correct answer is (B)

Torque $\to Nm$

Stress $\to N / m^{2}$

Latent heat $\to J / kg$

Power $\to N m / s$

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

4.(JEE Main 2021 (Online) 27th August Evening Shift )

Match List - I with List - II.

	List - I		List - II
(a)	$R_{H}$ (Rydberg constant)	(i)	$k g m^{- 1} s^{- 1}$
(b)	h (Planck's constant)	(ii)	$k g m^{2} s^{- 1}$
(c)	$μ_{B}$ (Magnetic field energy density)	(iii)	$m^{- 1}$
(d)	$η$ (coefficient of viscocity)	(iv)	$k g m^{- 1} s^{- 2}$

Choose the most appropriate answer from the options given below :

(A) (a)-(ii), (b)-(iii), (c)-(iv), (d)-(i)

(B) (a)-(iii), (b)-(ii), (c)-(iv), (d)-(i)

(C) (a)-(iv), (b)-(ii), (c)-(i), (d)-(iii)

(D) (a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)

Correct answer is (B)

SI unit of Rydberg const. = m^{$-$ 1}

SI unit of Plank's const. = kg m²s^{$-$ 1}

SI unit of Magnetic field energy density = kg m^{$-$ 1}s^{$-$ 2}

SI unit of coeff. of viscosity = kg m^{$-$ 1}s^{$-$ 1}

5.(JEE Main 2021 (Online) 27th August Morning Shift )

If E and H represents the intensity of electric field and magnetising field respectively, then the unit of E/H will be :

(A) ohm

(B) mho

(C) joule

(D) newton

Correct answer is (A)

Unit of $\frac{E}{H}$ is $\frac{v o l t / m e t r e}{A m p e r e / m e t r e} = \frac{v o l t}{A m p e r e} = o h m$