JEE Advanced (One or More Correct Option): Units & Measurement | Chapter-wise Tests for JEE Main & Advanced PDF Download

Q.1. Which of the following sets cannot enter into the list of fundamental quantities in any newly proposed system of units?
(a) length, mass and velocity
(b) pressure, density and velocity
(c) force, velocity and time
(d) force, momentum and time

Correct Answer is option (b, d)
For (A): Length [L], mass [M] and velocity [LT^–1] are independent.
For (B):  Pressure [M'L^–1T^–2], density [M'L^–3T⁰] and velocity [M⁰LT^–1] are dependent as
= 1(3 - 0) + 1(-1-0) -2(1 - 0) = 0
Note: Like coplanar vectors, for dependent quantites, determinant of powers of M, L, T’s must be zero.
For (C): Force [MLT^–2], velocity [LT^–1] and time [T] are independent as
 = 1(1 - 0) - 1 (0 - 0) - 2(0 - 0) = 1 ≠ 0
For (D): ⇒ force, momentum and time are dependent.

Q.2. If A and B are two physical quantities having different dimensions then which of the following can denote a new physical quantity?
(a)  A + A³/B
(b) exp (-A/B)
(c) AB² 
(d) A/B⁴

Correct Answer is option (a, c and d)
For (A): A and A³/B may have same dimension.
For (B): As A and B have different dimension so exp
meaningless.

For (C): AB² is meaningful.

For (D): AB^–4 is meaningful.

Q.3. If the dimensions of a physical quantity are given by M^xL^yT^z, then physical quantity may be
(a) acceleration due to gravity, if x = 0, y = 1, z = –2
(b) atmospheric pressure, if x = 1, y = 1, z = –2
(c) linear momentum, if x = 1, y = 1, z = –1
(d) potential energy, if x = 1, y = 2, z = –2

Correct Answer is option (a, c and d)
For (A): [Acceleration] = [LT^–2]
For (B): [Pressure] = [ML^–1T^–2]
For (C): [Momentum] = [MLT^–1]
For (D): [Energy] = [ML²T^–2]

Q.4. The Vander wall's equation for n moles of a real gas is given by  (v - nb) =  nRT, where P = pressure of gas
V = volume of gas
T = temperature of gas
R = molar gas constant
a & b = Vander wall's constants
Which of the following have the same dimensions as those of nRT.
(a) PV
(b) αV/b²
(c) PV²/nb
(d) nα/b

Correct Answer is option (a, b, c and d)

Here [P] = so [PV] = [nRT]
Also ⇒

Q.5. Let [∈₀] denote the dimensional formula of the permittivity of the vacuum and [µ₀] that of the permeability of the vacuum. If M = mass, L = length, T = time and I = electric current-
(a) [∈₀] = [M^-1L^-3T² I]
(b) [∈₀] = [M^-1L^-3T⁴ I²]
(c) [μ₀] = [MLT^-2 I^-2]
(d) [μ₀] = [ML²T^-1 I]

Correct Answer is option (b and c)

⇒ MLT^-2 =
⇒ [1/∈₀]= M¹L³A^–2T^–4  ⇒ [∈₀] = M^-1L^-3A + ²T⁴

[ML^–2] = [μ₀A²/L] ⇒  MLT^-2T^-2

Q.6. The SI unit of the inductance, the henry can by written as –
(a) Weber/ampere
(b) Volt–second/ampere
(c) Joule/(ampere)²
(d) Ohm–second 

Correct Answer is option (a, b, c and d)

 (Henery)

E = 1/2 

= Time constant; [L] = ohm–sec f = LI Þ weber Ampere = L(Henery) 

E = 1/2 ⇒ LI² =

Q.7. Dimension of Young's Modulus are same as
(a) Pressure
(b) Energy density
(c) Work per unit volume
(d) Torque

Correct Answer is option (a, b, c)

Q.8. Select the correct one -
(a) 1.5 × 1.5 = 2.3
(b) 1.5 × 1.5 = 2.2
(c) 1.5/1.5 = 1
(d) 1.5/1.5= 1.0

Correct Answer is option (b and d)
1.5 × 1.5 = 2.25
= 2.2 (2 Significant figure)
1.5/1.5 = 1.0 (2 significant figure)

Q.9. A book with many printing errors contains four different expressions for the displacement y of a particle executing simple harmonic motion -
(a) y = A sin (2πt/T)
(b) y = A sin vt
(c) y = (A/T) sin (t/A)
(d) y = (A/√2 ) (sin ωt + cos ωt) 

Correct Answer is option (b and c)
Find the wrong formulae on dimensional ground. (where A is length)
[vt] ≠ 1 ∴ option B wrong
[A/T] ≠ [y] ∴ option C wrong 

Q.10. Acceleration of a particle is given by a = Ax + B - x²/C , where x is position of the particle and A, B and C are constant
(a) Dimensional formula of A is [T^–2]
(b) Dimensional formula of B is [L²T^–2]
(c) Dimensional formula of C is [L⁺¹ T⁺²]
(d) Dimensional formula of B/C is [LT^–2]

Correct Answer is option (A, c and d)

[a] = [A] [x]