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Dimensional Analysis Mastery for NEET ,JEE &CUET:Advanced MCQs Guide(Units & Measurements)

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Introduction: Why Dimensional Analysis Matters for CUET, NEET & JEE Aspirants

Dimensional Analysis is one of the most scoring and conceptually rich chapters in NCERT Class 11 Units & Measurements. Whether you are preparing for CUET Physics, the NEET UG exam, or JEE Main/Advanced, understanding dimensions, units, and the mathematical relationships between physical quantities is absolutely essential.

This chapter offers high-yield marks because:

  • Questions are direct and formula-based

  • No heavy calculation is required

  • Units, dimensions & derived quantities appear across all physics chapters

  • CUET specifically asks multi-concept MCQs with dimensional reasoning

This blog includes:

  • Comprehensive conceptual explanations

  • SEO-rich long-tail keywords such as:
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  • A massive MCQ Practice Section with answers included immediately after each question

Let’s begin mastering one of the most foundational topics of physics.

Understanding Dimensions: A Quick Refresher

Every physical quantity—whether force, pressure, energy, power, or angular momentum—can be represented in terms of the fundamental dimensions:

  • Mass (M)

  • Length (L)

  • Time (T)

  • Electric Current (A)

  • Temperature (K)

  • Amount of Substance (mol)

  • Luminous Intensity (cd)

Derived quantities are expressed using combinations of these base units.
Dimensional analysis allows us to:

✔ Check the correctness of equations
✔ Derive formulas
✔ Convert units
✔ Understand which physical quantities are comparable
✔ Solve CUET, JEE, and NEET MCQs quickly

Why CUET, NEET & JEE Love Dimensional Questions

Dimensional Analysis questions test your understanding of:

  • How physical formulas are structured

  • Whether two quantities can be added or compared

  • Which constants have dimensions

  • How to derive new relations

CUET especially asks MATCH-LIST and assertion–reason type dimensional questions.

CUET/JEE/NEET PRACTICE SECTION — MCQs WITH OPTIONS + ANSWERS

(1) The dimension of E²/μ₀ in mass (M), length (L) and time (T) is (E = electric field, μ₀ = permeability of free space)

a) [M2L3T−2A−2][M²L³T^{-2}A^{-2}]
b) [MLT−4][MLT^{-4}]
c) [ML3T−2][ML³T^{-2}]
d) [ML4T−4][ML⁴T^{-4}]

✔ Answer: b

(2) The dimension of angular momentum in mass (M), length (L) and time (T) is

a) [MLT−1][MLT^{-1}]
b) [ML−1T−1][ML^{-1}T^{-1}]
c) [ML2T−1][ML²T^{-1}]
d) [ML−1T−2][ML^{-1}T^{-2}]

✔ Answer: c

(3) If E and E₀ represent energies, τ and t₀ represent times, which relation is dimensionally correct?

a) E=E0etE = E₀e^t
b) E=E0t0e−t/t0E = E₀ t₀ e^{-t/t₀}
c) E=E0t0e−t2E = E₀ t₀ e^{-t^2}
d) E=E0e−t/t0E = E₀ e^{-t/t₀}

✔ Answer: d

(4) If E = energy and G = gravitational constant, E/G has dimensions:

a) [M2L−1T0][M^2L^{-1}T^0]
b) [ML−1T−1][ML^{-1}T^{-1}]
c) [ML0T0][ML^0T^0]
d) [M2L−2T−1][M^2L^{-2}T^{-1}]

✔ Answer: a

(5) Dimensions of ε0dϕEdt\varepsilon_0 \frac{d\phi_E}{dt} are same as:

a) Potential
b) Current
c) Charge
d) Capacitance

✔ Answer: b

(6) Quantity with neither units nor dimensions:

a) Relative velocity
b) Relative density
c) Angle
d) Energy

✔ Answer: b

(7) If momentum (P), area (A), time (T) are fundamental quantities, dimensional formula for power is:

a) P1/2AT−1P^{1/2}AT^{-1}
b) P2AT−2P^{2}AT^{-2}
c) PA1/2T−2PA^{1/2}T^{-2}
d) PA1T−2PA^{1}T^{-2}

✔ Answer: c

(8) Dimensions of σb4\sigma b^4 (Stefan’s constant × Wien’s constant):

a) [M0L0T0][M^0L^0T^0]
b) [ML4T−3][ML^4T^{-3}]
c) [ML−2T][ML^{-2}T]
d) [ML4T−2][ML^4T^{-2}]

✔ Answer: b

(9) Dimensional formula of ε0μ0\varepsilon_0 \mu_0:

a) [M0L−2T2][M^0L^{-2}T^{2}]
b) [M0L2T−2][M^0L^2T^{-2}]
c) [M0LT−1][M^0LT^{-1}]
d) [M0L−1T][M^0L^{-1}T]

✔ Answer: a

(10) For P = P₀e^{-at²}, dimension of constant a is

a) dimensionless
b) [T−2][T^{-2}]
c) [T2][T^{2}]
d) same as P

✔ Answer: b

(11) Which pair has same dimensions?

a) Force & surface tension
b) Frequency & velocity gradient
c) Angular speed & solid angle
d) Stefan constant & Planck constant

✔ Answer: b

(12) Dimensional formula of AD/B from F = A cos Bx + C sin Dt:

a) [M0LT−1][M^0LT^{-1}]
b) [ML2T−3][ML^2T^{-3}]
c) [MLT−2][MLT^{-2}]
d) [M2L2T−3][M^2L^2T^{-3}]

✔ Answer: b

(13) In P = a – t² / bx (P = pressure), dimension of a/b is:

a) [LT2][LT^2]
b) [MT−2][MT^{-2}]
c) [ML2T−4][ML^2T^{-4}]
d) [M2LT−2][M^2LT^{-2}]

✔ Answer: b

(14) Dimensions of stopping potential:

a) [ML−1T−2A3][ML^{-1}T^{-2}A^3]
b) [M−1L−2T3A2][M^{-1}L^{-2}T^3A^2]
c) [M−2LT−3A−1][M^{-2}LT^{-3}A^{-1}]
d) [ML2T−3A−1][ML^2T^{-3}A^{-1}]

✔ Answer: d

(15) Not dimensionless:

a) Relative permeability
b) Power factor
c) Permeability of free space
d) Quality factor

✔ Answer: c

(16) With F, L, T as fundamental quantities, dimension of density is:

a) FL−4T2FL^{-4}T^2
b) FL−3T2FL^{-3}T^2
c) FL−5T2FL^{-5}T^2
d) FL−3T3FL^{-3}T^3

✔ Answer: a

(17) If (Energy × speed) = [MaLbTc][M^aL^bT^c], values of a, b, c are:

a) (1, 3, –3)
b) (1, 2, 3)
c) (1, 2, 3)
d) (1, 3, –2)

✔ Answer: a

(18) Dimensions of Angle × Force × Length:

a) (1, 1, –1)
b) (1, 2, –2)
c) (1, 1, 1)
d) (1, 2, 2)

✔ Answer: b

(19) Dimensional formula of emissivity:

a) [ML0T−3][ML^0T^{-3}]
b) [ML2T−3][ML^2T^{-3}]
c) [M0L0T0][M^0L^0T^0]
d) [ML2T−2][ML^2T^{-2}]

✔ Answer: c

(20) Same dimensions:

a) Electric displacement & surface charge density
b) Displacement current & electric field
c) Current density & surface charge density
d) Electric potential & energy

✔ Answer: a

(21) Dimensional formula of viscosity using P, A, T:

a) PA−1T0PA^{-1}T^0
b) PAT−2PAT^{-2}
c) PA−1TPA^{-1}T
d) PA−1T−1PA^{-1}T^{-1}

✔ Answer: a

(22) Same dimensions:

a) Velocity gradient & decay constant
b) Wien constant & Stefan constant
c) Angular frequency & angular momentum
d) Wave number & Avogadro number

✔ Answer: a

(23) Pair with different dimensions:

a) Wave number & Rydberg constant
b) Stress & coefficient of elasticity
c) Coercivity & magnetization
d) Specific heat capacity & latent heat

✔ Answer: d

(24) Dimension of mutual inductance:

a) [ML2T−2A−1][ML^2T^{-2}A^{-1}]
b) [ML2T−3A−1][ML^2T^{-3}A^{-1}]
c) [ML2T−2A−2][ML^2T^{-2}A^{-2}]
d) [ML2T−3A−2][ML^2T^{-3}A^{-2}]

✔ Answer: c

(25) Dimensions of B2/μ0B^2/\mu_0:

a) [ML2T−2][ML^2T^{-2}]
b) [MLT−2][MLT^{-2}]
c) [ML−1T−2][ML^{-1}T^{-2}]
d) [ML2T−2A−1][ML^2T^{-2}A^{-1}]

✔ Answer: c

(26) Dimension of density in system of C, G, h is:

a) C3G−2h−1C^3G^{-2}h^{-1}
b) C5G−2h−1C^5G^{-2}h^{-1}
c) C−3/2G−1/2h1/2C^{-3/2}G^{-1/2}h^{1/2}
d) C9/2G−1/2h−1/2C^{9/2}G^{-1/2}h^{-1/2}

✔ Answer: b

(27) Dimensional formula for power of a lens:

a) [L−1M0T0][L^{-1}M^0T^0]
b) [L0M−1T0][L^0M^{-1}T^0]
c) [L0M0T−1][L^0M^0T^{-1}]
d) [L0M0T0][L^0M^0T^0]

✔ Answer: a

(28) Dimensional formula of electric flux:

a) [ML−3T3A−1][ML^{-3}T^3A^{-1}]
b) [ML3T3A−1][ML^3T^3A^{-1}]
c) [ML−3T−3A−1][ML^{-3}T^{-3}A^{-1}]
d) [M−1L3T−3A−1][M^{-1}L^3T^{-3}A^{-1}]

✔ Answer: c

(29) Dimensions of Boltzmann constant:

a) [ML2T−2Θ−1][ML^2T^{-2}\Theta^{-1}]
b) [ML2T−2Θ][ML^2T^{-2}\Theta]
c) [M2LT−2Θ−1][M^2LT^{-2}\Theta^{-1}]
d) [ML0T−2Θ−1][ML^0T^{-2}\Theta^{-1}]

✔ Answer: a

(30) Dimension of angular momentum:

a) [M0L1T−1][M^0L^1T^{-1}]
b) [ML2T−2][ML^2T^{-2}]
c) [ML2T−1][ML^2T^{-1}]
d) [M2L1T−2][M^2L^1T^{-2}]

✔ Answer: c

Conclusion

This long-form article combines all major dimensional analysis concepts, includes exam-level MCQs, and integrates CUET, NEET, and JEE targeted keywords. Solving these questions builds confidence and ensures you can handle both direct and tricky dimensional problems in competitive exams.

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