Dimension of a Physical Quantity

Q 21 :

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

$F V^{- 2} T^{2}$
$F V^{- 4} T^{- 2}$
$F V^{4} T^{2}$
$F^{2} V^{- 2} T^{6}$

1

2

3

4

(2)

$M^{1} L^{- 3} T^{0} = {(M^{1} L T^{- 2})}^{a} {(L T^{- 1})}^{b} T^{c}$

$a = 1, b = - 4, c = - 2$

Q 22 :

The electric resistance of medium depends upon permeability $(μ)$ and permittivity $(ε)$ as given below $R \propto {(μ)}^{a} {(ε)}^{b}$ . If $a - b = N$ . The value of N is ...........

(1)

$M L^{2} T^{- 3} A^{- 2} = {[M L T^{- 2} A^{- 2}]}^{a} {[M^{- 1} L^{- 3} T^{4} A^{2}]}^{b}$

$a - b = 1$

$a - 3 b = 2$

$a = \frac{1}{2}, b = - \frac{1}{2}$

Q 23 :

An expression of energy density is given by $u = \frac{α}{β} \sin (\frac{α x}{k t})$ . Where $α, β$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the absolute temperature. The dimensions of $β$ will be:

$[M L^{2} T^{- 2} θ^{- 1}]$
$[M^{0} L^{2} T^{- 2}]$
$[M^{0} L^{0} T^{0}]$
$[M^{0} L^{2} T^{0}]$

1

2

3

4

(4)

$\sin (\frac{α x}{k t}) = Dimensionless$

$∴$ $\frac{α [L]}{[M L^{2} T^{- 2}]} = [M^{0} L^{0} T^{0}]$ $\Rightarrow α = [M L T^{- 2}]$

$\frac{α}{β} = \frac{Energy}{Volume} = \frac{[M L^{2} T^{- 2}]}{[L^{3}]}$

$\Rightarrow β = \frac{[M L T^{- 2}] [L^{3}]}{[M L^{2} T^{- 2}]}$

$= [M^{0} L^{2} T^{0}]$

Q 24 :

If F is force, V is velocity, H is latent heat, and s is specific heat, then match the quantity given in Column I with the dimensions given in Column II.

Column I Column II

i. F a. $L^{2} T^{- 2}$

ii. V b. $L^{2} T^{- 2} K^{- 1}$

iii. H c. $M L T^{- 2}$

iv. S d. $L T^{- 1}$

i → c, ii → d, iii → a, iv → b
i → a, ii → b, iii → c, iv → d
i → d, ii → a, iii → b, iv → c
i → c, ii → a, iii → b, iv → d

1

2

3

4

(1)

$i i i .$ $[H] =$ $[\frac{H e a t}{M a s s}] = \frac{M L^{2} T^{- 2}}{M} = L^{2} T^{- 2}$

$i v .$ $[s] = [\frac{H e a t}{M a s s \times T e m p e r a t u r e}] = \frac{M L^{2} T^{- 2}}{M K} = L^{2} T^{- 2} K^{- 1}$

Q 25 :

Match list I with list II:

List I List II

a) Torque (i) $M L T^{- 1}$

b) Impulse (ii) $M T^{- 2}$

c) Tension (iii) $M L^{2} T^{- 2}$

d) Surface tension (iv) $M L T^{- 2}$

Choose the most appropriate answer from the options given below:

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

1

2

3

4

(2)

$Torque - M L^{2} T^{- 2}$

$Impulse - M L T^{- 1}$

$Tension - M L T^{- 2}$

$Surface tension - M T^{- 2}$

Q 26 :

The dimensional formula of $\frac{1}{2} ε_{0} E^{2}$ ( $ε_{0}$ = permittivity of vacuum and $E$ = electric field) is $M^{a} L^{b} T^{c}$ . The value of $2 a - b + c$ = ______. [2026]

0
1
-1
2

1

2

3

4

(2)

$\frac{1}{2} ε_{0} E^{2} = \frac{d u}{d v} = \frac{Energy}{Volume}$

$∴$ $[\frac{1}{2} ε_{0} E^{2}] = \frac{M L^{2} T^{- 2}}{L^{3}} = M L^{- 1} T^{- 2}$

$∴$ $a = 1, b = - 1, c = - 2$

$∴$ $2 a - b + c = 2 + 1 - 2 = 1$

Q 27 :

Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$ , distance $(L)$ , mass $(M)$ and time $(T)$ are ______. [2026]

$[h T L M^{- 2}]$
$[h T^{- 1} L M^{- 2}]$
$[h T L^{2} M^{- 2}]$
$[h^{- 1} T^{- 1} L M^{- 2}]$

1

2

3

4

(2)

$G = M^{- 1} L^{3} T^{- 2}$ $. . . (i)$

$h = M L^{2} T^{- 1}$ $. . . (i i)$

$Dividing eq. (i) to eq. (ii)$

$\frac{G}{h} = \frac{M^{- 1} L^{3} T^{- 2}}{M L^{2} T^{- 1}}$

$G = M^{- 2} L T^{- 1} h^{1}$

Q 28 :

Match List-I with List-II.

List-I List-II

A. Planck’s constant I. $M L^{2} T^{- 2}$

B. Stopping potential II. $T^{- 1}$

C. Work function III. $M L^{2} T^{- 1}$

D. Threshold frequency IV. $M L^{2} T^{- 3} A^{- 1}$

Choose the correct answer from the options given below: [2026]

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

1

2

3

4

(1)

(A) $[h] = \frac{[E]}{[ν]} = \frac{M L^{2} T^{- 2}}{T^{- 1}} = M L^{2} T^{- 1}$

(B) $Stopping potential: E = q \cdot V_{0}$

$[V_{0}] = \frac{[E]}{[q]} = \frac{M L^{2} T^{- 2}}{A T} = M L^{2} T^{- 3} A^{- 1}$

(C) $Work function (ϕ) \to Energy form [ϕ] = M L^{2} T^{- 2}$

(D) $Threshold freq. [ν_{0}] = T^{- 1}$

Q 29 :

L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula $M L^{2} T^{- 4} A^{- 2}$ corresponds to ______. [2026]

$\frac{R}{\sqrt{L C}}$
$\frac{R}{L C}$
$\frac{C}{\sqrt{L R}}$
$\frac{1}{R} \sqrt{\frac{L}{C}}$

1

2

3

4

(1)

$R = \frac{V}{I} = \frac{W}{q I} = \frac{[M L^{2} T^{- 2}]}{[A^{2} T]} = [M L^{2} T^{- 3} A^{- 2}]$

$U = \frac{1}{2} L I^{2} \Rightarrow [M L^{2} T^{- 2}] = [L] [A^{2}]$

$[L] = [M L^{2} T^{- 2} A^{- 2}]$

$Q = C V \Rightarrow [A T] = [C] [M L^{2} T^{- 3} A^{- 1}]$

$[C] = [M^{- 1} L^{- 2} T^{4} A^{2}]$

$[L C] = [M L^{2} T^{- 2} A^{- 2}] \times [M^{- 1} L^{- 2} T^{4} A^{2}] = [T^{2}]$

$\frac{R}{\sqrt{L C}} = \frac{[M L^{2} T^{- 3} A^{- 2}]}{[T]} = [M L^{2} T^{- 4} A^{- 2}]$

Q 30 :

Match List-I with List-II.

List-I List-II

A. Meter (L) I. $\sqrt{\frac{h c}{G}}$

B. Second (S) II. $\sqrt{\frac{G h}{c^{5}}}$

C. Kilogram (M) III. $\sqrt{\frac{K^{2} L^{2} c^{3}}{G h}}$

D. Kelvin (K) IV. $\sqrt{\frac{G h}{c^{3}}}$

where $h$ (Planck’s constant), $G$ (gravitational constant) and $c$ (speed of light in vacuum) as fundamental units.

Choose the correct answer from the options given below: [2026]

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

1

2

3

4

(2)

$[h] = [M L^{2} T^{- 1}]$

$[c] = [L T^{- 1}] and [G] = [M^{- 1} L^{3} T^{- 2}]$

$then [\sqrt{\frac{h c}{G}}] = {[\frac{M L^{2} T^{- 1} L T^{- 1}}{M^{- 1} L^{3} T^{- 2}}]}^{1 / 2} = [M]$

$[\sqrt{\frac{G h}{c^{5}}}] = {[\frac{M^{- 1} L^{3} T^{- 2} M L^{2} T^{- 1}}{L^{5} T^{- 5}}]}^{1 / 2} = [T]$

$[\sqrt{\frac{K^{2} L^{2} c^{3}}{G h}}] = {[\frac{K^{2} L^{2} L^{3} T^{- 3}}{M^{- 1} L^{3} T^{- 2} M L^{2} T^{- 1}}]}^{1 / 2} = [K]$

$[\sqrt{\frac{G h}{c^{3}}}] = {[\frac{M^{- 1} L^{3} T^{- 2} M L^{2} T^{- 1}}{L^{3} T^{- 3}}]}^{1 / 2} = [L]$

$A→IV, B→II, C→I, D→III$

Q 31 :

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A \sqrt{x}}{x + B}$ , where $A$ and $B$ are constant with appropriate dimensions. The dimension of $A B$ are ______. [2026]

$[M^{1} L^{5 / 2} T^{- 2}]$
$[M^{3 / 2} L^{5 / 2} T^{- 2}]$
$[M^{1} L^{2} T^{- 2}]$
$[M^{1} L^{7 / 2} T^{- 2}]$

1

2

3

4

(4)

$[B] = [x] = [L]$

$[A] = \frac{[P E] \times [length]}{\sqrt{length}} = \frac{M L^{2} T^{- 2} \times L}{L^{1 / 2}}$

$[A] = [M L^{5 / 2} T^{- 2}]$

$[A \cdot B] = [M L^{5 / 2} T^{- 2}] \times [L] = [M L^{7 / 2} T^{- 2}]$

Q 32 :

Match List-I with List-II. [2026]

List-I List-II

A. Boltzmann constant I. $[M^{- 1} L^{3} T^{- 2}]$

B. Stefan’s constant II. $[M L^{2} T^{- 1}]$

C. Planck’s constant III. $[M L^{2} T^{- 2} K^{- 1}]$

D. Gravitational constant IV. $[M L^{0} T^{- 3} K^{- 4}]$

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

1

2

3

4

(3)

$Boltzmann constant = \frac{Energy}{Temp.}$

$\Rightarrow [k] = [M L^{2} T^{- 2} K^{- 1}]$

$σ \Rightarrow \frac{P}{A T^{4}} \Rightarrow [σ] = [M^{1} T^{- 3} K^{- 4}]$

$h = \frac{E}{ν} = E \cdot t \Rightarrow [h] = [M^{1} L^{2} T^{- 1}]$

$G = \frac{F r^{2}}{m^{2}} \Rightarrow [G] = [M^{- 1} L^{3} T^{- 2}]$

$Option (3) is correct.$

Q 33 :

Consider the equation $H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

Where $H$ = magnetising intensity; $E$ = electric field; $ε$ = permittivity, $x$ = distance, $t$ = time. The values of $p, q, r$ and $s$ respectively are [2026]

1, 1, 1, 1
-1, 1, 2, 1
1, -1, -2, 1
-1, -2, -2, 1

1

2

3

4

(1)

$As per problem if we take H as magnetic field then no option matching but if we take H as magnetising intensity instead of magnetic field then only we get answer$

$H = \frac{B}{μ_{0}} - N i \Rightarrow current per unit length$

$\Rightarrow [H] = [A L^{- 1}]$

$[E] = \frac{[M L T^{- 2}]}{[I T]} = [M L A^{- 1} T^{- 3}]$

$[ε] = \frac{[I^{2} T^{2}]}{[M L T^{- 2} L^{2}]} = [M^{- 1} L^{- 3} I^{2} T^{4}]$

$H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

$A L^{- 1} = \frac{L^{p} {(M^{- 1} L^{- 3} T^{4} A^{2})}^{q} {(M L T^{- 3} A^{- 1})}^{r}}{T^{s}}$

$- q + r = 0$ $. . . (i)$

$p - 3 q + r = - 1$ $. . . (i i)$

$4 q - 3 r - s = 0$ $. . . (i i i)$

$2 q - r = 1$ $. . . (i v)$

$Solving (i), (ii), (iii) and (iv)$

$p = 1, q = 1, r = 1, s = 1$

Q 34 :

A ball of radius $r$ and density $ρ$ dropped through a viscous liquid of density $σ$ and viscosity $η$ attains its terminal velocity at time $t$ , given by $t = A ρ^{a} r^{b} η^{c} σ^{d}$ , where $A$ is a constant and $a, b, c$ and $d$ are integers. The value of $\frac{b + c}{a + d}$ is ______. [2026]

(1)

$T^{1} = {[M L^{- 3}]}^{a} {[L]}^{b} {[M L^{- 1} T^{- 1}]}^{c} {[M L^{- 3}]}^{d}$

$M^{0} L^{0} T^{1} = M^{a + c + d} L^{- 3 a + b - c - 3 d} T^{- c}$

$On comparing$

$a + c + d = 0$ $. . . (i)$

$- 3 a + b - c - 3 d = 0$ $. . . (i i)$

$- c = 1$ $. . . (i i i)$

$From (i) and (iii): a + d = 1$

$From (ii): a + d = \frac{b - c}{3}$

$\frac{b + 1}{3} = 1 \Rightarrow b = 2$

$b + c = 2 + (- 1) = 1$

$\Rightarrow \frac{b + c}{a + d} = \frac{1}{1} = 1$

Topic Question Set

Q 21 :

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

Q 22 :

The electric resistance of medium depends upon permeability $(μ)$ and permittivity $(ε)$ as given below $R \propto {(μ)}^{a} {(ε)}^{b}$ . If $a - b = N$ . The value of N is ...........

Q 23 :

An expression of energy density is given by $u = \frac{α}{β} \sin (\frac{α x}{k t})$ . Where $α, β$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the absolute temperature. The dimensions of $β$ will be:

Q 24 :

If F is force, V is velocity, H is latent heat, and s is specific heat, then match the quantity given in Column I with the dimensions given in Column II.

Column I Column II

i. F a. $L^{2} T^{- 2}$

ii. V b. $L^{2} T^{- 2} K^{- 1}$

iii. H c. $M L T^{- 2}$

iv. S d. $L T^{- 1}$

Q 25 :

Match list I with list II:

List I List II

a) Torque (i) $M L T^{- 1}$

b) Impulse (ii) $M T^{- 2}$

c) Tension (iii) $M L^{2} T^{- 2}$

d) Surface tension (iv) $M L T^{- 2}$

Choose the most appropriate answer from the options given below:

Q 26 :

The dimensional formula of $\frac{1}{2} ε_{0} E^{2}$ ( $ε_{0}$ = permittivity of vacuum and $E$ = electric field) is $M^{a} L^{b} T^{c}$ . The value of $2 a - b + c$ = ______. [2026]

Q 27 :

Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$ , distance $(L)$ , mass $(M)$ and time $(T)$ are ______. [2026]

Q 28 :

Match List-I with List-II.

List-I List-II

A. Planck’s constant I. $M L^{2} T^{- 2}$

B. Stopping potential II. $T^{- 1}$

C. Work function III. $M L^{2} T^{- 1}$

D. Threshold frequency IV. $M L^{2} T^{- 3} A^{- 1}$

Choose the correct answer from the options given below: [2026]

Q 29 :

L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula $M L^{2} T^{- 4} A^{- 2}$ corresponds to ______. [2026]

Q 31 :

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A \sqrt{x}}{x + B}$ , where $A$ and $B$ are constant with appropriate dimensions. The dimension of $A B$ are ______. [2026]

Q 32 :

Match List-I with List-II. [2026]

List-I List-II

A. Boltzmann constant I. $[M^{- 1} L^{3} T^{- 2}]$

B. Stefan’s constant II. $[M L^{2} T^{- 1}]$

C. Planck’s constant III. $[M L^{2} T^{- 2} K^{- 1}]$

D. Gravitational constant IV. $[M L^{0} T^{- 3} K^{- 4}]$

Q 33 :

Consider the equation $H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

Where $H$ = magnetising intensity; $E$ = electric field; $ε$ = permittivity, $x$ = distance, $t$ = time. The values of $p, q, r$ and $s$ respectively are [2026]

Want Us to Email you About Special Offers & Updates?

	Column I		Column II
i.	F	a.	$L^{2} T^{- 2}$
ii.	V	b.	$L^{2} T^{- 2} K^{- 1}$
iii.	H	c.	$M L T^{- 2}$
iv.	S	d.	$L T^{- 1}$

	List I		List II
a)	Torque	(i)	$M L T^{- 1}$
b)	Impulse	(ii)	$M T^{- 2}$
c)	Tension	(iii)	$M L^{2} T^{- 2}$
d)	Surface tension	(iv)	$M L T^{- 2}$

	List-I		List-II
A.	Planck’s constant	I.	$M L^{2} T^{- 2}$
B.	Stopping potential	II.	$T^{- 1}$
C.	Work function	III.	$M L^{2} T^{- 1}$
D.	Threshold frequency	IV.	$M L^{2} T^{- 3} A^{- 1}$

	List-I		List-II
A.	Meter (L)	I.	$\sqrt{\frac{h c}{G}}$
B.	Second (S)	II.	$\sqrt{\frac{G h}{c^{5}}}$
C.	Kilogram (M)	III.	$\sqrt{\frac{K^{2} L^{2} c^{3}}{G h}}$
D.	Kelvin (K)	IV.	$\sqrt{\frac{G h}{c^{3}}}$

	List-I		List-II
A.	Boltzmann constant	I.	$[M^{- 1} L^{3} T^{- 2}]$
B.	Stefan’s constant	II.	$[M L^{2} T^{- 1}]$
C.	Planck’s constant	III.	$[M L^{2} T^{- 2} K^{- 1}]$
D.	Gravitational constant	IV.	$[M L^{0} T^{- 3} K^{- 4}]$

Topic Question Set

Q 21 : If force (F), velocity (V) and time (T) are considered as fundamental physical quantities, then dimensional formula of density will be:

Q 22 : The electric resistance of medium depends upon permeability (μ) and permittivity (ε) as given below R∝(μ)a(ε)b. If a-b=N. The value of N is ...........

Q 23 : An expression of energy density is given by u=αβsin(αxkt). Where α,β are constants, x is displacement, k is Boltzmann constant and t is the absolute temperature. The dimensions of β will be:

Q 24 : If F is force, V is velocity, H is latent heat, and s is specific heat, then match the quantity given in Column I with the dimensions given in Column II. Column I Column II i. F a. L2T-2 ii. V b. L2T-2K-1 iii. H c. MLT-2 iv. S d. LT-1

Q 25 : Match list I with list II: List I List II a) Torque (i) MLT-1 b) Impulse (ii) MT-2 c) Tension (iii) ML2T-2 d) Surface tension (iv) MLT-2 Choose the most appropriate answer from the options given below:

Q 26 : The dimensional formula of 12ε0E2 (ε0 = permittivity of vacuum and E = electric field) is MaLbTc. The value of 2a-b+c = ______. [2026]

Q 27 : Dimensions of universal gravitational constant (G) in terms of Planck's constant (h), distance (L), mass (M) and time (T) are ______. [2026]

Q 28 : Match List-I with List-II. List-I List-II A. Planck’s constant I. ML2T-2 B. Stopping potential II. T-1 C. Work function III. ML2T-1 D. Threshold frequency IV. ML2T-3A-1 Choose the correct answer from the options given below: [2026]

Q 29 : L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula ML2T-4A-2 corresponds to ______. [2026]

Q 31 : The potential energy of a particle changes with distance x from a fixed origin as V=Axx+B, where A and B are constant with appropriate dimensions. The dimension of AB are ______. [2026]

Q 32 : Match List-I with List-II. [2026] List-I List-II A. Boltzmann constant I. [M-1L3T-2] B. Stefan’s constant II. [ML2T-1] C. Planck’s constant III. [ML2T-2K-1] D. Gravitational constant IV. [ML0T-3K-4]

Q 33 : Consider the equation H=xpεqErts Where H = magnetising intensity; E = electric field; ε = permittivity, x = distance, t = time. The values of p, q, r and s respectively are [2026]

Q 34 : A ball of radius r and density ρ dropped through a viscous liquid of density σ and viscosity η attains its terminal velocity at time t, given by t=Aρarbηcσd, where A is a constant and a,b,c and d are integers. The value of b+ca+d is ______. [2026]

Want Us to Email you About Special Offers & Updates?

Q 21 :

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

Q 22 :

The electric resistance of medium depends upon permeability $(μ)$ and permittivity $(ε)$ as given below $R \propto {(μ)}^{a} {(ε)}^{b}$ . If $a - b = N$ . The value of N is ...........

Q 23 :

An expression of energy density is given by $u = \frac{α}{β} \sin (\frac{α x}{k t})$ . Where $α, β$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the absolute temperature. The dimensions of $β$ will be:

Q 24 :

If F is force, V is velocity, H is latent heat, and s is specific heat, then match the quantity given in Column I with the dimensions given in Column II.

Column I Column II

i. F a. $L^{2} T^{- 2}$

ii. V b. $L^{2} T^{- 2} K^{- 1}$

iii. H c. $M L T^{- 2}$

iv. S d. $L T^{- 1}$

Q 25 :

Match list I with list II:

List I List II

a) Torque (i) $M L T^{- 1}$

b) Impulse (ii) $M T^{- 2}$

c) Tension (iii) $M L^{2} T^{- 2}$

d) Surface tension (iv) $M L T^{- 2}$

Choose the most appropriate answer from the options given below:

Q 26 :

The dimensional formula of $\frac{1}{2} ε_{0} E^{2}$ ( $ε_{0}$ = permittivity of vacuum and $E$ = electric field) is $M^{a} L^{b} T^{c}$ . The value of $2 a - b + c$ = ______. [2026]

Q 27 :

Dimensions of universal gravitational constant $(G)$ in terms of Planck's constant $(h)$ , distance $(L)$ , mass $(M)$ and time $(T)$ are ______. [2026]

Q 28 :

Match List-I with List-II.

List-I List-II

A. Planck’s constant I. $M L^{2} T^{- 2}$

B. Stopping potential II. $T^{- 1}$

C. Work function III. $M L^{2} T^{- 1}$

D. Threshold frequency IV. $M L^{2} T^{- 3} A^{- 1}$

Choose the correct answer from the options given below: [2026]

Q 29 :

L, C and R represents physical quantities inductance capacitance and resistance respectively. The dimensional formula $M L^{2} T^{- 4} A^{- 2}$ corresponds to ______. [2026]

Q 31 :

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A \sqrt{x}}{x + B}$ , where $A$ and $B$ are constant with appropriate dimensions. The dimension of $A B$ are ______. [2026]

Q 32 :

Match List-I with List-II. [2026]

List-I List-II

A. Boltzmann constant I. $[M^{- 1} L^{3} T^{- 2}]$

B. Stefan’s constant II. $[M L^{2} T^{- 1}]$

C. Planck’s constant III. $[M L^{2} T^{- 2} K^{- 1}]$

D. Gravitational constant IV. $[M L^{0} T^{- 3} K^{- 4}]$

Q 33 :

Consider the equation $H = \frac{x^{p} ε^{q} E^{r}}{t^{s}}$

Where $H$ = magnetising intensity; $E$ = electric field; $ε$ = permittivity, $x$ = distance, $t$ = time. The values of $p, q, r$ and $s$ respectively are [2026]