1
JEE Main 2023 (Online) 29th January Evening Shift
+4
-1

The equation of a circle is given by $$x^2+y^2=a^2$$, 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 : $${(x - At)^2} + {\left( {y - {t \over B}} \right)^2} = {a^2}$$. The dimensions of t is given as $$[\mathrm{T^{-1}]}$$.

A
$$\mathrm{A=[L^{-1}T^{-1}],B=[LT^{-1}]}$$
B
$$\mathrm{A=[L^{-1}T^{-1}],B=[LT]}$$
C
$$\mathrm{A=[LT],B=[L^{-1}T^{-1}]}$$
D
$$\mathrm{A=[L^{-1}T],B=[LT^{-1}]}$$
2
JEE Main 2023 (Online) 29th January Morning Shift
+4
-1

Match List I with List II :

List I (Physical Quantity) List II (Dimensional Formula)
A. Pressure gradient I. $$\left[\mathrm{M}^{\circ} \mathrm{L}^{2} \mathrm{~T}^{-2}\right]$$
B. Energy density II. $$\left[\mathrm{M}^{1} \mathrm{L}^{-1} \mathrm{~T}^{-2}\right]$$
C. Electric Field III. $$\left[\mathrm{M}^{1} \mathrm{L}^{-2} \mathrm{~T}^{-2}\right]$$
D. Latent heat IV. $$\left[\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-3} \mathrm{~A}^{-1}\right]$$

Choose the correct answer from the options given below:

A
A-III, B-II, C-IV, D-I
B
A-III, B-II, C-I, D-IV
C
A-II, B-III, C-IV, D-I
D
A-II, B-III, C-I, D-IV
3
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

Match List I with List II

List I List II
A. Young's Modulus (Y) I. $$\mathrm{[ML^{-1}T^{-1}]}$$
B. Co-efficient of Viscosity ($$\eta$$) II. $$\mathrm{[ML^2T^{-1}]}$$
C. Planck's Constant (h) III. $$\mathrm{[ML^{-1}T^{-2}]}$$
D. Work function ($$\varphi$$) IV. $$\mathrm{[ML^2T^{-2}]}$$

Choose the correct answer from the options given below :

A
A-II, B-III, C-IV, D-I
B
A-I, B-II, C-III, D-IV
C
A-I, B-III, C-IV, D-II
D
A-III, B-I, C-II, D-IV
4
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1

Match List I with List II

List-I
List-II
A. Planck's constant (h) I. $$\mathrm{[{M^1}\,{L^2}\,{T^{ - 2}}]}$$
B. Stopping potential (Vs) II. $$\mathrm{[{M^1}\,{L^1}\,{T^{ - 1}}]}$$
C. Work function ($$\phi$$) III. $$\mathrm{[{M^1}\,{L^2}\,{T^{ - 1}}]}$$
D. Momentum (p) IV. $$\mathrm{[{M^1}\,{L^2}\,{T^{ - 3}}\,{A^{ - 1}}]}$$

Choose the correct answer from the options given below :

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