1
JEE Main 2023 (Online) 1st February Evening Shift
+4
-1

If the velocity of light $$\mathrm{c}$$, universal gravitational constant $$\mathrm{G}$$ and Planck's constant $$\mathrm{h}$$ are chosen as fundamental quantities. The dimensions of mass in the new system is :

A
$$\left[\mathrm{h}^{1} \mathrm{c}^{1} \mathrm{G}^{-1}\right]$$
B
$$\left[\mathrm{h}^{-1 / 2} \mathrm{c}^{1 / 2} \mathrm{G}^{1 / 2}\right]$$
C
$$\left[\mathrm{h}^{1 / 2} \mathrm{c}^{1 / 2} \mathrm{G}^{-1 / 2}\right]$$
D
$$\left[\mathrm{h}^{1 / 2} \mathrm{c}^{-1 / 2} \mathrm{G}^{1}\right]$$
2
JEE Main 2023 (Online) 31st January Evening Shift
+4
-1
Match List I with List II

LIST I LIST II
A. Angular momentum I. $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$
B. Torque II. $\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$
C. Stress III $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$
D. Pressure gradient IV. $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below:
A
A - I, B - IV, C - III, D - II
B
A - III, B - I, C - IV, D - II
C
A - IV, B - II, C - I, D - III
D
A - II, B - III, C - IV, D - I
3
JEE Main 2023 (Online) 30th January Evening Shift
+4
-1

Match List I with List II:

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

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
4
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
$$\mathrm{A=[L^{-1}T],B=[LT^{-1}]}$$
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