1
JEE Main 2023 (Online) 13th April Evening Shift
+4
-1

In the equation $$\left[X+\frac{a}{Y^{2}}\right][Y-b]=\mathrm{R} T, X$$ is pressure, $$Y$$ is volume, $$\mathrm{R}$$ is universal gas constant and $$T$$ is temperature. The physical quantity equivalent to the ratio $$\frac{a}{b}$$ is:

A
Impulse
B
Energy
C
D
Coefficient of viscosity
2
JEE Main 2023 (Online) 13th April Morning Shift
+4
-1

A body of mass $$(5 \pm 0.5) ~\mathrm{kg}$$ is moving with a velocity of $$(20 \pm 0.4) ~\mathrm{m} / \mathrm{s}$$. Its kinetic energy will be

A
$$(1000 \pm 140) ~\mathrm{J}$$
B
$$(500 \pm 0.14) ~\mathrm{J}$$
C
$$(1000 \pm 0.14) ~\mathrm{J}$$
D
$$(500 \pm 140) ~\mathrm{J}$$
3
JEE Main 2023 (Online) 12th April Morning Shift
+4
-1

Match List I with List II

LIST I LIST II
A. Spring constant I. $$\mathrm{[T^{-1}]}$$
B. Angular speed II. $$\mathrm{[MT^{-2}]}$$
C. Angular momentum III. $$\mathrm{[ML^2]}$$
D. Moment of inertia IV. $$\mathrm{[ML^2T^{-1}]}$$

Choose the correct answer from the options given below:

A
A-IV, B-I, C-III, D-II
B
A-II, B-III, C-I, D-IV
C
A-II, B-I, C-IV, D-III
D
A-I, B-III, C-II, D-IV
4
JEE Main 2023 (Online) 11th April Evening Shift
+4
-1

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

A
$$\mathrm{FV}^{-2} \mathrm{~T}^{2}$$
B
$$\mathrm{FV}^{4} \mathrm{~T}^{-6}$$
C
$$\mathrm{F}^{2} \mathrm{~V}^{-2} \mathrm{~T}^{6}$$
D
$$\mathrm{FV}^{-4} \mathrm{~T}^{-2}$$
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