1
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

A force is represented by $$F=a x^2+b t^{\frac{1}{2}}$$

where $$x=$$ distance and $$t=$$ time. The dimensions of $$b^2 / a$$ are:

A
$$\left[\mathrm{ML}^2 \mathrm{~T}^{-3}\right]$$
B
$$\left[\mathrm{ML}^3 \mathrm{~T}^{-3}\right]$$
C
$$\left[M L T^{-2}\right]$$
D
$$\left[M L^{-1} T^{-1}\right]$$
2
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is $$0.5 \mathrm{~mm}$$, the Vernier constant of traveling microscope is

A
0.01 mm
B
0.01 cm
C
0.1 mm
D
0.1 cm
3
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

If mass is written as $$m=k \mathrm{c}^{\mathrm{P}} G^{-1 / 2} h^{1 / 2}$$ then the value of $$P$$ will be : (Constants have their usual meaning with $k a$ dimensionless constant)

A
1/3
B
$$-$$1/3
C
1/2
D
2
4
JEE Main 2024 (Online) 30th January Morning Shift
+4
-1

Match List I with List II.

List I List II
(A) Coefficient of viscosity (I) $$\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-2}\right]$$
(B) Surface tension (II) $$\left[\mathrm{M} \mathrm{L}^2 \mathrm{~T}^{-1}\right]$$
(C) Angular momentum (III) $$\left[\mathrm{M} \mathrm{L}^{-1} \mathrm{~T}^{-1}\right]$$
(D) Rotational kinetic energy (IV) $$\left[\mathrm{M} \mathrm{L}^0 \mathrm{~T}^{-2}\right]$$

Choose the correct answer from the options given below :

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