Explanation:
To determine which pair of physical quantities does not have the same dimensional formula, we need to compare the dimensions of each quantity.

Let's analyze each pair:

a) Work and torque:
- Work is defined as the product of force and displacement. Its dimensions can be expressed as [M^1 L^2 T^-2].
- Torque is defined as the product of force and perpendicular distance from the axis of rotation. Its dimensions can be expressed as [M^1 L^2 T^-2].
- The dimensional formulas of work and torque are the same, [M^1 L^2 T^-2]. Therefore, option 'a' is not the correct answer.

b) Angular momentum and Planck's constant:
- Angular momentum is defined as the product of moment of inertia and angular velocity. Its dimensions can be expressed as [M^1 L^2 T^-1].
- Planck's constant is a fundamental constant in quantum mechanics and its dimensions can be expressed as [M^1 L^2 T^-1].
- The dimensional formulas of angular momentum and Planck's constant are the same, [M^1 L^2 T^-1]. Therefore, option 'b' is not the correct answer.

c) Tension and surface tension:
- Tension is the force transmitted through a string, rope, cable, or any other type of flexible connector. Its dimensions can be expressed as [M^1 L^1 T^-2].
- Surface tension is the force per unit length acting perpendicular to an imaginary line drawn on the surface of a liquid. Its dimensions can be expressed as [M^1 T^-2].
- The dimensional formulas of tension and surface tension are different. Therefore, option 'c' is the correct answer.

d) Impulse and linear momentum:
- Impulse is defined as the change in momentum of an object. Its dimensions can be expressed as [M^1 L^1 T^-1].
- Linear momentum is defined as the product of mass and velocity. Its dimensions can be expressed as [M^1 L^1 T^-1].
- The dimensional formulas of impulse and linear momentum are the same, [M^1 L^1 T^-1]. Therefore, option 'd' is not the correct answer.

Therefore, the correct answer is option 'C' - Tension and surface tension.