
"Let’s analyze the properties and functions of the given additives:
P. p-phenylenediamine is primarily used as an antioxidant in rubber and polymer materials, which protects them from oxidative degradation and extends their lifespan. Hence, p-phenylenediamine is associated with function 4 (Antiozonant).
Q. Trixylyl phosphate is often used as a plasticizer and flame retardant. It works to increase the flexibility of polymers and also acts as a flame retardant in polymer systems. This makes it suitable for function 1 (Flame retardant).
R. Polybutadiene rubber is a type of rubber used to improve impact strength in various materials like plastics. It is widely used to improve the toughness of materials, thus it fits with function 2 (Impact modifier).
S. Talc is a mineral that acts as a nucleating agent in the formation of crystalline structures in polymers. It is also used as a processing aid in plastics to improve their stiffness and heat resistance. Therefore, it is best associated with function 3 (Nucleating agent). Thus, the correct matching is:
- P (p-phenylenediamine) -> 4 (Antiozonant)
- Q (Trixylyl phosphate) -> 1 (Flame retardant)
- R (Polybutadiene rubber) -> 2 (Impact modifier)
- S (Talc) -> 3 (Nucleating agent)
Therefore, the correct answer is (D).
Potato slices weighing 50 kg is dried from 60% moisture content (wet basis) to 5% moisture content (dry basis). The amount of dried potato slices obtained (in kg) is ............ (Answer in integer)
Two Carnot heat engines (E1 and E2) are operating in series as shown in the figure. Engine E1 receives heat from a reservoir at \(T_H = 1600 \, {K}\) and does work \(W_1\). Engine E2 receives heat from an intermediate reservoir at \(T\), does work \(W_2\), and rejects heat to a reservoir at \(T_L = 400 \, {K}\). Both the engines have identical thermal efficiencies. The temperature \(T\) (in K) of the intermediate reservoir is ........ (answer in integer). 
A bar of length \( L = 1 \, {m} \) is fixed at one end. Before heating its free end has a gap of \( \delta = 0.1 \, {mm} \) from a rigid wall as shown in the figure. Now the bar is heated resulting in a uniform temperature rise of \( 10^\circ {C} \). The coefficient of linear thermal expansion of the material is \( 20 \times 10^{-6} / \degree C \) and the Young’s modulus of elasticity is 100 GPa. Assume that the material properties do not change with temperature.
The magnitude of the resulting axial stress on the bar is .......... MPa (in integer). 
A massless cantilever beam, with a tip mass \( m \) of 10 kg, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length \( L = 1 \, {m} \), with a circular cross-section of diameter \( d = 20 \, {mm} \). The Young’s modulus of the beam material is 200 GPa.
The natural frequency of the spring-mass system is ............ Hz (rounded off to two decimal places).
A simply-supported beam has a circular cross-section with a diameter of 20 mm, area of 314.2 mm\(^2\), area moment of inertia of 7854 mm\(^4\), and a length \( L \) of 4 m. A point load \( P = 100 \, {N} \) acts at the center and an axial load \( Q = 20 \, {kN} \) acts through the centroidal axis as shown in the figure.
The magnitude of the offset between the neutral axis and the centroidal axis, at \( L/2 \) from the left, is ............ mm (rounded off to one decimal place).