Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of 8 × 10² kg/m³ and specific heat of 2000 J kg^–1 K^–1 while liquid in B has density of 10³ kg m^–3 and specific heat of 4000 J kg^–1 K^–1. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)

Voltage rating of a parallel plate capacitor is 500V. Its dielectric can withstand a maximum electric field of 10⁶ V/m. The plate area is 10^–4 m². What is the dielectric constant is the capacitance is 15 pF? (given $$\varepsilon $$₀ = 8.86 × 10^–12 C²/Nm²)

A boy's catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms^–1. Neglect the change in the area of cross-section of the cord while stretched. The Young's modulus of rubber is closest to:

For the circuit shown, with R₁ = 1.0W, R₂ = 2.0 W, E₁ = 2 V and E₂ = E₃ = 4 V, the potential difference between the points 'a' and 'b' is approximately (in V):