Due to cold weather a 1 m water pipe of cross-sectional area 1 cm² is filled with ice at $$-$$10$$^\circ$$C. Resistive heating is used to melt the ice. Current of 0.5A is passed through 4 k$$\Omega$$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required? (Given latent heat of fusion for water/ice = 3.33 $$\times$$ 10⁵ J kg^$$-$$1, specific heat of ice = 2 $$\times$$ 10³ J kg^$$-$$1 and density of ice = 10³ kg/m³

A student determined Young's Modulus of elasticity using the formula $$Y = {{Mg{L^3}} \over {4b{d^3}\delta }}$$. The value of g is taken to be 9.8 m/s², without any significant error, his observation are as following.

Physical Quantity	Least count of the Equipment used for measurement	Observed value
Mass (M)	1 g	2 kg
Length of bar (L)	1 mm	1 m
Breadth of bar (b)	0.1 mm	4 cm
Thickness of bar (d)	0.01 mm	0.4 cm
Depression ($$\delta $$)	0.01 mm	5 mm

Then the fractional error in the measurement of Y is :

Two resistors R₁ = (4 $$\pm$$ 0.8) $$\Omega$$ and R₂ = (4 $$\pm$$ 0.4) $$\Omega$$ are connected in parallel. The equivalent resistance of their parallel combination will be :

Following plots show magnetization (M) vs magnetizing field (H) and magnetic susceptibility ($$\chi $$) vs temperature (T) graph :


Which of the following combination will be represented by a diamagnetic material?