1
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

If $$K_{1}$$ and $$K_{2}$$ are the thermal conductivities, $$L_{1}$$ and $$L_{2}$$ are the lengths and $$A_{1}$$ and $$A_{2}$$ are the cross sectional areas of steel and copper rods respectively such that $$\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2$$. Then, for the arrangement as shown in the figure, the value of temperature $$\mathrm{T}$$ of the steel - copper junction in the steady state will be:

A
$$18^{\circ} \mathrm{C}$$
B
$$14^{\circ} \mathrm{C}$$
C
$$45^{\circ} \mathrm{C}$$
D
$$150^{\circ} \mathrm{C}$$
2
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

B. Two bodies $$P$$ and $$Q$$ having equal surface areas are maintained at temperature $$10^{\circ} \mathrm{C}$$ and $$20^{\circ} \mathrm{C}$$. The thermal radiation emitted in a given time by $$\mathrm{P}$$ and $$\mathrm{Q}$$ are in the ratio $$1: 1.15$$.

C. A Carnot Engine working between $$100 \mathrm{~K}$$ and $$400 \mathrm{~K}$$ has an efficiency of $$75 \%$$.

D. When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice.

Choose the correct answer from the options given below :

A
A, B, C only
B
A, B only
C
A, C only
D
B, C, D only
3
JEE Main 2022 (Online) 27th July Morning Shift
+4
-1

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is $$1: 4$$, then

A. The r.m.s. velocity of gas molecules in two vessels will be the same.

B. The ratio of pressure in these vessels will be $$1: 4$$.

C. The ratio of pressure will be $$1: 1$$.

D. The r.m.s. velocity of gas molecules in two vessels will be in the ratio of $$1: 4$$.

Choose the correct answer from the options given below :

A
A and C only
B
B and D only
C
A and B only
D
C and D only
4
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

An ice cube of dimensions $$60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm}$$ is placed in an insulation box of wall thickness $$1 \mathrm{~cm}$$. The box keeping the ice cube at $$0^{\circ} \mathrm{C}$$ of temperature is brought to a room of temperature $$40^{\circ} \mathrm{C}$$. The rate of melting of ice is approximately :

(Latent heat of fusion of ice is $$3.4 \times 10^{5} \mathrm{~J} \mathrm{~kg}^{-1}$$ and thermal conducting of insulation wall is $$0.05 \,\mathrm{Wm}^{-1 \circ} \mathrm{C}^{-1}$$ )

A
$$61 \times 10^{-3} \mathrm{~kg} \mathrm{~s}^{-1}$$
B
$$61 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}$$
C
$$208 \mathrm{~kg} \mathrm{~s}^{-1}$$
D
$$30 \times 10^{-5} \mathrm{~kg} \mathrm{~s}^{-1}$$
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