JEE Main Ultimate Online Test Series - 2027
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A right-angled prism of refractive index $$\mu$$1 is placed in a rectangular block of refractive index $$\mu$$2, which is surrounded by a medium of refractive index $$\mu$$3, as shown in the figure. A ray of light e enters the rectangular block at normal incidence. Depending upon the relationships between $$\mu$$1, $$\mu$$2 and $$\mu$$3, it takes one of the four possible paths 'ef', 'eg', 'eh' or 'ei'.
Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:
| List I | List II | ||
|---|---|---|---|
| P. | $$e \to f$$ |
1. | $${\mu _1} > \sqrt 2 {\mu _2}$$ |
| Q. | $$e \to g$$ |
2. | $${\mu _2} > {\mu _1}$$ and $${\mu _2} > {\mu _3}$$ |
| R. | $$e \to h$$ |
3. | $${\mu _1} = {\mu _2}$$ |
| S. | $$e \to i$$ |
4. | $${\mu _2} < {\mu _1} < \sqrt 2 {\mu _2}$$ and $${\mu _2} > {\mu _3}$$ |
One mole of a monatomic ideal gas is taken along two cyclic processes E $$\to$$ F $$\to$$ G $$\to$$ E and E $$\to$$ F $$\to$$ H $$\to$$ E as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.
Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists :
| List I | List II | ||
|---|---|---|---|
| P. | $$G \to E$$ |
1. | 160$${P_0}{V_0}$$ln2 |
| Q. | $$G \to H$$ |
2. | 36$${P_0}{V_0}$$ |
| R. | $$F \to H$$ |
3. | 24$${P_0}{V_0}$$ |
| S. | $$F \to G$$ |
4. | 31$${P_0}{V_0}$$ |
Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists :
| List I | List II | ||
|---|---|---|---|
| P. | Alpha decay | 1. | $$_8^{15}O \to _7^{15}N + ...$$ |
| Q. | $${\beta ^ + }$$ decay | 2. | $$_{91}^{238}U \to _{90}^{234}Th + ...$$ |
| R. | Fission | 3. | $$_{83}^{185}Bi \to _{82}^{184}Pb + ...$$ |
| S. | Proton emission | 4. | $$_{94}^{239}Pu \to _{57}^{140}La + ...$$ |
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