| 1. | \(1000~\text K\) | 2. | \(3000~\text K\) |
| 3. | \(1000^\circ\text C\) | 4. | \(3000^\circ\text C\) |

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If \(\lambda_m\) denotes the wavelength at which the radioactive emission from a black body at a temperature \(T\) K is maximum, then:
1. \(\lambda_m\) is independent of \(T\)
2. \(\lambda_m \propto T\)
3. \(\lambda_m \propto T^{-1}\)
4. \(\lambda_m \propto T^{-4}\)

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| 1. | \(1000^\circ\text C\) | 2. | \(1000~\text K\) |
| 3. | \(10000~\text K\) | 4. | \(10^5~\text K\) |

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| 1. | Wien’s displacement Law |
| 2. | Kirchhoff’s Law |
| 3. | Newton’s Law of cooling |
| 4. | Stefan’s Law |

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The dimensions of Wien's constant are:
1. \( \left [ MLTK \right ]\)
2. \( \left [ M^0LT^0K \right ]\)
3. \( \left [ M^0L^0TK \right ]\)
4. \( \left [ MLTK^{-1} \right ]\)
A black body has a wavelength \(\lambda_m\) corresponding to maximum energy at \(2000~\text{K}\). Its wavelength corresponding to maximum energy at \(3000~\text{K}\) will be:
| 1. | \(\dfrac{3}{2}\lambda_m\) | 2. | \(\dfrac{2}{3}\lambda_m\) |
| 3. | \(\dfrac{16}{81}\lambda_m\) | 4. | \(\dfrac{81}{16}\lambda_m\) |

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| Statement I: | A blue star has a higher surface temperature than a red star. |
| Statement II: | According to Wien’s displacement law, the wavelength corresponding to the maximum spectral emissive power of a blackbody is inversely proportional to its absolute temperature. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |

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