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The spectral distribution of radiation from a black body at $T_1=3000 \: K$ has a maximum at wavelength $\lambda_{\text{max}}$. The body cools down to a temperature $T_2$. If the wavelength corresponding to the maximum of the spectral distribution at $T_2$ is $1.2$ times of the original wavelength $\lambda_{\text{max}}$, then the temperature $T_2$ is _________ $K$ (round off to nearest integer)
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