Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rod are $l_1$ and $l_2$ respectively. Though the temperature of brass and steel is increased, $(l_2 - l_1)$ is maintained same at all temperatures, which of the following relations holds good?
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Two spherical stars, A and B emit black body radiation. The radius of star A is $400$ times that of star B and star A emits power $10^4$ times emitted from star B. $\lambda_A$ and $\lambda_B$ are the wavelengths at which the peak occurs in their respective radiation curves such that $\lambda_A = x\,\lambda_B$. The value of $x$ is
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