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$A$ uniform rope of mass $0.1 ~kg$ and length $2.45 ~m$ hangs from a rigid support. The time taken by the transverse wave formed in the rope to travel through the full length of the rope is (Assume $g=9.8 ~m/s^2$) (in $~s$)

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The number of radial nodes of $3s$ and $2p$ orbitals respectively are

The thermo emf of a thermocouple is given by $E = aT + bT^2$,where $\frac{a}{b} = -200^{\circ}C$. If the cold junction is kept at $30^{\circ}C$,then the inversion temperature is ($\varepsilon$ in volt,$T$ in centigrade). (in $K$)

In a triangle,if $b=20, c=21$ and $\sin A=\frac{3}{5}$,then $a$ is equal to :

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