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The sound waves of wavelengths $5 ~m$ and $6 ~m$ produce $30$ beats in $3 ~s$. The velocity of sound is: (in $~m/s$)

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k=$

Match the following columns:
Column-$I$ Column-$II$
$(a)$ Gymnosperms $(p)$ Trimerous flowers
$(b)$ Monocots $(q)$ Absence of flowers
$(c)$ Dicots $(r)$ Primitive flowers
$(d)$ Pteridophytes $(s)$ Tetramerous or pentamerous flowers

Consider two reactions:
$I$. $Zn +$ conc. $HNO_3$ (hot) $\to Zn(NO_3)_2 + X + H_2O$
$II$. $Zn +$ dil. $HNO_3$ (cold) $\to Zn(NO_3)_2 + Y + H_2O$
Compounds $X$ and $Y$ are respectively:

During the depression in freezing point experiment,an equilibrium is established between the molecules of

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