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$A$ body of mass $200\,g$ is tied to a spring of spring constant $12.5\,N/m$,while the other end of the spring is fixed at point $O$. If the body moves about $O$ in a circular path on a smooth horizontal surface with a constant angular speed of $5\,rad/s$,then the ratio of the extension in the spring to its natural length will be:

The ratio of minimum wavelengths of Lyman and Balmer series will be

For the transistor circuit shown below,if $\beta = 100$ and the voltage drop between the emitter and base is $0.7\ V$,then the value of $V_{CE}$ will be.....$V$.

One mole of alkene $\underline{X}$ on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The $IUPAC$ name of $\underline{X}$ is

Solution $X$ contains $Na_2CO_3$ and $NaHCO_3$. $20 \ mL$ of $X$ when titrated using methyl orange indicator consumed $60 \ mL$ of $0.1 \ M$ $HCl$ solution. In another experiment,$20 \ mL$ of $X$ solution when titrated using phenolphthalein consumed $20 \ mL$ of $0.1 \ M$ $HCl$ solution. The concentrations (in $mol \ L^{-1}$) of $Na_2CO_3$ and $NaHCO_3$ in $X$ are respectively:

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