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How many moles of $KMnO_4$ are required to oxidize $1 \ mol$ of $FeC_2O_4$ in an acidic medium?

The integrating factor of the differential equation $x \log x \frac{dy}{dx} + y = 2 \log x$ is given by

Three metal rods of the same material and identical in all respects are joined as shown in the figure. The temperatures at the ends are maintained as indicated. Assuming no loss of heat from the curved surfaces of the rods,the temperature at the junction $X$ would be ....... $^oC$

In the circuit shown,the reading of the Ammeter is doubled after the switch is closed. Each resistor has a resistance $= 1\,\Omega$ and the ideal cell has an $e.m.f. = 10\,V$. Then,the Ammeter has a coil resistance equal to .............. $\Omega$.

Match the following lists:
List-$I$List-$II$
$A$. Ethane$1$. $2$ $sp$ carbons
$B$. Ethylene$2$. $6$ $sp^2$ carbons
$C$. Acetylene$3$. $2$ $sp^3$ carbons
$D$. Benzene$4$. $2$ $sp^2$ carbons
$5$. $1$ $sp$ and $1$ $sp^2$ carbons

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