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### $2MnO_4^- +bC_2O_4 ^{2-} + CH^+ $$\downarrow$$ xMn^{2+} + y CO_2 + z H_2 O$

$2MnO_4^- +bC_2O_4 ^{2-} + CH^+ \rightarrow xMn^{2+} + y CO_2 + z H_2 O$

If the above equation is balanced with integer coefficients, the value of c is _ _ _ _ . (Round off to the nearest integer)

Solution

$Mn^{7+} + 5e \rightarrow Mn^{2+}$ .......... (*)
$C_2 ^{3+} \rightarrow 2C^{4+} + 2e$ ...........(#)

2 $\times$ (*) + 5 $\times$ (#)

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$2Mn^{7+} + 5C_2 ^{3+} \rightarrow 2Mn^{2+} + 10 C ^{4+}$

So, $2MnO_4 ^- + 5C_2O_4 ^{2-} + 16 H^ + \rightarrow 2Mn^{2+} + 10 CO_2 + 8 H_2 O$

$\therefore c = 16$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$