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### $3^a=5^b=225$, $\frac {ab}{a+b}=?$

While trying to find $\frac {ab}{a+b}$ given $3^a=5^b=225$, a student follows the method below:

$3^a=5^b=225=9\times 25=3^2\times 5^2$

So, $3^a\times 5^b=(3^2\times 5^2)\times (3^2\times 5^2)$

Or, $3^a\times 5^b=3^4\times 5^4$

Since 3 & 5 are prime numbers, a=4 & b=4

Now, $\frac {ab}{a+b}=\frac {4\times 4}{4+4}=2$

Considering above solution, select correct options. More that 1 option may be correct.

(A) a = 4 is correct
(B) b = 4 is correct
(C) $\frac {ab}{a+b}=2$ is correct
(D) $\frac {1}{a}+\frac {1}{b}=\frac {1}{2}$ is correct

Key: (C) & (D)

### 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 = ${}^{12}{C_6} = 924$