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### Weighing Machine in Elevator

A man inside an elevator uses weighing machine to weigh himself. With what acceleration should the elevator descend so that the weighing machine reports the weight of the man to be half of its true value?

The reading of the weighing machine depends on the force by which the machine is pressed. Let us say the machine is pressed downwards by force N. The machine will exert an equal upward force N on the man.

Let m be the mass of the man. For the man system,

mg - N = ma

$mg - \frac{{mg}}{2} = ma$

$\Rightarrow a = \frac{g}{2}$

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