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### A glass tumbler having inner depth of 17.5 cm ....

A glass tumbler having inner depth of 17.5 cm is kept on a table. A student starts pouring water $(\mu = 4/3 )$ into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled?

(A) 11.7 cm
(B) 8.75 cm
(C) 7.5 cm
(D) 10 cm

Solution

$\mu = \frac {Real\, Depth}{Apparent\, Depth} = \frac {17.5-y}{y}$

$\therefore \frac {4}{3} = \frac {17.5-y}{y}$

$\therefore y = 7.5 cm$

Real Depth = 17.5 - y = 10 cm

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