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### One main scale division of a Vernier calipers is 'a' cm ....

One main scale division of a Vernier calipers is 'a' cm and $n^{th}$ division of the Vernier scale coincides with $(n-1)^{th}$ division of the main scale. The least count of the calipers in mm is:

(A) $\frac {10na}{(n-1)}$
(B) $\frac {10a}{(n-1)}$
(C) $\frac {10a}{n}$
(D) $(\frac {n-1}{10n})a$

Solution

We have, 1 main scale division MSD = a

1 VSD $= \frac {(n-1)a}{n}$

Least Count = 1 MSD - 1 VSD $= a - \frac {(n-1)a}{n}$

So, least count $= \frac {a}{n}$ cm $= \frac {10a}{n}$ mm

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