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Standard XII

Mathematics

Subset

Let set X = ...

Question

Let set X = { $1, 2, 3 . . . . . . . . .50$ }, sum of all elements in subsets X containing exactly $25$ elements is

\frac{2550}{2} \cdot 49_{C_{24}}

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\frac{1275}{2} \cdot 50_{C_{25}}

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{1275.49}_{C_{24}}

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2550 \cdot C_{24}

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Solution

The correct option is B $\frac{1275}{2} \cdot 50_{C_{25}}$
let us take mean of the given set $\frac{50 (50 + 1)}{2 \times 50}$
using arthematic sum
Mean $= \frac{51}{2}$
No. of subset $=^{50} C_{25}$
Therefore sum of elements will be $= {\frac{25 \times 51}{2}}^{50} C_{25}$
${\frac{1275}{2}}^{50} C_{25}$

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Let set X = { 1,2,3.........50}, sum of all elements in subsets X containing exactly 25 elements is

The correct option is B 12752⋅50C25let us take mean of the given set50(50+1)2×50using arthematic sumMean =512No. of subset =50C25Therefore sum of elements will be =25×51250C251275250C25

Let set X = { $1, 2, 3 . . . . . . . . .50$ }, sum of all elements in subsets X containing exactly $25$ elements is