NIMCET 2016 — Mathematics PYQ

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Question

NIMCET 2016 — Mathematics PYQ

NIMCET | Mathematics | 2016

Two finite sets A and B are having m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The value of m and n are

Choose the correct answer:

Explanation

Concept:
If a set contains n elements, then the total number of subsets will be $2^{n}$

**Calculation:**

Total number of subsets of the first is $2^{m}$ while total number of subsets of the second is $2^{n}$ .

Now it is given that
$2^{m} = 2^{n} + 56$

$\Rightarrow 2^{m} - 2^{n} = 56$

$\Rightarrow 2^{3} (2^{m - 3} - 2^{n - 3}) = 56$

$\Rightarrow (2^{m - 3} - 2^{n - 3}) = 7$

$\Rightarrow (2^{m - 3} - 2^{n - 3}) = 8 - 1$

$\Rightarrow (2^{m - 3} - 2^{n - 3}) = 2^{3} - 2^{0}$

Hence compare the terms,
$m - 3 = 3$ thus $m = 6$ and
$n - 3 = 0$ giving $n = 3$

Hence, $(m, n) = (6, 3)$