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  • Let  be a relation from the set <img alt="\mathrm{\{1,2,3, \ldots, 60\}}" src="/latex-image/?%5Cmathrm%7B%5C%7B1%2C2%2C3%2C%20%5Cld

Let \mathrm{R} be a relation from the set \mathrm{\{1,2,3, \ldots, 60\}}to itself such that \mathrm{R=\{(a, b): b=p q}, where \mathrm{p, q \geqslant 3} are prime numbers \}. Then, the number of elements in \mathrm{R} is:

Option: 1

600


Option: 2

660


Option: 3

540


Option: 4

720


Answers (1)

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\text{ Number of possible values of a=60, for b=pq,}\\ \text{ if p=3, q=3,5,7,11,13,17,19}\\ \mathrm{ if\; p=5 \quad q=5,7,11}\\ \mathrm{ if \;p=7 \quad q=7}\ \text{Total cases}\mathrm{ =60 \times 11=660}

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manish

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