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Question

If 29!+23!7!+15!5!=2ab! where a,bϵN then the ordered pair (a,b) is

A
(10,9)
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B
(10,7)
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C
(9,10)
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D
(5,10)
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Solution

The correct option is C (9,10)
29!+23!7!+15!5!
=19![2+2.8.93!+6.7.8.95!]=19![2+8×3+6.7.8.95.4.3.2]
=19![2+24+1265]=19![26+1265]=256×29!.5×2=51210!2910!
Hence a=9,b=10

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