what is the value of p , for which 7 power 7 dividded 7 power-p = 7 power 10
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Answer:
Highest power of 2:
2
10
=5,
2
5
=2.5−>2,
2
2
=1⇒5+2+1=8
Thus, p=8
Highest power of 3:
3
10
=3.3−>3,
3
3
=1⇒3+1=4
Thus, q=4
Highest power of 5:
5
10
=2
Thus, r=2
Highest power of 7:
7
10
=1
Thus, s=1
Thus, p×q×r×s=64
Now, 10! has prime factors 2,3,5 and 7. Hence, number of factors = (p+1)(q+1)(r+1)(s+1)=270
Thus, number of ways of writing 10! as a product of 2 factors =
2
270
=135
Hence, (a)(b) and (d) are correct.
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