COMEDK · Maths · 4. Permutation Combination
How many factors of \(2^5 \times 3^6 \times 5^2\) are perfect squares?
- A 22
- B 12
- C 16
- D 24
Answer & Solution
Correct Answer
(D) 24
Step-by-step Solution
Detailed explanation
The given number is \(N = 2^{5} \times 3^{6} \times 5^{2}\). A factor of \(N\) is of the form \(2^{a} \times 3^{b} \times 5^{c}\), where \(0 \le a \le 5\), \(0 \le b \le 6\), and \(0 \le c \le 2\). For the factor to be a perfect square, the exponents \(a, b, c\) must be even…
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