JEE Mains · Maths · STD 11 - 6. permutation and combination
The total number of \(4-\)digit numbers whose greatest common divisor with \(54\) is \(2\) , is \(..........\).
- A \(3000\)
- B \(1000\)
- C \(1500\)
- D \(3600\)
Answer & Solution
Correct Answer
(A) \(3000\)
Step-by-step Solution
Detailed explanation
\(N\) should be divisible by \(2\) but not by \(3\) \(N =(\) Numbers divisible by \(2\))-( Numbers divisible by \(6\) ) \(N =\frac{9000}{2}-\frac{9000}{6}=4500-1500=3000\)
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