A=[aij]3×3 is a diagonal matrix such that |A|=27000 and x1,x2,x3∈N are elements along principal diagonal, then
A
Number of such matrix is ′N′ then ′N′ is perfect square
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B
Minimum value of x1+x2+x3 is 60
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C
Number of such matrix is ′N′ then ′N′ is perfect cube
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D
Minimum value of x1+x2+x3 is 90
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Solution
The correct option is D Minimum value of x1+x2+x3 is 90 |A|=x1x2x3=27000
Now, x1+x2+x33≥(x1x2x3)1/3 x1+x2+x3≥90 (x1+x2+x3)min=90
Also x1x2x3=233353
No. of solution 3+3−1C3−1×3+3−1C3−1×3+3−1C3−1 =5C2×5C2×5C2 =103 perfect cube