The last digit of $3^{2001} - 2^{2001}$ equals

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Solution

The correct option is A 1
Last digit of $3^{4 k}$ = 1
Last digit of $3^{4 k + 1}$ = 3
Last digit of $3^{4 k + 2}$ = 9
Last digit of $3^{4 k + 3}$ = 7
2001 is in 4k+1 form.
$∴$ Last digit of $3^{2001}$ = 3
Last digit of $2^{4 k + 1}$ = 2
Last digit of $2^{4 k + 2}$ = 4
Last digit of $2^{4 k + 3}$ = 8
Last digit of $2^{4 k}$ = 16
$∴$ Last digit of $2^{2001}$ = 2
$∴$ Last digit of $3^{2001} - 2^{2001}$ = 3-2 = 1

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