model 4 finding unit place of a number Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (b)

$(4)^{2m}$ gives 6 at unit digit.

$(4)^{2m +1}$ gives 4 at unit digit.

$(5)^n$ gives 5.

The same is the case with 1.

Required digit = Unit’s digit in the product of 4×5 × 1 = 0

Answer: (b)

$2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, 2^5 = 32$

Unit digit in the product of $(122)^173$

= Unit digit in $(122)^1$ = 2

(1 = remainder when 173 is divided by 4).

Answer: (d)

$(251)^98$ = ......1

$(21)^29$ = ....1

$(106)^100$ = ......6

$(705)^35$ = ....5

$(16)^4$ = .....6

259 = ......9

∴ Required answer = 1 + 1 – 6 + 5 – 6 + 9 = 16 – 12 = 4

Answer: (b)

Unit's digit in $(1570)^2$ = 0

Unit's digit in $(1571)^2$ = 1

Unit's digit in $(1572)^2$ = 4

Unit's digit in $(1573)^2$ = 9

∴ Required unit’s digit = Unit’s digit (0 +1+4 + 9) = 4

Answer: (a)

$4^1 = 4, 4^2 = 16, 4^3 = 64, 4^4 = 256, 4^5 = 1024$

Remainder on dividing 372 by 4 = 0

Remainder on dividing 373 by 4 = 1

Required unit digit = Unit digit of the sum of 6 + 4 = 0