model 4 finding unit place of a number Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Unit’s digit in $3^4$ = 1

So, unit digit in $3^164$ = 1

Now, unit's digit in $(2153)^167$ = unit digit in $3^167$

= unit digit in $3^3$ = 7

Answer: (a)

$7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401$

$3^1 = 3; 3^2 = 9; 3^3 = 27; 3^4 = 81;$

i.e. the digit at unit’s place gets repeated after power 4. Unit 6 remains same for any power.

∴ Required unit’s digit = Unit’s digit in the product of $7^3 × 6 × 3^1$ = 4

Answer: (d)

$7^1 = 7$, $7^2 = 9$, $7^3 = 3$, $7^4 = 1$

$7^5 = 7$, $7^6 = 9$, $7^7 = 3$, ... $7^104 = 1$

ie, $105/4$ = [R(1)]

ie, $7^105$= 7

Answer: (a)

$7^1 = 7, 7^2 = 49, 7^3 = 343, 7^4 = 2401, 7^5$ = 16807

i.e. The unit’s digit repeats itself after power 4.

Remainder after we divide 245 by 4 = 1

Unit’s digit in the product of $(4387)^245 × (621)^72$ = Unit’s digit in the product of $(4387)^1 × (621)^72$ = 7 × 1 = 7

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

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