Unit Digit Calculation - Practice Test Solved MCQs UPSC Prelims Paper 2

Explanation:

Unit digit in 3⁴ = 1  Unit digit in (3⁴)¹⁶ = 1

 Unit digit in 3⁶⁵ = Unit digit in [ (3⁴)¹⁶ x 3 ] = (1 x 3) = 3

Unit digit in 6⁵⁹ = 6

Unit digit in 7⁴  Unit digit in (7⁴)¹⁷ is 1.

Unit digit in 7⁷¹ = Unit digit in [(7⁴)¹⁷ x 7³] = (1 x 3) = 3

 Required digit = Unit digit in (3 x 6 x 3) = 4.

Explanation:

Unit digit in 7¹⁰⁵ = Unit digit in [ (7⁴)²⁶ x 7 ]

But, unit digit in (7⁴)²⁶ = 1

 Unit digit in 7¹⁰⁵ = (1 x 7) = 7

The unit digit of each number is considered: 4, 8, 7, and 3. Multiplying these step by step:

• First, multiply 4 × 8 = 32; the unit digit is 2.
• Then, multiply this result (2) by 7 = 14; the unit digit is 4.
• Finally, multiply this result (4) by 3 = 12; the unit digit is 2.

Therefore, the unit digit of the product is 2.

Solution: The required answer is the unit digit of the sum of the unit digits of the numbers in given sum. i.e., The unit digit of (1289 + 2541 + 8215 + 6137) = the unit digit of (9+1+5+7) = the unit digit of (22) = 2 Hence the answer is 2.

a)2

Solution:

The required answer is the unit digit of the product of the unit digits of the numbers in given product.
i.e, The unit digit of (1022 x 729 x 889 x 971)
= the unit digit of (2 x 9 x 9 x 1)
= the unit digit of (162)
= 2

Hence, the answer is 2.