Question : Let $x$ = (433)24 – (377)38 + (166)54. What is the unit digit of $x$ ?
Option 1: 8
Option 2: 9
Option 3: 7
Option 4: 6
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Correct Answer: 8
Solution : Given: $x$ = (433)24 – (377)38 + (166)54 We can write 43324 = 433(4 × 5) + 4, 37738 = 377(4 × 9) + 2 So, the unit digit of 4334 = 1 and the unit digit of 3772 = 9 The last digit for the(166)54 will always be 6 as the unit digit of a power of a number having the last digit 6 will always be 6. $\therefore$ $x$ = 1 – 9 + 6 = 7 – 9 → Unit digit = 17 – 9 = 8 Hence, the correct answer is 8.
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Question : Directions: By Interchanging the given two numbers which of the following equations will be not correct? 9 and 6
Option 1: 7 + 6 × 4 ÷ 9 – 8 = 5
Option 2: 6 × 8 – 9 ÷ 3 + 5 = 75
Option 3: 9 × 7 + 4 ÷ 1 – 6 = 38
Option 4: 7 × 6 ÷ 3 + 9 – 8 = 19
Question : What is the simplified form of the expression (1 + x) (1 + x2) (1 + x4) (1 + x8) (1 - x)?
Option 1: 1 – x40
Option 2: 1 – x32
Option 3: 1 – x16
Option 4: 1 – x42
Question : For what value of k will the expression x6 – 18x3 + k be a perfect square?
Option 1: –9
Option 2: –81
Option 3: 9
Option 4: 81
Question : Direction: After interchanging + and -, 8 and 7, which one of the following becomes correct?
Option 1: 8 - 7 + 3 x 5 = 35
Option 2: 7 x 8 + 6 - 9 = 25
Option 3: 6 + 8 x 2 - 7 = 0
Option 4: 8 x 2 + 7 - 6 = 9
Question : Direction: If BEAT = 25 – 22 – 26 – 7 and RUST = 9 – 6 – 8 – 7, then how will you code BURST?
Option 1: 25 – 22 – 9 – 8 – 7
Option 2: 25 – 9 – 6 – 8 – 7
Option 3: 25 – 9 – 8 – 7 – 6
Option 4: 25 – 6 – 9 – 8 – 7
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