Adam took a surprise test of the students of his class on a topic which was taught in the class two weeks earlier. The test consisted of seven questions out of which students needed to attempt only five questions. Shane, a student of his class attempted five questions and copied these five questions on a notebook so that he could solve these questions at his home, and verify whether he answered these questions correctly or not. Help Shane in verifying the answer to these questions.

Find the unit digit of $(100! + 2) (100! + 3) (100! + 6)$ .

6

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8

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0

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4

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Solution

The correct option is A $6$
We know that the unit digit of $100!$ is $0$ .

So, the unit digit of $(100! + 2), (100! + 3),$ and $(100! + 6)$ will be $2, 3,$ and $6$ respectively.

Thus, the unit digit of $(100! + 2) (100! + 3) (100! + 6) =$ Unit digit of $2 (3) (6) = 6$

Hence, option $B$ is the correct answer.

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Similar questions

Q. Adam took a surprise test of the students of his class on a topic which was taught in the class two weeks earlier. The test consisted of seven questions out of which students needed to attempt only five questions. Shane, a student of his class attempted five questions and copied these five questions on a notebook so that he could solve these questions at his home, and verify whether he answered these questions correctly or not. Help Shane in verifying the answer to these questions.

What will be the unit digit of

(0! + 1! + 2! + 3!) \times 7 \times 53 \times 99 \times 1236

7^{333} \times 5^{11} \times 4^{234} \times 3^{11}

In a class test containing ten questions, $5$ marks are awarded for every correct answer and $(- 2)$ are awarded for every incorrect answer and $0$ for the questions not attempted. Ram gets two correct and five incorrect out of seven questions he attempts. What is his score?

In a class test containing 10 questions, 3 marks are awarded for every correct answer, (-1) mark is awarded for every incorrect answer and 0 for the questions not attempted. Srinu gets two correct and six incorrect answers out of eight questions he attempted. What is his total score?

In a class test containing 10 questions, 5 marks are awarded for every correct answer and (-2) marks are awarded for every incorrect answer and 0 for questions not attempted.

(i) Mohan gets four correct and six incorrect answers. What is his score?

(ii) Reshma gets five correct answers and five incorrect answers, what is her score?

(iii) Heena gets two correct answers and five incorrect answers out of seven questions she attempts. What is her score?

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The correct option is A 6 We know that the unit digit of 100! is 0. So, the unit digit of (100!+2),(100!+3), and (100!+6) will be 2,3, and 6 respectively. Thus, the unit digit of (100!+2)(100!+3)(100!+6)= Unit digit of 2(3)(6)=6 Hence, option B is the correct answer.