Predicting Last Digit of an Exponent

Q.

A company decides a new identity code for all its employees. The identity code would comprise five letter initials that can be formed using the alphabets of the English language such that the fifth letter is always a consonant. How many such combinations are possible?

Q.

The smallest three digit number which is divisible by 9, 18 and 27 is 162.

1. True

2. False

Q. Find the unit digit of the numeric expression:
16²³ + 71⁴⁸ + 59⁶¹

Q.

Which of the following will have $4$ at the units place?

1. ${14}^2$

2. ${62}^2$

3. ${27}^2$

4. ${35}^2$

Q.

The largest two-digit multiple of 19 is ___ .

Q. Write the following set in roaster form:
H = {x: x is a 2 digit natural number such that the sum of its digits is 5}

Q. $\text{Numbers of factors of 496 are}$.

1. $10$
2. $9$
3. $8$
4. $7$

Q. $\text{Mass of a dust particle which is}$
$0.0000000007\text{kg},\text{in standard form it can be written as}$.

1. $7\times {10}^{-10}$
2. $7\times {10}^{-9}$
3. $7\times {10}^{-11}$
4. $7\times {10}^{-8}$

Q.

Write a whole number which is not a natural number.

Q.

What is the last digit of $5^{209}$?

1. 4

2. 5

3. 6

4. 0

Q. Find the unit digit of 124¹²⁸ × 126¹²⁴

Q.

Express the following numbers in the scientific notation or standard from:

$23,85,00,00,000$

Q.

What are the factors of 12?

1. 2, 2, 2

2. 3, 2, 2

3. 4, 2, 2

4. 3, 3, 2

Q. Find number of digits ${1025}^{th}$ term of the sequence $1,2,2,4,4,4,4,8,8,8,8,8,8,8,8,.........$

Q.

What is the last digit of $2^{100}$?

1. 2

2. 4

3. 8

4. 6

Q.

Whole numbers consists of all the natural numbers and 0.

1. True

2. False

Q.

For $495$ find the sum of all factors less than $250$.

Q. Shikha has an order from a golf course designer to put palm trees through $a(\times 2^3)$ machine and then through $(\times 3^3)$ machine. She thinks she can do the job with a single repeater machine. What single repeater machine should she use?

Q.

What is the last digit of 10⁹?

1. 1

2. 10

3. 0

4. 9

Q.

What is the last digit of $6^{109}$?

1. 4

2. 6

3. 3

4. 8

Q.

Split the factors and solve the problems using re-arrangement

$24\times 500=\_\_$

Q. What is the last digit of $6^{109}$?

Q. $\text{The age of the Earth which is}$
$4,600,000,000\text{year}$,
$\text{can be written in standard form as}$
$4.6\times {10}^9$.

1. False
2. True

Q.

What power of do we get on dividing 5⁶ by 5¹⁰?

Q. The last digit of 2137${}^{753}$ is

1. 9
2. 7
3. 3
4. 1

Q. How many digits are there in the number $2^3\times 5^4\times {20}^5$?

Q.

State true or `false for each of the following statements:

Zero is the smallest natural number.

1. True
2. False

Q. $149A$ is a $4$-digit number where $A$ is a digit at the ones place. If product, $149A\times ?$, lies between $50000$ and $59000$, which of these could be the value of $(?)$?

1. $40$
2. $35$
3. $350$
4. $400$

Q. How do you find all factors of $36$ ?

Q. $4.5\text{billion years can be written}$
$\text{as}45\times {10}^8$.

1. True
2. False