Divisibility by 2

Q.

How do I find $\frac{2}{3}$ of a whole number?

Q.

The sum of two consecutive odd numbers is always divisible by $4$. Verify this statement with the help of some examples.

Q.

On the set of integers $Z$, define $f:Z\to Z$ as

$f\left(n\right)=\left\{\begin{array}{l}\frac{n}{2},n\text{is even}\\ 0,n\text{is odd}\end{array}\right.$

Then $f$ is

1. injective but not surjective

2. neither injective nor surjective

3. surjective but not injective

4. bijective

Q. Question 74

If 56x32y is divisible by 18, find the least value of y.

Q. If three digit number 24 x is divisible by 9 what is the value of x?

Q.

If the division $N÷2$ leaves no remainder, what might be the units digit of N?
[2 MARKS]

Q. If the number at the units place is an even number, then it is always divisible by _______.

1. 9
2. 5
3. 3
4. 2

Q.

Which of the following number can be used as terminating or non termating number: 1.$\frac{1}{4}$ 2.$\frac{11}{15}$ 3.$\frac{38}{81}$

Q.

$n$is selected from the set $\left\{1,2,3,...,100\right\}$ and the number $2^n+3^n+5^n$ is formed. Total number of ways of selecting $n$ so that the formed number is divisible by $4$, is equal to

1. $50$

2. $49$

3. $48$

4. None of these

Q. Write true $\left(T\right)$ or False $\left(F\right)$ for the following statements:
If $a$ divides $b,$ then $a^3$ divides $b^3$

Q. The sum of the numbers 123, 231 and 312 is divisible by 37.

1. True
2. False

Q. Question 34

In the given question, state whether the given statement is True or False.

A two-digit number ab is always divisible by 2, if b is an even number.

Q.

Using divisibility test, determine $726352$ is divisible by $4$ and divisible by $8$:

Q.

Which of the following number is divisible by $10$?

1. $2011$

2. $2014$

3. $2015$

4. $2120$

Q.

The number 98754256 is divisible by:

1. 4

2. 8

3. 4 and 8

4. 4, 8 and 12

Q.

Number $21084$ is divisible by $8.$

1. True
2. False

Q.

Using digits 4, 5, 6, 7, 8 and 9. Make any three numbers each with 8 digits. Put commas for care of reading.

Q.

How many numbers from 1001 to 2000 are divisible by 4?

Q. Simplify and write the answer in the exponential form
$-3^4\times {\left(\frac{5}{3}\right)}^4$
[3 marks]

Q.

For some integer m, every even integer is of the form:

1. $m$

2. $m+1$

3. $2m$

4. $2m+1$

Q.

Find which of the following numbers are divisible by 2:

(i) 192 (ii) 1660

(iii) 1101 (iv) 2079

Q.

$3134673$is divisible by$3$ and ______.

Q.

When any natural number is divided by $10$ what is the sum of all possible remainders?

Q.

Write the following set in tabular form.

The set of multiples of $5$ less than $50$.

Q.

Find the smallest number that should be added to 1727 to make it divisible by 3.

1. 1

2. 0

3. 5

4. 6

Q.

Test the divisibility of the following numbers by $2$

$42990$

Q. Which of the following is divisible by 2?

1. $144÷4$
2. $186÷6$
3. $200÷8$
4. $210÷2$

Q.

The divisibility of a number by 2, 5 and 10 depends on its last 2 digits.

1. True

2. False

Q.

Using divisibility tests, determine the given number $7,89,651$ is divisible by $9$.

Q.

Using divisibility test, determine $12159$ is divisible by $4$ and $8$: