Tag: maths

Questions Related to maths

If m, n, o, p and q are integers then $m(n + o) (p - q)$ must be even then which of the following is even?

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $m + n$

  2. $n + p$

  3. m

  4. p

Show answer
Correct Option: C
Explanation:

$ Given\quad that\quad m,n,o,p\quad and\quad q\quad are\quad integers.\ \therefore \quad (n+o)\quad is\quad an\quad integer\ \quad \quad (p-q)\quad is\quad an\quad integer\ \therefore \quad m(n+o)(p-q)\quad is\quad a\quad product\quad of\quad 3\quad integers.\ The\quad product\quad to\quad be\quad even\quad one\quad of\quad the\quad factors\quad to\quad be\quad even.\ either\quad m\quad be\quad even\longrightarrow option\quad C\ or\quad (n+o)\quad be\quad even\longrightarrow no\quad option\ or\quad (p-q)\quad be\quad even\longrightarrow no\quad option.\ \therefore \quad option\quad C\quad is\quad the\quad answer. $

State whether following statement is true or false. 
Sum of two odd numbers is always an odd number.

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. True

  2. False

Show answer
Correct Option: B
Explanation:
$1+3=4\\7+9=16$
Sum of $2$ odd nos. is even

Pick odd ineger:
$3, -4, -3, 5$

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $-4, 5$

  2. $-4,-3$

  3. $3, -3, 5$

  4. $-4$

Show answer
Correct Option: C
Explanation:
An odd number is an integer which is not divisible by two. If it is divided by two, then the result is a fraction. The set of odd integers is $-5,-3,-1,1,3,5,7,.....$

Hence, the odd integers are $3,-3,5$, whereas $-4$ is not an odd integer because it is divisible by $2$.

If you add two odd numbers together, the answer is

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. Always Even

  2. Always Odd

  3. Sometimes Even

  4. 1

Show answer
Correct Option: A
Explanation:

If we add two odd numbers the sum is always even.

Let $2n-1$ and $2m-1$ be two odd numbers. 
Sum $=2n-1+2m-1$
Sum $=2n+2m-2$
Sum $=2(n+m-1)$
which is divisible by $2$ . So the sum is even.
Option $A$ is correct.

Write two odd integers lesser than $1$.

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $1,3$

  2. $-1,-3$

  3. $-3,5$

  4. $0,1$

Show answer
Correct Option: B
Explanation:
An odd number is an integer which is not divisible by two. If it is divided by two, then the result is a fraction. The set of odd integers is $-5,-3,-1,1,3,5,7,.....$

The following set of integers is lesser than $1$:

$.....-5,-3,-1,1$

Hence, two of the odd integers lesser than $1$ are $-1,-3$.

If k is a positive integer, then $k(k+1)(k+3)$ is

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. even only when k is even

  2. even only when k is odd

  3. Always odd

  4. Always even

Show answer
Correct Option: D
Explanation:

Suppose $k$ is even

Then $k(k+1)(k+3)$ is even as $k$ will be divisible by $2$
Now if $k$ is odd.
Then $(k+1)$ and $(k+3)$ are even
$\Rightarrow k(k+1)(k+3)$ is also even.
So $k(k+1)(k+3)$ is always even.
So option $D$ is correct.

Write $2$ even integers greater than  $-4$

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $-2,-6$

  2. $-6,-8$

  3. $6,8$

  4. $-3,2$

Show answer
Correct Option: C
Explanation:
An even number is an integer which is "evenly divisible" by two. This means that if the integer is divided by $2$, it yields no remainder. The set of even integers is $-6,-4,-2,2,4,6,8,.....$

The following set of integers is greater than $-4$:

$-2,2,4,6,8,.....$

Hence, two of the even integers greater than $-4$ are $6,8$.

Example of an even number from the following is:

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. $10351$

  2. $20989$

  3. $69007$

  4. $973572$

Show answer
Correct Option: D
Explanation:

The number which ends with $2,4,6,8,0$ are divisible by $2$.

So, only $973572$ is divisible by $2$.
Hence, the answer is $973572$.

The numbers which are not multiples of $2$ are called _______.

maths negative numbers and integers odd and even numbers operations on integers different types of numbers

  1. even

  2. odd

  3. prime

  4. composite

Show answer
Correct Option: B
Explanation:

The numbers $1,3,5,7,9$ etc are called odd number which is not divisible by $2$ and any number which ends which these numbers are also called odd number. 

So, the numbers which are not multiples of $2$ are called odd.
Hence, the answer is odd.

The diameter of a metallic sphere is $6 cm$. It was melted to make a wire of diameter $4 mm$. Find the length of the wire.

maths surface areas and volumes volume of a sphere problems involving volume of combined solids application of surface area and volume of solids

  1. $90mm$

  2. $90cm$

  3. $9cm$

  4. $9m$

Show answer
Correct Option: D
Explanation:

Volume of metallic sphere = $\dfrac{4}{3} \times \pi \times {r^3}$

                                            = $\dfrac{4}{3} \times \pi \times 6^3$
Volume of cylindrical wire = $ \pi \times r^{2} \times h$

Now,
Volume of metallic sphere = Volume of cylindrical wire
$\therefore \dfrac{4}{3} \times \pi \times 6^3$ = $\pi \times 0.02^2 \times h$
$\therefore h = 900 cm=9 m$