Tag: maths

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Questions Related to maths

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

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?

  1. $m + n$
  2. $n + p$

  3. m

  4. p
Reveal answer Fill a bubble to check yourself
C Correct answer
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. $

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

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

  1. $-4, 5$
  2. $-4,-3$
  3. $3, -3, 5$
  4. $-4$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $2$.
Multiple choice maths negative numbers and integers odd and even numbers operations on integers different types of numbers

Write two odd integers lesser than $1$.

  1. $1,3$
  2. $-1,-3$
  3. $-3,5$
  4. $0,1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $-1,-3$.
Multiple choice maths negative numbers and integers odd and even numbers operations on integers different types of numbers

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

  1. even only when k is even

  2. even only when k is odd

  3. Always odd

  4. Always even
Reveal answer Fill a bubble to check yourself
D Correct answer
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.

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

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

  1. $-2,-6$
  2. $-6,-8$
  3. $6,8$
  4. $-3,2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $6,8$.
Multiple choice maths negative numbers and integers odd and even numbers operations on integers different types of numbers

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

  1. even

  2. odd

  3. prime

  4. composite
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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.

  1. $90mm$
  2. $90cm$
  3. $9cm$
  4. $9m$
Reveal answer Fill a bubble to check yourself
D Correct answer
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
$\therefore \dfrac{4}{3} \times \pi \times 6^3$ = $\pi \times 0.02^2 \times h$
$\therefore h = 900 cm=9 m$