Tag: maths

Questions Related to maths

If $|z^2-1|=|z^2|+1$, then z lies on?

maths complex numbers and linear inequations argand plane and polar representation geometric representation of a complex number complex numbers and quadratic equations

  1. The real axis

  2. The imaginary axis

  3. A circle

  4. An ellipse

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Correct Option: A

LCM of the numbers $12, 24$ and $36$ is 

maths hcf-lcm introduction to multiples multiples lcm

  1. $36$

  2. $24$

  3. $72$

  4. $108$

Show answer
Correct Option: C
Explanation:

Taking out the factors of the given numbers,

$12 = 2 \times 2 \times 3$
$24 = 2 \times 2 \times 2 \times 3 $
$ 36 = 2 \times 2 \times 3 \times 3$
$\therefore $ LCM of $12,24$ and $36$ $= 2 \times 2 \times 2 \times 3 \times 3 = 72$

LCM of the numbers $36$ and $72$ is 

maths hcf-lcm introduction to multiples multiples lcm

  1. $36$

  2. $72$

  3. $108$

  4. $2$

Show answer
Correct Option: B
Explanation:

$36 = 2 \times 2 \times 3 \times 3$
$72 = 2 \times 2 \times 2 \times 3 \times 3$
$\therefore $ L.C.M of $36$  and $72$  $= 2 \times 2 \times 2 \times 3 \times 3 = 72$

Three common multiples of $18$ and $6$ are 

maths hcf-lcm introduction to multiples multiples lcm

  1. $18,6,9$

  2. $18,36,6$

  3. $36,54,72$

  4. None

Show answer
Correct Option: C
Explanation:

Multiples of $ 18 = 18, 36, 54...$
Multiples of $ 6 = 6, 12, 18, ... $
The first common multiple will be $ 18 $
And the next common multiples will be multiples of $ 18 $
Hence, first three common multiples of $ 18, 6 $ are $ 18, 36, 54 $

LCM of the numbers $4$ and $9$ is

maths hcf-lcm introduction to multiples multiples lcm

  1. $32$

  2. $40$

  3. $45$

  4. $36$

Show answer
Correct Option: D
Explanation:

Factors of the given numbers are,

$4 = 2 \times 2 $
$9 = 3 \times 3 $
$\therefore$ LCM of $4$ and $9$ $ = 2 \times 2 \times 3 \times 3 = 36$

LCM of the numbers $17$ and $5$ is 

maths hcf-lcm introduction to multiples multiples lcm

  1. $105$

  2. $95$

  3. $85$

  4. $5$

Show answer
Correct Option: C
Explanation:

Factors are $ 17 = 1 \times 17$
$5 = 1 \times 5 $
$\therefore $ LCM of $17$ and $5$  $= 1 \times 17 \times 5 = 85$

LCM of two co-prime numbers is their

maths hcf-lcm introduction to multiples multiples lcm

  1. sum

  2. difference

  3. product

  4. quotient

Show answer
Correct Option: C
Explanation:

LCM of two co -prime numbers is their product.
Example: Consider $6$ and $7,$
Multiple of $6$ $ = 6,12,18,24,30,36,42, 48$
Multiple of $7$ $= 7,14,21,28,35,42$
L.C.M of $6$ and $7$ $= 42$
The product of $6$ and $7$ $= 6 \times 7 = 42$

The multiple(s) of $12$ is/are

maths hcf-lcm introduction to multiples multiples lcm

  1. $12$

  2. $36$

  3. $4$

  4. All of the above

Show answer
Correct Option: A,B
Explanation:

$12\times 1=12$
$12\times 3=36$
$\therefore 12$ and $36$ are multiples,

 while $4$ is a factor of $12$
So, options $A$ and $B$ are both correct.

Multiple(s) of $14$ is/are

maths hcf-lcm introduction to multiples multiples lcm

  1. $7$

  2. $1$

  3. $28$

  4. All of the above

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Correct Option: C
Explanation:

Multiples of $14$ are $14\times 1, 14\times 2$ ....
And $7$ and $1$ are the factors of $14$.

So, option $C$ is correct.

The LCM of co-prime numbers is the .........

maths hcf-lcm introduction to multiples multiples lcm

  1. difference of numbers

  2. sum of numbers

  3. quotient of numbers

  4. product of numbers

Show answer
Correct Option: D
Explanation:

$LCM \times HCF =$ product of numbers

HCF of co-prime numbers $=1$  
So, $LCM=$ product of numbers
Therefore, $D$ is the correct answer.