Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

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

  1. The real axis

  2. The imaginary axis

  3. A circle

  4. An ellipse
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let z = x + iy. Then z^2 = (x^2 - y^2) + i(2xy), so |z^2| = x^2 + y^2 and |z^2 - 1| = sqrt((x^2 - y^2 - 1)^2 + (2xy)^2). The given equation becomes |z^2 - 1| = |z^2| + 1. Squaring both sides yields (x^2 - y^2 - 1)^2 + 4x^2y^2 = (x^2 + y^2 + 1)^2, which simplifies to x^2 = 0, meaning x = 0. Thus, z lies on the imaginary axis.

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

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

  1. $36$
  2. $24$
  3. $72$
  4. $108$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $36$ $= 2 \times 2 \times 2 \times 3 \times 3 = 72$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

LCM of the numbers $36$ and $72$ is 

  1. $36$
  2. $72$
  3. $108$
  4. $2$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $72$  $= 2 \times 2 \times 2 \times 3 \times 3 = 72$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

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

  1. $18,6,9$
  2. $18,36,6$
  3. $36,54,72$

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

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

  1. $32$
  2. $40$
  3. $45$
  4. $36$
Reveal answer Fill a bubble to check yourself
D Correct answer
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$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

LCM of the numbers $17$ and $5$ is 

  1. $105$
  2. $95$
  3. $85$
  4. $5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

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

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

LCM of two co-prime numbers is their

  1. sum

  2. difference

  3. product

  4. quotient
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $7$ $= 6 \times 7 = 42$

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

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

  1. $12$
  2. $36$
  3. $4$

  4. All of the above
Reveal answer Fill a bubble to check yourself
A,B Correct answer
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 choice maths hcf-lcm introduction to multiples multiples lcm

Multiple(s) of $14$ is/are

  1. $7$
  2. $1$
  3. $28$

  4. All of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

Multiple choice maths hcf-lcm introduction to multiples multiples lcm

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

  1. difference of numbers

  2. sum of numbers

  3. quotient of numbers

  4. product of numbers
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$LCM \times HCF =$ product of numbers

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