Tag: maths

Questions Related to maths

Find a possible value of $v$, if the least common multiple of $9, 10, 12$ and $v$ is $540$.

maths hcf-lcm introduction to multiples multiples lcm

  1. 18

  2. 24

  3. 27

  4. 36

  5. 45

Show answer
Correct Option: C
Explanation:

LCM of 9,10,12

$9=3\times 3$
$10=2\times 5$
$12=2\times 2\times 3$
$LCM(9,10,12)=2\times 2\times 3\times 3\times 5=180$
180 is also multiply of 18,36,45.If v is 18,36 and 45 than LCM of all the number would be 180 but its 540 so the answer is Option C.

What is the least common multiple of $10$ and $20$?

maths hcf-lcm introduction to multiples multiples lcm

  1. $2$

  2. $5$

  3. $10$

  4. $20$

  5. $200$

Show answer
Correct Option: D
Explanation:

$10=2\times5$
$20=2^2\times 5$

LCM$=2\times2 \times 5=20$
Ans-Option $D$.

The greatest number with four digits which when divided by $3, 5, 7, 9$ leaves the remainders $1, 3, 5, 7$ respectively, is _______.

maths hcf-lcm introduction to multiples multiples lcm

  1. $9763$

  2. $9673$

  3. $9367$

  4. $9969$

Show answer
Correct Option: A
Explanation:

Since on dividing by $3$ the remainder is $1$, the sum of digits of the number must add upto a number, dividing which by $3$ we get remainder $1$

Since on dividing by $5$ remainder is $3$, unit place digit has to be either $3$ or $8$
Since on dividing by $9$ remainder is $7$, sum of digits should give remainder $7$ when divided by $9$ 
Only options (A), (B) satisfy these criteria
Since (A) is bigger, we divide it by $7$ and find remainder which turns out to be $5$. 

When $31513$ ad $34369$ are divided by a certain three digit number, the remainders are equal, then the remainder is ______.

maths hcf-lcm introduction to multiples multiples lcm

  1. $86$

  2. $97$

  3. $374$

  4. $113$

Show answer
Correct Option: B
Explanation:

Let the divisor be $a$ and remainder be $r$

Let $31513 = am+r$
and $34369 = an+r$
Then, $a(n-m) = 2856 = 24\times119 = 12\times238 = 8\times357= 6\times476=4\times714$
All three digit numbers give same remainder $=$ $97$

The numbers which are multiples of $2$ are called ____.

maths hcf-lcm introduction to multiples multiples lcm

  1. odd

  2. even

  3. prime

  4. composite

Show answer
Correct Option: B
Explanation:

The numbers $2,4,6,8,10$ are known as even number. 

The numbers which are completely divisible by $2$ are known as even numbers.
So, the numbers which are multiples of $2$ are called even numbers.

Distance of line $y=5$ from $x$ axis is  ____ units.

maths lines equations of lines parallel to the x-axis and y-axis graphs of linear equations graph of linear equations in two variables

  1. $-5$

  2. $5$

  3. $10$

  4. $-10$

Show answer
Correct Option: B
Explanation:

Since, if a line at a distance $a$ from $x$-axis and parallel to $x$-axis it is given by $y=+a$ or $y=-a$
Here line is $y=5$
Distance of given line from $x$-axis is $5$ units.

Distance of the line $x=64$ from the $y$ axis is _____ units

maths lines equations of lines parallel to the x-axis and y-axis graphs of linear equations graph of linear equations in two variables

  1. $0$

  2. $-64$

  3. $64$

  4. $32$

Show answer
Correct Option: C
Explanation:

Since, any line of type $x=a$ is parallel to $y$-axis and at a distance $a$ from $y$-axis.

So, distance of line $x=64$ from y-axis is $64$ units.

$4x-3=0$ is a line parallel to 

maths lines equations of lines parallel to the x-axis and y-axis graphs of linear equations graph of linear equations in two variables

  1. $y$ axis

  2. $x$ axis

  3. $y=x$ 

  4. $y=2x$ 

Show answer
Correct Option: A
Explanation:

Given, $4x-3=0$
$\Rightarrow 4x=3$
$\Rightarrow x=\dfrac 34$
Since, every line of type $x=a$ is parallel to $y$ axis.
So, option A is correct.

A straight line parallel to the $x$-axis has equation 

maths lines equations of lines parallel to the x-axis and y-axis graphs of linear equations graph of linear equations in two variables

  1. $x = a$

  2. $y = a$

  3. $y = x$

  4. $y = -x$

Show answer
Correct Option: B
Explanation:

Let the equation of line be $y=mx+c  ...(1)$
Since, the line is parallel to $x$-axis, so slope of line, $m =0$
So, equation $(1)$ becomes $y=c$
Let the line is at a distance of $a$ from $x$-axis.
$a=c$
$\Rightarrow y=a$

The graph of the equation $x= b$ is also a straight line parallel to _____

maths lines equations of lines parallel to the x-axis and y-axis graphs of linear equations graph of linear equations in two variables

  1. $y$-axis

  2. $x$-axis

  3. Cannot be determined

  4. Not Parallel

Show answer
Correct Option: A
Explanation:

The graph of the equation x = b is always a straight line parallel to y-axis.