Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths position and movement reflection w.r.t a line transformation transformation and symmetry in geometrical shapes

If $\displaystyle \left ( -2, 6 \right )$ is the image of the point $\displaystyle \left ( 4,2 \right )$ with respect to the line $\displaystyle L=0$, then $\displaystyle L=$

  1. $\displaystyle 6x-4y-7=0$
  2. $\displaystyle 2x-3y-5=0$
  3. $\displaystyle 3x-2y+5=0$
  4. $\displaystyle 3x-2y+10=0$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Slope of line joining the image $Q(-2,6)$ and the point $P(4,2)$ is $\displaystyle -\frac{2}{3}$

So, the slope of mirror $L$ is $\displaystyle \frac{3}{2}$

Mid-point of $PQ$ is $(1,4)$

Since, the image and point are equidistant from mirror. So, this point $(1,4)$ lies on the mirror.

So, the equation of mirror is
$y-4=\displaystyle \frac{3}{2} (x-1)$

$\Rightarrow 3x-2y+5=0$

Multiple choice maths position and movement reflection w.r.t a line transformation transformation and symmetry in geometrical shapes

The equation of image of pair of lines $y=|x-1|$ with respect to y-axis is 

  1. ${x^2} - {y^2} - 2x + 1 = 0$
  2. ${x^2} - {y^2} - 4x + 4 = 0$
  3. $4{x^2} - 4x - {y^2} + 1 = 0$
  4. ${x^2} - {y^2} + 2x + 1 = 0$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

We have $y=|x-1|$


$\Rightarrow y^2=(x-1)^2$

Change $x$ by $-x$, then the required image is 

$y^2=(-x-1)^2$

$\Rightarrow y^2=x^2+2x+1$

$\Rightarrow x^2-y^2+2x+1=0$

Multiple choice maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

A train leaves the station at $8:15$ pm and reach destination at $6:25$ am . The duration of the journey is 

  1. $10$ hours $15$ minutes
  2. $9$ hours $25$ minutes
  3. $10$ hours $10$ minutes
  4. $9$ hours $40$ minutes
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The time interval between $8:15$ pm and $6:25 am$ = $10\,\, hrs\,\, 10\,\, min$


Therefore, the duration of the journey of the train is $10\,\, hr \,\,10\,\, min.$

Therefore, option C is correct.

Multiple choice maths decimal numbers adding and subtracting decimals addition and subtraction of decimals operations on decimals

Expressing $0.\overline { 23 } +0.2\overline { 3 } $ as a single decimal, we get

  1. $0.46\bar { 5 } $
  2. $0.4\overline { 65 } $
  3. $0.\bar { 465 } $

  4. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\Rightarrow$  $0.\overline {23}$ means $0.232323....$


and $0.2\bar{3}$ means $0.233333...$

$\Rightarrow$  $0.\overline {23}+0.{2\bar3}=0.23232323+0.23333333$
                            $=0.4656565$

                            $=0.4\overline {65}$