Tag: maths

Questions Related to maths

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 $\displaystyle L=$

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

  1. $\displaystyle 6x-4y-7=0$

  2. $\displaystyle 2x-3y-5=0$

  3. $\displaystyle 3x-2y+5=0$

  4. $\displaystyle 3x-2y+10=0$

Show answer
Correct Option: C
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
$y-4=\displaystyle \frac{3}{2} (x-1)$

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

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

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

  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. ${x^2} - {y^2} + 2x + 1 = 0$

Show answer
Correct Option: D
Explanation:

We have $y=|x-1|$


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

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

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

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

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

$617 + 6.017 + 0.617 + 6.0017 =$?

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

  1. $6.2963$

  2. $62.965$

  3. $629.6357$

  4. None of these

Show answer
Correct Option: C
Explanation:

 $617.00$
     $6.017$
     $0.617$
$+$ $6.0017$
-----------------
  $629.6357$
-----------------

Solve the given expression:
$3.005+4.7$

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

  1. $3.052$

  2. $3.475$

  3. $7.705$

  4. $3.007$

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Correct Option: C
Explanation:

Addition of $3.005$ and $4.7$ gives $3.005+4.7=7.705$

Find the sum of $1.2$ and $2.3$.

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

  1. $35$

  2. $3.5$

  3. $0.35$

  4. $1.23$

Show answer
Correct Option: B
Explanation:

The sum of $1.2$ and $2.3$ will be $1.2+2.3=3.5$

A couple has five married sons and each one of them have four children. How many members are there in the family?

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

  1. 10

  2. 27

  3. 30

  4. 32

Show answer
Correct Option: D
Explanation:

Total member =2[2+(5×2)+(5×4)]=32

$2.\bar {3}-0.\bar {4}=$______.

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

  1. $1.\bar {9}$

  2. $1.\bar {8}$

  3. $1.\bar {7}$

  4. $1.\bar {6}$

Show answer
Correct Option: A
Explanation:

$2.\bar{3}-0.\bar{4}=1.\bar{9}$

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

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

  1. $10$ hours $15$ minutes

  2. $9$ hours $25$ minutes

  3. $10$ hours $10$ minutes

  4. $9$ hours $40$ minutes

Show answer
Correct Option: C
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.

Find the value of $\dfrac{2}3+\dfrac {4}{3}+\dfrac{4}{5}+\dfrac{6}{5}$

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

  1. 4

  2. 6

  3. -4

  4. -7

Show answer
Correct Option: A
Explanation:

$\dfrac 23+\dfrac 43+\dfrac 45+\dfrac 65\\dfrac {2+4}3+\dfrac {4+6}5\2+2=4$

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

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

  1. $0.46\bar { 5 } $

  2. $0.4\overline { 65 } $

  3. $0.\bar { 465 } $

  4. none of these

Show answer
Correct Option: B
Explanation:

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


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

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

                            $=0.4\overline {65}$