Tag: maths

Questions Related to maths

Mid point of $A(0, 0)$ and $B(1024, 2050)$ is ${A _1}$. mid point of ${A _1}$ and B is ${A _2}$ and so on. Coordinates of ${A _{10}}$ are.

maths linear graphs quadrants the cartesian plane the cartesian system

  1. $(1022, 2044)$

  2. $(1025, 2050)$

  3. $(1023, 2046)$

  4. $(1, 2)$

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Correct Option: C

If the coordinates of the extermities of diagonal of a square are $(2,-1)$ and $(6,2)$, then the coordinates of extremities of other diagonal are 

maths linear graphs quadrants the cartesian plane the cartesian system

  1. $\left(\dfrac{5}{2},\dfrac{5}{2}\right)$

  2. $\left(\dfrac{11}{2},\dfrac{3}{2}\right)$

  3. $\left(\dfrac{11}{2},\dfrac{-3}{2}\right)$

  4. $\left(\dfrac{5}{2},-\dfrac{5}{2}\right)$

Show answer
Correct Option: C
Explanation:

$\begin{array}{l} Coordination\, \, of\, \, mid-po{ { int } }\, \, 0 \ =\left( { \frac { { 6+2 } }{ 2 } ,\frac { { 2-1 } }{ 2 }  } \right)  \ =\left( { 4,\frac { 1 }{ 2 }  } \right)  \ AB=BC \ \Rightarrow { \left( { { x _{ 1 } }-2 } \right) ^{ 2 } }+{ \left( { { y _{ 1 } }+1 } \right) ^{ 2 } }={ \left( { { x _{ 1 } }-6 } \right) ^{ 2 } }+{ \left( { { y _{ 1 } }-2 } \right) ^{ 2 } } \ \Rightarrow 8{ x _{ 1 } }+6{ y _{ 1 } }=35\to (i) \ AO=BO \ \Rightarrow { \left( { 2-4 } \right) ^{ 2 } }+{ \left( { -1-\frac { 1 }{ 2 }  } \right) ^{ 2 } }={ \left( { { x _{ 1 } }-4 } \right) ^{ 2 } }+{ \left( { { y _{ 1 } }-\frac { 1 }{ 2 }  } \right) ^{ 2 } } \ \Rightarrow 4+\frac { 9 }{ 4 } =x _{ _{ 1 } }^{ 2 }+y _{ 1 }^{ 2 }-8{ x _{ 1 } }-{ y _{ 1 } }+16+\frac { 1 }{ 4 }  \ \Rightarrow x _{ 1 }^{ 2 }+y _{ 1 }^{ 2 }-8{ x _{ 1 } }-{ y _{ 1 } }=-10\to (ii) \ from\, \, equation\, \, (i) \ put \ { x _{ 1 } }=\frac { { 35-6{ y _{ 1 } } } }{ 8 } \, \, in\, \, equation\, \, (ii) \ \Rightarrow { \left( { \frac { { 35-6{ y _{ 1 } } } }{ 8 }  } \right) ^{ 2 } }+y _{ 1 }^{ 2 }-\left( { 35-6{ y _{ 1 } } } \right) { y _{ 1 } }=-10 \ \Rightarrow 4y _{ 1 }^{ 2 }-4{ y _{ 1 } }-15=0 \ \Rightarrow \left( { 2{ y _{ 1 } }+3 } \right) \left( { { y _{ 1 } }-5 } \right) =0 \ \Rightarrow { y _{ 1 } }=\frac { { -3 } }{ 2 } ,5 \ { y _{ 1 } }=\frac { { -3 } }{ 2 } \to { x _{ 1 } }=\frac { { 35-6\times -\frac { 3 }{ 2 }  } }{ 8 } =\frac { { 11 } }{ 2 }  \ { y _{ 1 } }=5\to { x _{ 1 } }=\frac { { 35-6\times 5 } }{ 8 } =\frac { 5 }{ 8 }  \ The\, \, vertices\, of\, \, other\, \, two\, vertices\, \, are \ \left( { \frac { { 11 } }{ 2 } ,\frac { { -3 } }{ 2 }  } \right) \, \, and\, \, \left( { \frac { 5 }{ 8 } ,5 } \right)  \end{array}$

O is a point that lies in the interior of $\Delta ABC$. Then $2(OA - OB -OC) > \text{Perimeter}\ of\ \Delta ABC$.

maths construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

  1. True

  2. False

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Correct Option: B
Explanation:
From the $\triangle ABC,$ by triangle inequality,
$ OA+OB>AB$ ....... $(i)$
$ OB+OC>BC$ ........ $(ii)$
$ OA+OC>AC$ ........ $(iii)$
By adding $(i),(ii)$ and $(iii)$
$ 2(OA+OB+OC)>AB+BC+AC$
$ \therefore 2(OA+OB+OC)>\text{Perimeter of triangle } ABC$
Hence, the statement is false.

Sum of the length of any two sides of a triangle is always greater than the length of third side.

maths construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

  1. True

  2. False

Show answer
Correct Option: A
$\dfrac{\sin 2x}{2\cos x}=\tan x \ \ ?$
maths construction of parallel lines and triangles triangle inequality related to lines and triangles sum of the lengths of two sides of a triangle triangle inequality

  1. True

  2. False

Show answer
Correct Option: A
Explanation:
LHS

$\dfrac{\sin 2x}{2\cos x}$

$\dfrac{2\sin x \cos x}{2\cos x}$

$\implies \dfrac{\sin x}{\cos x}$

$\implies \tan x $

Hence proved.

Which of the following is a non-positive and non-negative integer ?

maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

  1. 1

  2. 0

  3. -1

  4. 3

Show answer
Correct Option: B
Explanation:

The correct answer is 0 (b)

Since zero is neither positive nor negative .

Ram scored $30$% marks and failed by $15$ marks. Aditya score $40$% marks and obtained $35$ marks more than those required to pass. The pass percentage is?

maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

  1. $33$%

  2. $38$%

  3. $43$%

  4. $46$%

Show answer
Correct Option: A
Explanation:
Let the total no of marks for $x$
Let the passing marks for y
$\dfrac{30}{100}x+15=y$ ______(1)
$\dfrac{40}{100}x=y+35$
$\dfrac{40}{100}x-35=y$_______(2)
(1) - (2)
$\dfrac{-10x}{100}+50=0$
$\dfrac{10x}{100}=50\Rightarrow x=500$
$y=\dfrac{40}{100}\times 500-35=200-35=165$
$m\%$ of $x=y$
$\dfrac{m}{100}\times 500=165$
$m=33\%$

If $35\% $ of a number is $175$, then what percent of $175$ is that number ?

maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

  1. $35\% $

  2. $65\% $

  3. $285.71\% $

  4. $420\% $

Show answer
Correct Option: C
Explanation:
Let the required number be $x$

It is given that $35$% of that number is $175$

=> $\dfrac { 35 \times  x }{ 100 } =175$

=> $x= \dfrac { 175 \times  100 }{ 35 }$

=> $x= 500$

Now, the question requires the percentage that $500$ is of that number

Let that percentage be $y \%$.

Now, $\dfrac { y \times  175 }{ 100 } =500$

=>$ y=\dfrac { 500 \times  100 }{ 175 } $

=>$ y = 285.714$

Hence the answer is $ 285.71\%$

$2.7$ is what percent of $18$ ?

maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

  1. $12$%

  2. $13$%

  3. $14$%

  4. $15$%

Show answer
Correct Option: D
Explanation:

Percentage = $\dfrac {2.7}{18}$ $\times 100$


= $\dfrac {270}{18}$

= $\dfrac {30}{2}$ (removing common factor of 9)


= $15$%

If $2\, \displaystyle \frac{1}{2}\, \%$ofa a number is 0.2, then what will be 120 % of it?

maths percentages finding one number as percentage of another money and metric measures as percentage expressing one quantity as a percentage of another

  1. 10.8

  2. 4.8

  3. 9.6

  4. None

Show answer
Correct Option: C
Explanation:

$2\, \displaystyle \frac{1}{2}\, \%$ of x = 0.2


$\displaystyle \frac{5}{200}\, \times\, x\, =\, 0.2$

$x\, =\, 0.2\, \times\, \displaystyle \frac{200}{5}\, =\, 8$

120 % of $8\, =\, \displaystyle \frac{120}{100}\, \times\, 8\, =\, 9.6$