Tag: maths

Questions Related to maths

The graph of $x =8 $ represents:

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

  1. line parallel to $y$-axis and at a distance of $8$ units. 

  2. line parallel to $x$-axis and at a distance of $8$ units. 

  3. line parallel to $y$-axis and at a distance of $0$ units. 

  4. None of these

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Correct Option: A
Explanation:

The line $x=8$ or a point $(8,0)$ lies on the $x$-axis whwich is parallel to $y$-axis and at a distance of $8$ units.

$(5,0)$ is a point that lies on 

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

  1. $y$-axis

  2. $x$-axis

  3. $y=x$

  4. $y=5x$

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Correct Option: B
Explanation:

Any point on $x$ axis is of the form $(x,0)$ and any point on $y$ axis is of the form $(0,y)$. 

Therefore, $(5,0)$ is a point that lies on $x$ axis.

The graph of $|x| + |y|$ consists of

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

  1. one straight line

  2. a pair of straight lines

  3. the sides of a square

  4. a circle

  5. a point

Show answer
Correct Option: C
Explanation:

Given $|x|+|y|$

  1. For $x>0$ and $y>0$ , we have $x+y$
  2. For $x>0$ and $y<0$ , we have $x-y$
  3. For $x<0$ and $y>0$ , we have $-x+y$
  4. For $x<0$ and $y<0$ , we have $-x-y$
  5. observe that the four equations will form a square

From a solid sphere of radius $R$, a concentric solid sphere of radius $\dfrac{R}{2}$ is removed. The total surface area increases by

maths surface area and volume of sphere solids surface area of a prism surface area of a prism and a pyramid volume of a sphere surface areas and volumes of solids problems involving volume of combined solids application of surface area and volume of solids

  1. $0\%$

  2. $25\%$

  3. $50\%$

  4. $75\%$

Show answer
Correct Option: B
Explanation:
Solution:- (B) $25 \%$
Initial area of sphere $ \left( {A} _{1} \right) = 4 \pi {R}^{2}$
New area of sphere $\left( {A} _{2} \right) = 4 \pi {R}^{2} + 4 \pi {\left( \cfrac{R}{2} \right)}^{2} = 5 \pi {R}^{2}$
$\therefore$ Increase in area $= \cfrac{{A} _{2} - {A} _{1}}{{A} _{1}} \times 100$
$\Rightarrow$ Increase in area $= \cfrac{5 \pi {R}^{2} - 4 \pi {R}^{2}}{4 \pi {R}^{2}} \times 100 = 25 \%$
Hence the area will be increased by $25 \%$.

The volume of triangular prism whose adjacent sides are $\bar a,\ \bar b,\ \bar c$ each of magnitude $4$ units and each is inclined at an angel $\dfrac {\pi}{3}$ with other two is  

maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $16\sqrt {2}$

  2. $16\sqrt {3}$

  3. $8\sqrt {3}$

  4. $8\sqrt {2}$

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Correct Option: B

If angle of minimum deviation through an equilateral prism is $40^o$, angle of incidence (being equal to angle of emergence) would be

maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $50^o$

  2. $60^o$

  3. $40^o$

  4. none of these

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Correct Option: A
Explanation:
For minimum deviation $ i=ei=e $
$a+δm=i+ea+δm=i+e $
$a+δm=2ia+δm=2i $
$60^o+40^o=2i$
$i=50^o$

If a regular square pyramid has a base of side $8 cm$ and height of $30 cm$, then its volume is

maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $120 cm^3.$

  2. $240 cm^3.$

  3. $640 cm^3.$

  4. $900 cm^3.$

Show answer
Correct Option: C
Explanation:
Given that:
Side $a=8\ cm$, Height $h=30\ cm$
As we know that
Volume of regular square pyramid 
$\Rightarrow a^2\dfrac{h}{3}$
$\Rightarrow 8^2\dfrac{30}{3}$
$\Rightarrow 64\times 10$
$\Rightarrow 640\ cm^3$
This is the required solution.

A square pyramid can contain $16\ m^3$ of water. The height of the pyramid is $3\ m$. Calculate the length of base of the square pyramid.

maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $16\ m$

  2. $12\ m$

  3. $4\ m$

  4. $2\ m$

Show answer
Correct Option: C
Explanation:

Volume of square pyramid  $=16{ m }^{ 3 }$

$\Rightarrow \quad \dfrac { 1 }{ 3 } \times { a }^{ 2 }\times h=16{ m }^{ 3 }\Rightarrow \dfrac { 1 }{ 3 } \times { a }^{ 2 }\times 3=16\Rightarrow a=\sqrt { 16 } =4cm$
$\therefore $  Length of base $= 4m$

$VPQRS$ is rectangle based pyramid where $PQ = 30\ cm, QR = 20\ cm$ and volume is $2000\ {cm}^3$, then height (in cm) is

maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. $20$

  2. $40$

  3. $10$

  4. $30$

Show answer
Correct Option: C
Explanation:

Given : Length of base$(l)=30\ cm$, width of base$(h)=20\ cm$, Volume of pyramid$=2000\ cm^3$

Let $h$ be the height of the pyramid
We know that, volume of pyramid $=\dfrac{l\times w\times h}{3}$
$\implies 2000\ cm^3 = \dfrac{30 cm\times 20 cm\times h}{3}$
$\implies h=\dfrac{2000\times 3}{30\times 20} cm=10 cm$
Hence, height is $10 cm$.

State whether true or false : 

If $s$ is the perimeter of the base of a prism, $n$ is the number of sides of the base, $S$ is the total length of the edges and $h$ is the height, then $S=nh+2s$.

maths measures and the circle surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

True. Total length of Prism $= S$
Length of all the heights $= nh$
Perimeter of base and head $= 2s$
$\therefore S = nh + 2s$