Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

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

The graph of $x =8 $ represents:

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

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

  1. one straight line

  2. a pair of straight lines

  3. the sides of a square

  4. a circle

  5. a point
Reveal answer Fill a bubble to check yourself
C Correct answer
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

Multiple choice 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

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

  1. $0\%$
  2. $25\%$
  3. $50\%$
  4. $75\%$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $25 \%$.
Multiple choice maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

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

  1. $120 cm^3.$
  2. $240 cm^3.$
  3. $640 cm^3.$
  4. $900 cm^3.$
Reveal answer Fill a bubble to check yourself
C Correct answer
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.
Multiple choice maths perimeter, area and volume surface area and volume of sphere surface area of a prism surface area of a prism and a pyramid

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.

  1. $16\ m$
  2. $12\ m$
  3. $4\ m$
  4. $2\ m$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $= 4m$

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

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

  1. $20$
  2. $40$
  3. $10$
  4. $30$
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $10 cm$.

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

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 $S=nh+2s$.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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