Tag: maths

Questions Related to maths

If we rotate a right triangle about his height then we get a ..........

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. Rectangle

  2. Cube

  3. Cuboid

  4. Cone

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Correct Option: D
Explanation:

If we rotate a right triangle about its height then we get a cone.

Which of the following is true for the net of a solid?

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid.

  2. A net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure.

  3. A solid may have different nets.

  4. All of the above

Show answer
Correct Option: D
Explanation:
A geometry net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or a solid. Or a net is a pattern made when the surface of a three-dimensional figure is laid out flat showing each face of the figure. A solid may have different nets.
Here are some steps to determine whether a net forms a solid:

1. Make sure that the solid and the net have the same number of faces and that the shapes of the faces of the solid match the shapes of the corresponding faces in the net. 
2. Visualize how the net is to be folded to form the solid and make sure that all the sides fit together properly.

Nets are helpful when we need to find the surface area of the solids.
Thus, all the statements are true.

How many squares does a net of a cube contain?

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. $4$

  2. $6$

  3. $8$

  4. None of these

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Correct Option: B
Explanation:

There are six faces of a cube hence there are six squares.

How many rectangles are there in net of a rectangular prism?

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. 1

  2. 6

  3. 3

  4. 4

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Correct Option: D

If a solid figure has $15$ edges and $10$ vertices, then the number of faces of a solid figure is 

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. $9$

  2. $7$

  3. $11$

  4. $5$

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Correct Option: B
Explanation:
Using Euler's formula

$V+F=E+2$ 

$E=15$

$V=10 $

$\therefore 10+F = 15+2$

$\therefore  F= 17-10 $

$\therefore F=7 $

The number of dimensions, a point has

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. 0

  2. 1

  3. 2

  4. 3

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Correct Option: A
Explanation:

A point just marks a place which has no length, no breadth and no thickness.

So a point is devoid of these three fundamental dimensions.
$\quad \therefore \quad $ A point has 0 number of dimension.
Ans- Option A.

......... of solid shapes can be folded to make the solid.

maths open shapes of regular solids nets of a solid nets of three-dimensional shapes net of a cone

  1. 2D space

  2. 3D space

  3. nets

  4. none

Show answer
Correct Option: C
Explanation:

Nets of solid shapes can be folded to make a solid

When the axes are rotated through an angle $\dfrac{\pi}{6}$ , find the new coordinate for $(1,0)$

combining transformations transformations vectors and transformations maths

  1. $(\dfrac{\sqrt3}{2},\dfrac{-1}{2})$

  2. $(\dfrac{\sqrt4}{2},\dfrac{-1}{2})$

  3. $(\dfrac{\sqrt5}{2},\dfrac{-1}{2})$

  4. $(\dfrac{\sqrt3}{2},\dfrac{-1}{3})$

Show answer
Correct Option: A
Explanation:

$\\ sin(\frac{\pi}{6})=(\frac{b}{1})\\\therefore b= (\frac{1}{2})\\ so new y-coordinate wil be  = (\frac{-1}{2})\\cos(\frac{\pi}{6})=(\frac{a}{1})\\\therefore a=(\frac{\sqrt3}{2})\\\therefore new x-coordinate =(\frac{\sqrt3}{2})$

The point to which is shifted in order to remove the first degree terms in $ 2x^{ 2 }+5xy+3y^{ 2 }+6x+7y+1=0 $ is

combining transformations transformations vectors and transformations maths

  1. (2,1)

  2. (1,-2)

  3. (2,-1)

  4. (1,2)

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Correct Option: A

If the transformed equation of a curve is $9x^{2}+16y^{2}=144$ when the axes rotated through an angle of $45^{o}$ then the original equation of a curve is:

combining transformations transformations vectors and transformations maths

  1. $25x^{2}+14yxy+25y^{2}=228$

  2. $25x^{2}-14yxy+25y^{2}=228$

  3. $25x^{2}+14yxy-25y^{2}=228$

  4. $25x^{2}-14yxy-25y^{2}=228$

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Correct Option: A