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Lesson Posted on 24/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

I have 15 years of experience in 10th level and 6+ years of experience in 12th level.I have taught more...

If two linear equations are given, then we can find the values of variables, by solving those equations simultaneously. 2x+3y=10---(1) x-3y=8-------(2) These are the two linear equations, we can find the values of variables x&y, by solving those equations simultaneously. Method:- 1) identify... read more

If two linear equations are given, then we can find the values of variables, by solving those equations simultaneously.

2x+3y=10---(1)

x-3y=8-------(2)

These are the two linear equations, we can find the values of variables x&y, by solving those equations

simultaneously.

Method:-

1) identify out of two variables here x and y, the coefficient of any variable is equal in both the equations.

2) if similar go to the 3rd step, if not same, make the co-efficient either one variable in both equations equivalent by multiplying through either one or both the equations.

3) Either add or subtract the equations to eliminate the corresponding coefficient variable.

4) Find the value of one variable first.

5)Next, find the value of another variable by substituting the importance of the first found variable in either equation.

Solutions:- In above-given equations, the coefficient of y is the same, i.e. 3 in both equations.

Hence Adding the equations (1) and (2) we get

2x+3y=10---(1)

x-3y=8-------(2)

------------------------

3x =18

∴ x =18/3=6

now by substituting the value of x in equation (1)

2(6) +3y = 10

∴ 12 + 3y = 10

∴ 3y = 10 - 12

∴ 3y = 2

∴ y = 3/2

∴ x=6 and y = 3/2 are solutions of given simultanious equations.

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Comments Lesson Posted on 24/12/2018 CBSE/Class 10/Mathematics

Area of the Triangle Using Base & Height

Ramakrishna Dhooli

I have 15 years of experience in 10th level and 6+ years of experience in 12th level.I have taught more...

HOW TO FIND THE AREA OF THE TRIANGLE WHEN BASE & HEIGHT ARE GIVEN if the base of the triangle = b and height of the triangle = h then, area of the triangle = (1/2) x b xh square units Ex:- if base of the triangle = b = 20cm and height of the triangle = h = 8 cm then, area of the triangle... read more

HOW TO FIND THE AREA OF THE TRIANGLE WHEN BASE & HEIGHT ARE GIVEN

if the base of the triangle = b

and height of the triangle = h

then, area of the triangle = (1/2) x b xh square units

Ex:-

if base of the triangle = b = 20cm

and height of the triangle = h = 8 cm

then, area of the triangle = (1/2) x b xh

= (1/2) x 20 x8

=10 x 8 = 80 cm2

Ex:-

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Comments Lesson Posted on 22/12/2018 CBSE/Class 10/Mathematics

Mid Point Formula (Co Ordinate Geometry)

Ramakrishna Dhooli

I have 15 years of experience in 10th level and 6+ years of experience in 12th level.I have taught more...

If co ordinates of end points of line segment AB are A(x1,y1) and B(x2,y2) And P(x,y) is the mid point of segment AB ,Then, x=(x1+x2)/2 and y=(y1+y2)/2 Ex:- If,A(2,-5) and B(-4,9) And P(x,y) is the mid point of segment AB, Then x=(x1+x2)/2 Here x1=2,y1=-5 and x2=-4,y2=9 ∴x=(2-4)/2=-2/2=1 y=(y1+Y2)/2 ∴y=(-5+9)/2=4/2=2 co... read more

If co ordinates of end points of line segment AB are A(x_{1,}y1) and B(x2,y2)

And P(x,y) is the mid point of segment AB ,Then,

x=(x_{1}+x2)/2 and y=(y1+y2)/2

Ex:-

If,A(2,-5) and B(-4,9) And P(x,y) is the mid point of segment AB, Then

x=(x_{1}+x2)/2

Here x1=2,y1=-5 and x2=-4,y2=9

∴x=(2-4)/2=-2/2=1

y=(y_{1+Y}_{2)/2}

_{∴y=(-5+9)/2=4/2=2}

_{co ordinates of Mid point P(x,y) are P(1,2)}

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Comments Lesson Posted on 22/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

If edge(side) of the cube = x cm Then Volume of the Cube= (x)3 Ex:- If edge(side) of the cube = x = 5cm Then Volume of the Cube= (x)3 = (5 )3=125 cm3 read more

If edge(side) of the cube = x cm

Then Volume of the Cube= (x)^{3}

Ex:-

If edge(side) of the cube = x = 5cm

Then Volume of the Cube= (x)^{3 } = (5^{ })3=125 cm3

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Comments Lesson Posted on 22/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

VOLUME OF CUBOID:- If Length of Cuboid= l Breadth(width) of Cuboid= b Height of Cuboid= h Then, Volume of the cuboid= l x b x h cubic units Ex:- If Length of Cuboid= l = 15cm Breadth(width) of Cuboid= b = 8cm Height of Cuboid= h = 4cm Then, Volume of the cuboid= l x b x h ... read more

**VOLUME OF CUBOID:- **

If Length of Cuboid= l

Breadth(width) of Cuboid= b

Height of Cuboid= h

Then,

Volume of the cuboid= l x b x h cubic units

Ex:-

If Length of Cuboid= l = 15cm

Breadth(width) of Cuboid= b = 8cm

Height of Cuboid= h = 4cm

Then,

Volume of the cuboid= l x b x h

=15 x 8 x 4

=480 cm3

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Comments Lesson Posted on 22/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

FACTORISE THE FOLLOWING: TYPE 1:- a2-b2 =(a+b)(a-b) Ex:- 1) x2-64 =x2-82 =(x+8)(x-8) TYPE 2:- splitting the middle term Method:- split the middle term in two terms so that- 1)Their alzebric sum should be equal to middle term and 2)Their product should be equal to product of... read more

FACTORISE THE FOLLOWING:

TYPE 1:-

a2-b2 =(a+b)(a-b)

Ex:-

1) x2-64 =x^{2}-8^{2}

^{ =(x+8)(x-8)}

^{TYPE 2:- splitting the middle term}

^{Method:-}

^{ split the middle term in two terms so that-}

^{1)Their alzebric sum should be equal to middle term and}

^{2)Their product should be equal to product of 1st and 3rd term.}

^{3)Make the group of twq terms each}

^{4)Remove out the common in each group.}

^{Ex:- }

x2-10x+24

=x2-6x-4x+24

=x(x-6)-4(x-6)

=(x-6)(x-4)

^{ }

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Comments Lesson Posted on 20/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

VOLUME OF THE CONE If, r=radis of the cone h= perpendicular height Then, 1)The volume of the cone =( 1/3 )πr2h Ex- If,r=14 cm, h=15cm, then 1)The volume of the cone =( 1/3 )πr2h =(1/3)x(22/7)x14x14x15 ... read more

VOLUME OF THE CONE

If, r=radis of the cone

h= perpendicular height

Then,

1)The volume of the cone =( 1/3 )πr^{2}h

Ex- If,r=14 cm, h=15cm, then

1)The volume of the cone =( 1/3 )πr^{2}h

=(1/3)x(22/7)x14x14x15

=22x2x14x5

=3080 cubic cm

=2640 square cm

2)Total surface Area of cone= πr(r+l)

=22/7x28(28+30)

= 22x4(58)

=5104 square cm

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Comments Lesson Posted on 20/12/2018 CBSE/Class 10/Mathematics

Surface Area of Hemi (Semi) Sphere

Ramakrishna Dhooli

If, the radius of a sphere=r Then, 1)CURVED SURFACE AREA OF SEMI(HEMI) SPHERE= 2πr2 2)TOTAL SURFACE AREA OF SEMI(HEMI) SPHERE= 3πr2 Ex;- If,radius of a sphere=r=14cm 1)CURVED SURFACE AREA OF SEMI(HEMI) SPHERE= 2πr2 ... read more

If, the radius of a sphere=r

Then,

1)CURVED SURFACE AREA OF SEMI(HEMI) SPHERE= **2πr ^{2}**

^{2)TOTAL SURFACE AREA OF SEMI(HEMI) SPHERE= 3πr2}

^{Ex;-}

^{If,radius of a sphere=r=14cm}

1)CURVED SURFACE AREA OF SEMI(HEMI) SPHERE= **2πr ^{2}**

** =**2X(22/7)X14X14

^{ =2x22X2x14}

^{ =1232cm2 }

^{ } 2)TOTAL SURFACE AREA OF SEMI(HEMI) SPHERE= **3πr ^{2}**

^{ =}3X(22/7)X14X14

^{ =3x22X2x14}

^{ =1848 cm2 }

^{ }

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Comments Lesson Posted on 21/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

If, the radius of a Hemi sphere=r Then, VOLUME OF THE HEMI SPHERE=(2/3)πr3 Ex;- If,radius of a sphere=r=21cm VOLUME OF OF SPHERE=(2/3)πr3 =(2/3)x(22/7)x21x21X21 =2x22x2x14X21X21 ... read more

If, the radius of a Hemi sphere=r

Then,

**VOLUME OF THE HEMI SPHERE=(2/3)πr3**

^{Ex;-}

^{If,radius of a sphere=r=21cm}

^{VOLUME OF OF SPHERE=(2/3)πr3}

^{ =(2/3)x(22/7)x21x21X21}

^{ =2x22x2x14X21X21}

^{ } =543312cm^{3 }

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Comments Lesson Posted on 21/12/2018 CBSE/Class 10/Mathematics

Ramakrishna Dhooli

#As shown in the above diagram The cube has 6 square surfaces.they are equal in area. # The cube has 12 equal edges or sides TOTAL SURFACE AREA OF CUBE:- If edge(side) of the cube = a Then,Total surface Area of cube = 6a2 Ex:- If edge(side) of the cube = a=10cm Then,Total surface Area of... read more

#As shown in the above diagram The cube has 6 square surfaces.they are equal in area.

# The cube has 12 equal edges or sides

**TOTAL SURFACE AREA OF CUBE****:-**

If edge(side) of the cube = a

Then,Total surface Area of cube = 6a^{2 }

^{Ex:-}

If edge(side) of the cube = a=10cm

Then,Total surface Area of cube = 6a^{2 }= 6x(10)^{2}

=6x100

=600 cm2

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