CBSE Class 8

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3.

• Introduction to Graphs Class 8 Ex 15.1
• Introduction to Graphs Class 8 Ex 15.2

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3

Question 1.
Draw the graphs for the following tables of values, with suitable scales on the axes.
(a) Cost of apples

(b) Distance travelled by a car

(i) How much distance the car cover during the period 7.30 a.m. to 8 a.m.?
(ii) What was the time when the car had covered a distance of 100 km since it starts?

(c) Interest on deposits for a year.

(i) Does the graph pass through the origin?
(ii) Use the graph to find the interest on? 2500 for a year.
(iii) To get an interest of ? 280 per year, how much money should be deposited?
Solution.
(a)

Scale:
On horizontal axis:         2 units = 1 apple
On vertical axis:              1 unit = ₹ 5
• Mark number of apples on the horizontal axis.
• Mark cost (in ?) on the vertical axis.
• Plot the points: (1, 5), (2, 10), (3, 15), (4, 20) and (5, 25)
• Join the points.
We get a linear graph.

(b)

Scale:
On horizontal axis:      2 units = 1 hour
On vertical axis:           2 units = 40 km
• Mark time (in hours) on the horizontal axis.
• Mark distances (in km) on the vertical axis.
• Plot the points (6 a.m., 40), (7 a.m., 80) (8 a.m., 120) and (9 a.m., 160).
• Join the points.
We get a linear graph.
(i) Distance covered during 7.30 a.m. to 8 a.m.
= 120 km – 100 km = 20 km
(ii) The time when the car had covered a distance of 100 km since its start was 7.30 a.m.

(c)
Scale:
On horizontal axis:       2 units = ₹ 1000
On vertical axis:            2 units = ₹ 80
• Mark deposit (in ₹ on the horizontal axis.
• Mark simple interest (in ₹) on the vertical axis.
• Plot the points (1000, 80), (2000, 160), (3000, 240) (4000, 320) and (5000, 400).
• Join the points.
We get a linear graph.
(i) Yes! The graph passes through the origin.
(ii) Interest on ₹ 2500 for a year = ₹ 200
(iii) To get an interest of ₹ 280 per year, ₹ 3500 should be deposited.

Question 2.
Draw a graph for the following:
(i)

Is it a linear graph?
(ii)

Is it a linear graph?
Solution.
(i)

Scale:
On horizontal axis:     1 unit = 1 cm
On vertical axis:          1 unit = 4 cm
• Mark side of the square (in cm) on the horizontal axis.
• Mark perimeter (in cm) on the vertical axis.
• Plot the points (2, 8), (3, 12), (3.5. 14) (5, 20) and (6, 24).
• Join the points.
Yes ; it is a linear graph.

(ii)

• Scale:
On horizontal axis: 2 units = 2 cm
On vertical axis: 1 unit = 2 cm
• Mark side of the square (in cm) on the horizontal axis.
• Mark area (in cm ) on the vertical axis.
• Plot the points (2, 4) (3, 9), (4, 16), (5, 25) and (6, 36).
• Join the points.
The graph we get is not linear.

We hope the NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2.

• Introduction to Graphs Class 8 Ex 15.1
• Introduction to Graphs Class 8 Ex 15.3

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2

Question 1.
Plot the following points on a graph sheet. Verify if they lie on a line.
(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)
(b) P(l, 1), Q(2, 2), R(3, 3), S(4, 4)
(c) K(2, 3), L(5, 3), M(5, 5), N(2, 5)
Solution.

(a) The points lie on a line.
(b) The points lie on a line.
(c) The points do not lie on a line.

Question 2.
Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at which this line meets the x-axis and y-axis.
Solution.
The coordinates of the points at which this line meets the x-axis and y-axis are (5, 0) and (0, 5) respectively. See the graph given above.

Question 3.
Write the coordinates of the vertices of each of these adjoining figures.

Solution.
O → (0, 0)
A → (2,0)
B → (2, 3)
C → (0,3)

P → (4, 3)
Q → (6, 1)
R → (6, 5)
S → (4, 7)

K → (10, 5)
L → (7, 7)
M → (10, 8)

Question 4.
State whether True or False. Correct that is false.
(i) A point whose x-coordinate is zero and y-coordinate is non-zero will lie on the y-axis.
(ii) A point whose y-coordinate is zero ‘ and x-coordinate is 5 will lie on y-axis.
(iii) The coordinates of the origin are (0, 0).
Solution.
(i) True
(ii) False; A point whose y-coordinate is zero and x-coordinate is 5 will lie on x-axis.
(iii) True

We hope the NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Ex 15.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4.

• Factorisation Class 8 Ex 14.1
• Factorisation Class 8 Ex 14.2
• Factorisation Class 8 Ex 14.3

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4

Find and correct the errors in the following mathematical statements.
Question 1.
4(x – 5) = 4x – 5
Solution.
4(x – 5) = 4x – 20

Question 2.
x(3x + 2) = \({ 3x }^{ 2 }+2\)
Solution.
x(3x + 2) = \({ 3x }^{ 2 }+2x\)

Question 3.
2x + 3y = 5xy
Solution.
2x + 3y = 2x + 3y

Question 4.
x + 2x + 3x = 5x
Solution.
x + 2x + 3x = 6x

Question 5.
5y + 2y + y – 7y = 0
Solution.
5y + 2y + y – 7y – y

Question 6.
3x + 2x = \({ 5x }^{ 2 }\)
Solution..
3x + 2x = 5x

Question 7.
\({ \left( 2x \right) }^{ 2 } + 4(2x) + 7 = { 2x }^{ 2 } + 8x + 7 \)
Solution.
\({ \left( 2x \right) }^{ 2 } + 4(2x) + 7 = { 4x }^{ 2 } + 8x + 7 \)

Question 8.
\({ \left( 2x \right) }^{ 2 } + 5x = 4x + 5x = 9x \)
Solution.
\({ \left( 2x \right) }^{ 2 } + 5x = { 4x }^{ 2 } + 5x \)

Question 9.
\({ \left( 3x+2 \right) }^{ 2 } = { 3x }^{ 2 } + 6x + 4. \)
Solution.
\({ \left( 3x+2 \right) }^{ 2 } = { 9x }^{ 2 }+ 12x + 4. \)

Question 10.

Solution.

Question 11.
\({ \left( y-3 \right) }^{ 2 } = { y }^{ 2 } – 9 \)
Solution.
\({ \left( y-3 \right) }^{ 2 } = { y }^{ 2 } – 2(y)(3) + { 3 }^{ 2 }\)
= \({ y }^{ 2 } – 6y + 9 \)
and not equal to \({ y }^{ 2 } – 9 \)

Question 12.
\({ \left( z+5 \right) }^{ 2 } = { z }^{ 2 } + 25 \)
Solution.
\({ \left( z+5 \right) }^{ 2 } = { z }^{ 2 } + 2(z) (5) + { 5}^{ 2 }\)
= \({ z }^{ 2 } + 10z + 25 \)
and not equal to \({ z }^{ 2 } + 25 \)

Question 13.
\(\left( 2a+36 \right) \left( a-b \right) = { 2a }^{ 2 }-{ 3b }^{ 2 }\)
Solution.

Question 14.
\(\left( a+4 \right) \left( a+2 \right) = { a}^{ 2 } + 8 \)
Solution.

Question 15.
\(\left( a-4 \right) \left( a-2 \right) = { a}^{ 2 }-8 \)
Solution.

Question 16.
\(\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } =0\)
Solution.
\(\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } =1\) and not equal to 0

Question 17.
\(\frac { { 3x }^{ 2 }+1 }{ { 3x }^{ 2 } } =1+1=2\)
Solution.
\(\frac { { 3x }^{ 2 }+1 }{ { 3x }^{ 2 } } =\frac { { 3x }^{ 2 } }{ { 3x }^{ 2 } } +\frac { 1 }{ { 3x }^{ 2 } } \)
=\(1+\frac { 1 }{ { 3x }^{ 2 } }\) and not equal to 1 + 1 = 2

Question 18.
\(\frac { 3x }{ 3x+2 } =\frac { 1 }{ 2 } \)
Solution.
\(\frac { 3x }{ 3x+2 } =\frac { 3x }{ 3x+2 } \) and not equal to \(\frac { 1 }{ 2 }\)

Question 19.
\(\frac { 3 }{ 4x+3 } =\frac { 1 }{ 4x } \)
Solution.
\(\frac { 3 }{ 4x+3 } =\frac { 3 }{ 4x+3 } \) and not equal to \(\frac { 1 }{ 4x }\)

Question 20.
\(\frac { 4x+5 }{ 4x } =5\)
Solution.
\(\frac { 4x+5 }{ 4x } =\frac { 4x }{ 4x } +\frac { 5 }{ 4x } =1+\frac { 5 }{ 4x } \) and not equal to 5

Question 21.
\(\frac { 7x+5 }{ 5 } =7x\)
Solution.
\(\frac { 7x+5 }{ 5 } =\frac { 7x }{ 5 } +\frac { 5 }{ 5 } =\frac { 7x }{ 5 } +1\) and not equal to 7x

We hope the NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1.

• Factorisation Class 8 Ex 14.1
• Factorisation Class 8 Ex 14.2
• Factorisation Class 8 Ex 14.4

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3

Question 1.
Carry out the following divisions:

Solution.

Question 2.
Divide the given polynomial by the given monomial:

Solution.

Question 3.
Work out the following divisions:

Solution.

Question 4.
Divide as directed.

Solution.

Question 5.
Factorise the expressions and divide them as directed.

Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2.

• Factorisation Class 8 Ex 14.1
• Factorisation Class 8 Ex 14.3
• Factorisation Class 8 Ex 14.4

NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2

Question 1.
Factorise the following expressions:

Solution.

Question 2.
Factorise:

Solution.

Question 3.
Factorise the expressions:

Solution.

Question 4.
Factorise:

Solution.

Question 5.
Factorise the following expressions:

Solution.

We hope the NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2 help you. If you have any query regarding NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.2, drop a comment below and we will get back to you at the earliest.