RD SHARMA Solutions for Class 9 Maths Chapter 7 - Linear Equations in Two Variables

If you love numbers & have a deep interest in statistics, then Mathematics is probably one of the scoring subject ever. A Class 9th CBSE Mathematics is one of the challenging subject one can undergo as, it involves a lot of crunching of complex numbers, geometrical formulae, diagrams & much more. Hence, to simplify the mathematical complexity, TopperLearning has framed a customise solution that involves Test preparation notes, Textbook solutions, Videos, & several other study material that help the student to memorise the concepts quickly. We have bifurcated our CBSE Class 9 Study Material (Solution) into 3 Different parts namely: 

- CBSE Class 9 Practice Test includes Revision notes, Question bank & Sample Paper 
- TopperLearning Classroom that includes Videos, Ask the Experts & Preparation Tips
- Text Book Solutions, etc

TopperLearning packages involves all the ingredients of CBSE Class 9 Study Material that includes Solved Question Papers, High Animated Videos, Solutions by SME (Subject Matter Expert), CBSE class 9 Preparation Tips, Update to CBSE 9th Mathematics syllabus, Practice books, Reference Materials, etc that help you to score great marks with glorious marks.

Getting a good score is now relatively easy if you prefer TopperLearning solutions for CBSE Class 9th Mathematics subject. By purchasing our package, you will be accessed to guaranteed success in your examination!

Read  more
Page / Exercise

Chapter 7 - Linear Equations in Two Variables Exercise 7.33

Question 1

If (4, 19) is a solution of the equation y = ax + 3, then a = 

(a) 3

(b) 4

(c) 5

(d) 6

Solution 1

y = ax + 3

If (4, 19) is its solution, then it must satisfy the equation.

Thus, we have

19 = a × 4 + 3

i.e. 4a = 16

i.e. a = 4

Hence, correct option is (b).

Question 2

If (a, 4) lies on the graph of 3x + y = 10, then the value of a is

(a) 3

(b) 1

(c) 2

(d) 4

Solution 2

3x + y = 10

If (a, 4) lies on its graph, then it must satisfy the equation.

Thus, we have

3(a) + 4 = 10

i.e. 3a = 6

i.e. a = 2

Hence, correct option is (c).

Question 3

The graph of the linear equation 2x - y = 4 cuts x-axis at

(a) (2, 0)

(b) (-2, 0)

(c) (0, -4)

(d) (0, 4)

Solution 3

On x-axis, the y-co-ordinate is always 0.

So, 2x - y = 4 will cut the x-axis where y = 0

i.e. 2x = 4

i.e. x = 2

Thus, 2x - y = 4 will cut the x-axis at (2, 0).

Hence, correct option is (a).

Question 4

How many linear equations are satisfied by x = 2 and y = -3?

(a) Only one

(b) Two

(c) Three

(d) Infinitely many

Solution 4

From Point (2, -3) there are infinitely many lines passing in every-direction.

So (2, -3) is satisfied with infinite linear equations.

Hence, correct option is (d).

Question 5

The equation x - 2 = 0 on number line is represented by

(a) a line

(b) a point

(c) infinitely many lines

(d) two lines

Solution 5

Given equation is x – 2 = 0.

If this is treated as an equation in one variable x only, then it has the unique solution x = 2, which is a point on the number line. 

However, when treated as an equation in two variables, it can be expressed as x - 2 = 0.

So as, an equation in two variables, x – 2 = 0 is represented by a single line parallel to y-axis at a distance of 2 units.

Hence, correct option is (a).

Question 6

x = 2, y = -1 is a solution of the linear equation

(a) x + 2y = 0

(b) x + 2y = 4

(c) 2x + y = 0

(d) 2x + y = 5

Solution 6

Substituting x = 2 and y = -1 in the following equations:

L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 = R.H.S.

L.H.S. = x + 2y = 2 + 2(-1) = 2 - 2 = 0 ≠ 4 ≠ R.H.S.

L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 0 ≠ R.H.S.

L.H.S. = 2x + y = 2(2) + (-1) = 4 - 1 = 3 ≠ 5 ≠ R.H.S.

Hence, correct option is (a).

Question 7

If (2k - 1, k) is a solution of the equation 10x - 9y = 12, then k =

(a) 1

(b) 2

(c) 3

(d) 4

Solution 7

If (2k - 1, k) is solution of equation 10x - 9y = 12, then it must satisfy this equation.

Thus, we have

10(2k - 1) - 9k = 12

20k - 10 - 9k = 12

11k = 22

k = 2

Hence, correct option is (b).

Question 8

The distance between the graph of the equations x = -3 and x = 2 is

(a) 1

(b) 2

(c) 3

(d) 5

Solution 8

The distance between the graph of the equations x = -3 and x = 2

= 2 - (-3)

= 2 + 3

= 5

Hence, correct option is (d).

Question 9

The distance between the graphs of the equations y = -1 and y = 3 is

(a) 2

(b) 4

(c) 3

(d) 1

Solution 9

The distance between given two graphs

= 3 - (-1)

= 3 + 1

= 4

Hence, correct option is (b).

Question 10

If the graph of the equation 4x + 3y = 12 cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length

(a) 4 units

(b) 3 units

(c) 5 units

(d) none of these

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.1

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.2

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 9

If x = 1 and y = 6 is solution of the equation 8x - ay + a2= 0, find the value of a.

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 10

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the follwoing equation: 5x - 2y = 10

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 11

Write two solutions of the form x = 0, y = a and x = b, y = 0 for the following equation: -4x + 3y = 12

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.3

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 11

Plot the points (3,5) and (-1,3) on a graph paper and verify that the straight line passing through these points also passes through the point (1,4).

Solution 11

The given points on the graph:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

It is dear from the graph, the straight line passing through these points also passes through the point (1,4).

Question 12

From the choices given below, choose the equation whose graph is given in fig.,

(i) y = x

(ii) x + y = 0

(iii) y = 2x

(iv) 2 + 3y = 7x

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 13

From the choices given below, choose the equation whose graph is given in fig.,

(i) y = x + 2

(ii) y = x - 2

(iii) y = -x + 2

(iv) x + 2y = 6

 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 15

Draw the graph of the equation 2x + 3y = 12. Find the graph, find the coordinates of the point.

(i) whose y-coordinate is 3.

(ii) whose x-coordinate is -3

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two VariablesRd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 21

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 22

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten's digit of the number are x and y respectively, then write the linear equation representing the above statement.

Solution 22

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 23

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 24

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 25

Draw the graph of y = |x|.

Solution 25

We have,

y = |X|                               ...(i)

Putting x = 0, we get y = 0

Putting x = 2, we get y = 2

Putting x = -2, we get y = 2

Thus, we have the following table for the points on graph of |x|.

x 0 2 -2
y 0 2 2



The graph of the equation y = |x|:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 26

Draw the graph of y = |x| + 2.

Solution 26

We have,

y = |x| + 2                                                  ...(i)

Putting x = 0, we get y = 2

Putting x = 1, we get y = 3

Putting x = -1, we get y = 3

Thus, we have the following table for the points on graph of |x| + 2:

x 0 1 -1
y 2 3 3



The graph of the equation y = |x| + 2:

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 27

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 28

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 29

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 30

Ravish tells his daughter Aarushi, "Seven years ago, I was seven times as old as you were then. Also, three years form now, I shall be three times as old as you will be". If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Solution 30

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 31

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 31

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Chapter 7 - Linear Equations in Two Variables Exercise Ex. 7.4

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

y + 3 = 0

y = -3

Point A represents -3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = -3

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

y = 3

Point A represents 3 on number line.

On Cartesian plane, equation represents all points on x axis for which y = 3

Question 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 6

Give the geometrical representation of 2x + 13 = 0 as an equation in

One variable

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 7

Give the geometrical representation of 2x + 13 = 0 as an equation in

Two variables

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 8

Solve the equation 3x + 2 = x - 8, and represent the solution on (i) the number line.

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Question 9

Solve the equation 3x + 2 = x - 8, and represent the solution on (ii) the Cartesian plane.

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

On Cartesian plane, equation represents all points on y axis for which x = -5

Question 10

Write the equation of the line that is parallel to x-axis and passing through the point

(i) (0,3)

(ii) (0,-4)

(iii) (2,-5)

(iv) (3,4)

Solution 10

(i) The equation of the line that is parallel to x-axis and passing through the point (0,3) is y = 3

(ii) The equation of the line that is parallel to x-axis and passing through the point (0,-4) is y = -4

(iii) The equation of the line that is parallel to x-axis and passing through the point (2,-5) is y = -5

(iv) The equation of the line that is parallel to x-axis and passing through the point (3, 4) is y = 4

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Linear Equations In Two Variables

CBSE Class 9 Maths Homework Help

Clear all your doubts instantly at our “Ask Doubt” section. Get expert help and guidance at your comfort. To know the syllabus in detail, click here.

 

NCERT Textbooks are the rich stimulant for those students who want to score better in the CBSE examinations. By solving our papers the students have achieved a better and higher result. One of the primary objectives of creating ncert solution for class 9  is that the student gets access to an easy solution; which acts as a strong catalyst in improving the marks. We usually focus that the students don’t find any difficulty in understanding the concepts and can memorize them easily.